pair_meam_sw_spline.cpp
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Created: Sun, May 26, 02:16

pair_meam_sw_spline.cpp
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	/* ----------------------------------------------------------------------
	LAMMPS - Large-scale Atomic/Molecular Massively Parallel Simulator
	http://lammps.sandia.gov, Sandia National Laboratories
	Steve Plimpton, sjplimp@sandia.gov

	Copyright (2003) Sandia Corporation. Under the terms of Contract
	DE-AC04-94AL85000 with Sandia Corporation, the U.S. Government retains
	certain rights in this software. This software is distributed under
	the GNU General Public License.

	See the README file in the top-level LAMMPS directory.
	------------------------------------------------------------------------- */

	/* ----------------------------------------------------------------------
	Contributing author: Robert Rudd (LLNL), robert.rudd@llnl.gov
	Based on the spline-based MEAM routine written by
	Alexander Stukowski (LLNL), alex@stukowski.com
	see LLNL copyright notice at bottom of file
	------------------------------------------------------------------------- */

	/* ----------------------------------------------------------------------
	* File history of changes:
	* 01-Aug-12 - RER: First code version.
	------------------------------------------------------------------------- */

	#include "math.h"
	#include "stdio.h"
	#include "stdlib.h"
	#include "string.h"
	#include "pair_meam_sw_spline.h"
	#include "atom.h"
	#include "force.h"
	#include "comm.h"
	#include "memory.h"
	#include "neighbor.h"
	#include "neigh_list.h"
	#include "neigh_request.h"
	#include "memory.h"
	#include "error.h"

	using namespace LAMMPS_NS;

	/* ---------------------------------------------------------------------- */

	PairMEAMSWSpline::PairMEAMSWSpline(LAMMPS *lmp) : Pair(lmp)
	{
	single_enable = 0;
	restartinfo = 0;
	one_coeff = 1;
	manybody_flag = 1;

	nelements = 0;
	elements = NULL;

	Uprime_values = NULL;
	//ESWprime_values = NULL;
	nmax = 0;
	maxNeighbors = 0;
	twoBodyInfo = NULL;

	comm_forward = 1;
	comm_reverse = 0;
	}

	/* ---------------------------------------------------------------------- */

	PairMEAMSWSpline::~PairMEAMSWSpline()
	{
	if (elements)
	for (int i = 0; i < nelements; i++) delete [] elements[i];
	delete [] elements;

	delete[] twoBodyInfo;
	memory->destroy(Uprime_values);
	//memory->destroy(ESWprime_values);

	if(allocated) {
	memory->destroy(setflag);
	memory->destroy(cutsq);
	delete [] map;
	}
	}

	/* ---------------------------------------------------------------------- */

	void PairMEAMSWSpline::compute(int eflag, int vflag)
	{
	if (eflag \|\| vflag) ev_setup(eflag, vflag);
	else evflag = vflag_fdotr =
	eflag_global = vflag_global = eflag_atom = vflag_atom = 0;

	double cutforcesq = cutoff*cutoff;

	// Grow per-atom array if necessary

	if (atom->nmax > nmax) {
	memory->destroy(Uprime_values);
	//memory->destroy(ESWprime_values);
	nmax = atom->nmax;
	memory->create(Uprime_values,nmax,"pair:Uprime");
	//memory->create(ESWprime_values,nmax,"pair:ESWprime");
	}

	double** const x = atom->x;
	double** forces = atom->f;
	int nlocal = atom->nlocal;
	bool newton_pair = force->newton_pair;

	int inum_full = listfull->inum;
	int* ilist_full = listfull->ilist;
	int* numneigh_full = listfull->numneigh;
	int** firstneigh_full = listfull->firstneigh;

	// Determine the maximum number of neighbors a single atom has

	int newMaxNeighbors = 0;
	for(int ii = 0; ii < inum_full; ii++) {
	int jnum = numneigh_full[ilist_full[ii]];
	if(jnum > newMaxNeighbors) newMaxNeighbors = jnum;
	}

	// Allocate array for temporary bond info

	if(newMaxNeighbors > maxNeighbors) {
	maxNeighbors = newMaxNeighbors;
	delete[] twoBodyInfo;
	twoBodyInfo = new MEAM2Body[maxNeighbors];
	}

