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pair_meam_sw_spline.cpp
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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
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			*
			* Our Preamble Notice
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			*
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lammps/src/USER-MISC/pair_meam_sw_spline.cpp775e8f3cc8f5lammm-master-deprecated

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lammps/src/USER-MISC/pair_meam_sw_spline.cpp
775e8f3cc8f5lammm-master-deprecated

pair_meam_sw_spline.cpp
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