	// Sum three-body contributions to charge density and
	// compute embedding energies

	for(int ii = 0; ii < inum_full; ii++) {
	int i = ilist_full[ii];
	double xtmp = x[i][0];
	double ytmp = x[i][1];
	double ztmp = x[i][2];
	int* jlist = firstneigh_full[i];
	int jnum = numneigh_full[i];
	double rho_value = 0;
	double rhoSW_value = 0;
	int numBonds = 0;
	MEAM2Body* nextTwoBodyInfo = twoBodyInfo;

	for(int jj = 0; jj < jnum; jj++) {
	int j = jlist[jj];
	j &= NEIGHMASK;

	double jdelx = x[j][0] - xtmp;
	double jdely = x[j][1] - ytmp;
	double jdelz = x[j][2] - ztmp;
	double rij_sq = jdelxjdelx + jdelyjdely + jdelz*jdelz;

	if(rij_sq < cutforcesq) {
	double rij = sqrt(rij_sq);
	double partial_sum = 0;
	double partial_sum2 = 0;

	nextTwoBodyInfo->tag = j;
	nextTwoBodyInfo->r = rij;
	nextTwoBodyInfo->f = f.eval(rij, nextTwoBodyInfo->fprime);
	nextTwoBodyInfo->F = F.eval(rij, nextTwoBodyInfo->Fprime);
	nextTwoBodyInfo->del[0] = jdelx / rij;
	nextTwoBodyInfo->del[1] = jdely / rij;
	nextTwoBodyInfo->del[2] = jdelz / rij;

	for(int kk = 0; kk < numBonds; kk++) {
	const MEAM2Body& bondk = twoBodyInfo[kk];
	double cos_theta = (nextTwoBodyInfo->del[0]*bondk.del[0] +
	nextTwoBodyInfo->del[1]*bondk.del[1] +
	nextTwoBodyInfo->del[2]*bondk.del[2]);
	partial_sum += bondk.f * g.eval(cos_theta);
	partial_sum2 += bondk.F * G.eval(cos_theta);
	}

	rho_value += nextTwoBodyInfo->f * partial_sum;
	rhoSW_value += nextTwoBodyInfo->F * partial_sum2;
	rho_value += rho.eval(rij);

	numBonds++;
	nextTwoBodyInfo++;
	}
	}

	// Compute embedding energy and its derivative

	double Uprime_i;
	double embeddingEnergy = U.eval(rho_value, Uprime_i) - zero_atom_energy;
	double SWEnergy = rhoSW_value;
	double ESWprime_i = 1.0;
	Uprime_values[i] = Uprime_i;
	// ESWprime_values[i] = ESWprime_i;
	if(eflag) {
	if(eflag_global) eng_vdwl += embeddingEnergy + SWEnergy;
	if(eflag_atom) eatom[i] += embeddingEnergy + SWEnergy;
	}

	double forces_i[3] = {0, 0, 0};

	// Compute three-body contributions to force

	for(int jj = 0; jj < numBonds; jj++) {
	const MEAM2Body bondj = twoBodyInfo[jj];
	double rij = bondj.r;
	int j = bondj.tag;

	double f_rij_prime = bondj.fprime;
	double F_rij_prime = bondj.Fprime;
	double f_rij = bondj.f;
	double F_rij = bondj.F;

	double forces_j[3] = {0, 0, 0};

	MEAM2Body const* bondk = twoBodyInfo;
	for(int kk = 0; kk < jj; kk++, ++bondk) {
	double rik = bondk->r;

	double cos_theta = (bondj.del[0]*bondk->del[0] +
	bondj.del[1]*bondk->del[1] +
	bondj.del[2]*bondk->del[2]);
	double g_prime;
	double g_value = g.eval(cos_theta, g_prime);
	double G_prime;
	double G_value = G.eval(cos_theta, G_prime);
	double f_rik_prime = bondk->fprime;
	double f_rik = bondk->f;
	double F_rik_prime = bondk->Fprime;
	double F_rik = bondk->F;

	double fij = -Uprime_i * g_value * f_rik * f_rij_prime;
	double fik = -Uprime_i * g_value * f_rij * f_rik_prime;
	double Fij = -ESWprime_i * G_value * F_rik * F_rij_prime;
	double Fik = -ESWprime_i * G_value * F_rij * F_rik_prime;

	double prefactor = Uprime_i * f_rij * f_rik * g_prime;
	double prefactor2 = ESWprime_i * F_rij * F_rik * G_prime;
	double prefactor_ij = prefactor / rij;
	double prefactor_ik = prefactor / rik;
	fij += prefactor_ij * cos_theta;
	fik += prefactor_ik * cos_theta;
	double prefactor2_ij = prefactor2 / rij;
	double prefactor2_ik = prefactor2 / rik;
	Fij += prefactor2_ij * cos_theta;
	Fik += prefactor2_ik * cos_theta;

	double fj[3], fk[3];

	fj[0] = bondj.del[0] * fij - bondk->del[0] * prefactor_ij;
	fj[1] = bondj.del[1] * fij - bondk->del[1] * prefactor_ij;
	fj[2] = bondj.del[2] * fij - bondk->del[2] * prefactor_ij;
	fj[0] += bondj.del[0] * Fij - bondk->del[0] * prefactor2_ij;
	fj[1] += bondj.del[1] * Fij - bondk->del[1] * prefactor2_ij;
	fj[2] += bondj.del[2] * Fij - bondk->del[2] * prefactor2_ij;
	forces_j[0] += fj[0];
	forces_j[1] += fj[1];
	forces_j[2] += fj[2];

	fk[0] = bondk->del[0] * fik - bondj.del[0] * prefactor_ik;
	fk[1] = bondk->del[1] * fik - bondj.del[1] * prefactor_ik;
	fk[2] = bondk->del[2] * fik - bondj.del[2] * prefactor_ik;
	fk[0] += bondk->del[0] * Fik - bondj.del[0] * prefactor2_ik;
	fk[1] += bondk->del[1] * Fik - bondj.del[1] * prefactor2_ik;
	fk[2] += bondk->del[2] * Fik - bondj.del[2] * prefactor2_ik;
	forces_i[0] -= fk[0];
	forces_i[1] -= fk[1];
	forces_i[2] -= fk[2];

	int k = bondk->tag;
	forces[k][0] += fk[0];
	forces[k][1] += fk[1];
	forces[k][2] += fk[2];

	if(evflag) {
	double delta_ij[3];
	double delta_ik[3];
	delta_ij[0] = bondj.del[0] * rij;
	delta_ij[1] = bondj.del[1] * rij;
	delta_ij[2] = bondj.del[2] * rij;
	delta_ik[0] = bondk->del[0] * rik;
	delta_ik[1] = bondk->del[1] * rik;
	delta_ik[2] = bondk->del[2] * rik;
	ev_tally3(i, j, k, 0.0, 0.0, fj, fk, delta_ij, delta_ik);
	}
	}

	forces[i][0] -= forces_j[0];
	forces[i][1] -= forces_j[1];
	forces[i][2] -= forces_j[2];
	forces[j][0] += forces_j[0];
	forces[j][1] += forces_j[1];
	forces[j][2] += forces_j[2];
	}

	forces[i][0] += forces_i[0];
	forces[i][1] += forces_i[1];
	forces[i][2] += forces_i[2];
	}

	// Communicate U'(rho) values

	comm->forward_comm_pair(this);

	int inum_half = listhalf->inum;
	int* ilist_half = listhalf->ilist;
	int* numneigh_half = listhalf->numneigh;
	int** firstneigh_half = listhalf->firstneigh;

	// Compute two-body pair interactions

	for(int ii = 0; ii < inum_half; ii++) {
	int i = ilist_half[ii];
	double xtmp = x[i][0];
	double ytmp = x[i][1];
	double ztmp = x[i][2];
	int* jlist = firstneigh_half[i];
	int jnum = numneigh_half[i];

	for(int jj = 0; jj < jnum; jj++) {
	int j = jlist[jj];
	j &= NEIGHMASK;

	double jdel[3];
	jdel[0] = x[j][0] - xtmp;
	jdel[1] = x[j][1] - ytmp;
	jdel[2] = x[j][2] - ztmp;
	double rij_sq = jdel[0]jdel[0] + jdel[1]jdel[1] + jdel[2]*jdel[2];

	if(rij_sq < cutforcesq) {
	double rij = sqrt(rij_sq);

	double rho_prime;
	rho.eval(rij, rho_prime);
	double fpair = rho_prime * (Uprime_values[i] + Uprime_values[j]);

	double pair_pot_deriv;
	double pair_pot = phi.eval(rij, pair_pot_deriv);
	fpair += pair_pot_deriv;

	// Divide by r_ij to get forces from gradient

	fpair /= rij;

	forces[i][0] += jdel[0]*fpair;
	forces[i][1] += jdel[1]*fpair;
	forces[i][2] += jdel[2]*fpair;
	forces[j][0] -= jdel[0]*fpair;
	forces[j][1] -= jdel[1]*fpair;
	forces[j][2] -= jdel[2]*fpair;
	if (evflag) ev_tally(i, j, nlocal, newton_pair,
	pair_pot, 0.0, -fpair, jdel[0], jdel[1], jdel[2]);
	}
	}
	}

	if(vflag_fdotr) virial_fdotr_compute();
	}

	/* ---------------------------------------------------------------------- */

	void PairMEAMSWSpline::allocate()
	{
	allocated = 1;
	int n = atom->ntypes;

	memory->create(setflag,n+1,n+1,"pair:setflag");
	memory->create(cutsq,n+1,n+1,"pair:cutsq");

	map = new int[n+1];
	}

	/* ----------------------------------------------------------------------
	global settings
	------------------------------------------------------------------------- */

	void PairMEAMSWSpline::settings(int narg, char **arg)
	{
	if(narg != 0) error->all(FLERR,"Illegal pair_style command");
	}

	/* ----------------------------------------------------------------------
	set coeffs for one or more type pairs
	------------------------------------------------------------------------- */

	void PairMEAMSWSpline::coeff(int narg, char **arg)
	{
	int i,j,n;

	if (!allocated) allocate();

	if (narg != 3 + atom->ntypes)
	error->all(FLERR,"Incorrect args for pair coefficients");

	// insure I,J args are * *

	if (strcmp(arg[0],"") != 0 \|\| strcmp(arg[1],"") != 0)
	error->all(FLERR,"Incorrect args for pair coefficients");

	// read args that map atom types to elements in potential file
	// map[i] = which element the Ith atom type is, -1 if NULL
	// nelements = # of unique elements
	// elements = list of element names

	if (elements) {
	for (i = 0; i < nelements; i++) delete [] elements[i];
	delete [] elements;
	}
	elements = new char*[atom->ntypes];
	for (i = 0; i < atom->ntypes; i++) elements[i] = NULL;

	nelements = 0;
	for (i = 3; i < narg; i++) {
	if (strcmp(arg[i],"NULL") == 0) {
	map[i-2] = -1;
	continue;
	}
	for (j = 0; j < nelements; j++)
	if (strcmp(arg[i],elements[j]) == 0) break;
	map[i-2] = j;
	if (j == nelements) {
	n = strlen(arg[i]) + 1;
	elements[j] = new char[n];
	strcpy(elements[j],arg[i]);
	nelements++;
	}
	}

	// for now, only allow single element

	if (nelements > 1)
	error->all(FLERR,
	"Pair meam/sw/spline only supports single element potentials");

	// read potential file

	read_file(arg[2]);

	// clear setflag since coeff() called once with I,J = * *

	n = atom->ntypes;
	for (int i = 1; i <= n; i++)
	for (int j = i; j <= n; j++)
	setflag[i][j] = 0;

	// set setflag i,j for type pairs where both are mapped to elements

	int count = 0;
	for (int i = 1; i <= n; i++)
	for (int j = i; j <= n; j++)
	if (map[i] >= 0 && map[j] >= 0) {
	setflag[i][j] = 1;
	count++;
	}

	if (count == 0) error->all(FLERR,"Incorrect args for pair coefficients");
	}

	/* ----------------------------------------------------------------------
	set coeffs for one or more type pairs
	------------------------------------------------------------------------- */

	#define MAXLINE 1024

	void PairMEAMSWSpline::read_file(const char* filename)
	{
	if(comm->me == 0) {
	FILE *fp = force->open_potential(filename);
	if(fp == NULL) {
	char str[1024];
	sprintf(str,"Cannot open spline MEAM potential file %s", filename);
	error->one(FLERR,str);
	}

	// Skip first line of file.
	char line[MAXLINE];
	fgets(line, MAXLINE, fp);

	// Parse spline functions.
	phi.parse(fp, error);
	F.parse(fp, error);
	G.parse(fp, error);
	rho.parse(fp, error);
	U.parse(fp, error);
	f.parse(fp, error);
	g.parse(fp, error);

	fclose(fp);
	}

	// Transfer spline functions from master processor to all other processors.
	phi.communicate(world, comm->me);
	rho.communicate(world, comm->me);
	f.communicate(world, comm->me);
	U.communicate(world, comm->me);
	g.communicate(world, comm->me);
	F.communicate(world, comm->me);
	G.communicate(world, comm->me);

	// Calculate 'zero-point energy' of single atom in vacuum.
	zero_atom_energy = U.eval(0.0);

	// Determine maximum cutoff radius of all relevant spline functions.
	cutoff = 0.0;
	if(phi.cutoff() > cutoff) cutoff = phi.cutoff();
	if(rho.cutoff() > cutoff) cutoff = rho.cutoff();
	if(f.cutoff() > cutoff) cutoff = f.cutoff();
	if(F.cutoff() > cutoff) cutoff = F.cutoff();

	// Set LAMMPS pair interaction flags.
	for(int i = 1; i <= atom->ntypes; i++) {
	for(int j = 1; j <= atom->ntypes; j++) {
	setflag[i][j] = 1;
	cutsq[i][j] = cutoff;
	}
	}

	// phi.writeGnuplot("phi.gp", "Phi(r)");
	// rho.writeGnuplot("rho.gp", "Rho(r)");
	// f.writeGnuplot("f.gp", "f(r)");
	// U.writeGnuplot("U.gp", "U(rho)");
	// g.writeGnuplot("g.gp", "g(x)");
	// F.writeGnuplot("F.gp", "F(r)");
	// G.writeGnuplot("G.gp", "G(x)");
	}

	/* ----------------------------------------------------------------------
	init specific to this pair style
	------------------------------------------------------------------------- */
	void PairMEAMSWSpline::init_style()
	{
	if(force->newton_pair == 0)
	error->all(FLERR,"Pair style meam/sw/spline requires newton pair on");

	// Need both full and half neighbor list.
	int irequest_full = neighbor->request(this,instance_me);
	neighbor->requests[irequest_full]->id = 1;
	neighbor->requests[irequest_full]->half = 0;
	neighbor->requests[irequest_full]->full = 1;
	int irequest_half = neighbor->request(this,instance_me);
	neighbor->requests[irequest_half]->id = 2;
	neighbor->requests[irequest_half]->half = 0;
	neighbor->requests[irequest_half]->half_from_full = 1;
	neighbor->requests[irequest_half]->otherlist = irequest_full;
	}

	/* ----------------------------------------------------------------------
	neighbor callback to inform pair style of neighbor list to use
	half or full
	------------------------------------------------------------------------- */
	void PairMEAMSWSpline::init_list(int id, NeighList *ptr)
	{
	if(id == 1) listfull = ptr;
	else if(id == 2) listhalf = ptr;
	}

	/* ----------------------------------------------------------------------
	init for one type pair i,j and corresponding j,i
	------------------------------------------------------------------------- */
	double PairMEAMSWSpline::init_one(int i, int j)
	{
	return cutoff;
	}

	/* ---------------------------------------------------------------------- */

	int PairMEAMSWSpline::pack_forward_comm(int n, int list, double buf,
	int pbc_flag, int *pbc)
	{
	int* list_iter = list;
	int* list_iter_end = list + n;
	while(list_iter != list_iter_end)
	buf++ = Uprime_values[list_iter++];
	return n;
	}

	/* ---------------------------------------------------------------------- */

	void PairMEAMSWSpline::unpack_forward_comm(int n, int first, double *buf)
	{
	memcpy(&Uprime_values[first], buf, n * sizeof(buf[0]));
	}

	/* ---------------------------------------------------------------------- */

	int PairMEAMSWSpline::pack_reverse_comm(int n, int first, double *buf)
	{
	return 0;
	}

	/* ---------------------------------------------------------------------- */

	void PairMEAMSWSpline::unpack_reverse_comm(int n, int list, double buf)
	{
	}

	/* ----------------------------------------------------------------------
	Returns memory usage of local atom-based arrays
	------------------------------------------------------------------------- */
	double PairMEAMSWSpline::memory_usage()
	{
	return nmax * sizeof(double); // The Uprime_values array.
	}


	/// Parses the spline knots from a text file.
	void PairMEAMSWSpline::SplineFunction::parse(FILE* fp, Error* error)
	{
	char line[MAXLINE];

	// Parse number of spline knots.
	fgets(line, MAXLINE, fp);
	int n = atoi(line);
	if(n < 2)
	error->one(FLERR,"Invalid number of spline knots in MEAM potential file");

	// Parse first derivatives at beginning and end of spline.
	fgets(line, MAXLINE, fp);
	double d0 = atof(strtok(line, " \t\n\r\f"));
	double dN = atof(strtok(NULL, " \t\n\r\f"));
	init(n, d0, dN);

	// Skip line.
	fgets(line, MAXLINE, fp);

	// Parse knot coordinates.
	for(int i=0; i<n; i++) {
	fgets(line, MAXLINE, fp);
	double x, y, y2;
	if(sscanf(line, "%lg %lg %lg", &x, &y, &y2) != 3) {
	error->one(FLERR,"Invalid knot line in MEAM potential file");
	}
	setKnot(i, x, y);
	}

	prepareSpline(error);
	}

	/// Calculates the second derivatives at the knots of the cubic spline.
	void PairMEAMSWSpline::SplineFunction::prepareSpline(Error* error)
	{
	xmin = X[0];
	xmax = X[N-1];

	isGridSpline = true;
	h = (xmax-xmin)/((double)(N-1));
	hsq = h*h;

	double* u = new double[N];
	Y2[0] = -0.5;
	u[0] = (3.0/(X[1]-X[0])) * ((Y[1]-Y[0])/(X[1]-X[0]) - deriv0);
	for(int i = 1; i <= N-2; i++) {
	double sig = (X[i]-X[i-1]) / (X[i+1]-X[i-1]);
	double p = sig * Y2[i-1] + 2.0;
	Y2[i] = (sig - 1.0) / p;
	u[i] = (Y[i+1]-Y[i]) / (X[i+1]-X[i]) - (Y[i]-Y[i-1])/(X[i]-X[i-1]);
	u[i] = (6.0 * u[i]/(X[i+1]-X[i-1]) - sig*u[i-1])/p;

	if(fabs(h*i+xmin - X[i]) > 1e-8)
	isGridSpline = false;
	}

	double qn = 0.5;
	double un = (3.0/(X[N-1]-X[N-2])) * (derivN - (Y[N-1]-Y[N-2])/(X[N-1]-X[N-2]));
	Y2[N-1] = (un - qnu[N-2]) / (qn Y2[N-2] + 1.0);
	for(int k = N-2; k >= 0; k--) {
	Y2[k] = Y2[k] * Y2[k+1] + u[k];
	}

	delete[] u;

	#if !SPLINE_MEAM_SUPPORT_NON_GRID_SPLINES
	if(!isGridSpline)
	error->one(FLERR,"Support for MEAM potentials with non-uniform cubic splines has not been enabled in the MEAM potential code. Set SPLINE_MEAM_SUPPORT_NON_GRID_SPLINES in pair_spline_meam.h to 1 to enable it");
	#endif

	// Shift the spline to X=0 to speed up interpolation.
	for(int i = 0; i < N; i++) {
	Xs[i] = X[i] - xmin;
	#if !SPLINE_MEAM_SUPPORT_NON_GRID_SPLINES
	if(i < N-1) Ydelta[i] = (Y[i+1]-Y[i])/h;
	Y2[i] /= h*6.0;
	#endif
	}
	xmax_shifted = xmax - xmin;
	}

	/// Broadcasts the spline function parameters to all processors.
	void PairMEAMSWSpline::SplineFunction::communicate(MPI_Comm& world, int me)
	{
	MPI_Bcast(&N, 1, MPI_INT, 0, world);
	MPI_Bcast(&deriv0, 1, MPI_DOUBLE, 0, world);
	MPI_Bcast(&derivN, 1, MPI_DOUBLE, 0, world);
	MPI_Bcast(&xmin, 1, MPI_DOUBLE, 0, world);
	MPI_Bcast(&xmax, 1, MPI_DOUBLE, 0, world);
	MPI_Bcast(&xmax_shifted, 1, MPI_DOUBLE, 0, world);
	MPI_Bcast(&isGridSpline, 1, MPI_INT, 0, world);
	MPI_Bcast(&h, 1, MPI_DOUBLE, 0, world);
	MPI_Bcast(&hsq, 1, MPI_DOUBLE, 0, world);
	if(me != 0) {
	X = new double[N];
	Xs = new double[N];
	Y = new double[N];
	Y2 = new double[N];
	Ydelta = new double[N];
	}
	MPI_Bcast(X, N, MPI_DOUBLE, 0, world);
	MPI_Bcast(Xs, N, MPI_DOUBLE, 0, world);
	MPI_Bcast(Y, N, MPI_DOUBLE, 0, world);
	MPI_Bcast(Y2, N, MPI_DOUBLE, 0, world);
	MPI_Bcast(Ydelta, N, MPI_DOUBLE, 0, world);
	}

	/// Writes a Gnuplot script that plots the spline function.
	///
	/// This function is for debugging only!
	void PairMEAMSWSpline::SplineFunction::writeGnuplot(const char* filename, const char* title) const
	{
	FILE* fp = fopen(filename, "w");
	fprintf(fp, "#!/usr/bin/env gnuplot\n");
	if(title) fprintf(fp, "set title \"%s\"\n", title);
	double tmin = X[0] - (X[N-1] - X[0]) * 0.05;
	double tmax = X[N-1] + (X[N-1] - X[0]) * 0.05;
	double delta = (tmax - tmin) / (N*200);
	fprintf(fp, "set xrange [%f:%f]\n", tmin, tmax);
	fprintf(fp, "plot '-' with lines notitle, '-' with points notitle pt 3 lc 3\n");
	for(double x = tmin; x <= tmax+1e-8; x += delta) {
	double y = eval(x);
	fprintf(fp, "%f %f\n", x, y);
	}
	fprintf(fp, "e\n");
	for(int i = 0; i < N; i++) {
	fprintf(fp, "%f %f\n", X[i], Y[i]);
	}
	fprintf(fp, "e\n");
	fclose(fp);
	}

	/* ----------------------------------------------------------------------
	* Spline-based Modified Embedded Atom Method plus
	* Stillinger-Weber (MEAM+SW) potential routine.
	*
	* Copyright (2012) Lawrence Livermore National Security, LLC.
	* Produced at the Lawrence Livermore National Laboratory.
	* Written by Robert E. Rudd (<robert.rudd@llnl.gov>).
	* Based on the spline-based MEAM routine written by
	* Alexander Stukowski (<alex@stukowski.com>).
	* LLNL-CODE-588032 All rights reserved.
	*
	* The spline-based MEAM+SW format was first devised and used to develop
	* potentials for bcc transition metals by Jeremy Nicklas, Michael Fellinger,
	* and Hyoungki Park at The Ohio State University.
	*
	* This program is free software; you can redistribute it and/or modify it under
	* the terms of the GNU General Public License (as published by the Free
	* Software Foundation) version 2, dated June 1991.
	*
	* This program is distributed in the hope that it will be useful, but
	* WITHOUT ANY WARRANTY; without even the IMPLIED WARRANTY OF MERCHANTABILITY
	* or FITNESS FOR A PARTICULAR PURPOSE. See the terms and conditions of the
	* GNU General Public License for more details.
	*
	* Our Preamble Notice
	* A. This notice is required to be provided under our contract with the
	* U.S. Department of Energy (DOE). This work was produced at the
	* Lawrence Livermore National Laboratory under Contract No.
	* DE-AC52-07NA27344 with the DOE.
	*
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