diff --git a/src/SPIN/min_spin_oso_cg2.cpp b/src/SPIN/min_spin_oso_cg2.cpp new file mode 100644 index 0000000000..23873e24f2 --- /dev/null +++ b/src/SPIN/min_spin_oso_cg2.cpp @@ -0,0 +1,665 @@ +/* ---------------------------------------------------------------------- + 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 authors: Aleksei Ivanov (University of Iceland) + Julien Tranchida (SNL) + + Please cite the related publication: + Ivanov, A. V., Uzdin, V. M., & Jónsson, H. (2019). Fast and Robust + Algorithm for the Minimisation of the Energy of Spin Systems. arXiv + preprint arXiv:1904.02669. +------------------------------------------------------------------------- */ + +#include +#include +#include +#include +#include "min_spin_oso_cg2.h" +#include "universe.h" +#include "atom.h" +#include "citeme.h" +#include "force.h" +#include "update.h" +#include "output.h" +#include "timer.h" +#include "error.h" +#include "memory.h" +#include "modify.h" +#include "math_special.h" +#include "math_const.h" +#include "universe.h" +#include + +using namespace LAMMPS_NS; +using namespace MathConst; + +static const char cite_minstyle_spin_oso_cg2[] = + "min_style spin/oso_cg2 command:\n\n" + "@article{ivanov2019fast,\n" + "title={Fast and Robust Algorithm for the Minimisation of the Energy of " + "Spin Systems},\n" + "author={Ivanov, A. V and Uzdin, V. M. and J{\'o}nsson, H.},\n" + "journal={arXiv preprint arXiv:1904.02669},\n" + "year={2019}\n" + "}\n\n"; + +// EPS_ENERGY = minimum normalization for energy tolerance + +#define EPS_ENERGY 1.0e-8 + +#define DELAYSTEP 5 + + +/* ---------------------------------------------------------------------- */ + +MinSpinOSO_CG2::MinSpinOSO_CG2(LAMMPS *lmp) : + Min(lmp), g_old(NULL), g_cur(NULL), p_s(NULL) +{ + if (lmp->citeme) lmp->citeme->add(cite_minstyle_spin_oso_cg2); + nlocal_max = 0; + + // nreplica = number of partitions + // ireplica = which world I am in universe + + nreplica = universe->nworlds; + ireplica = universe->iworld; + use_line_search = 1; + maxepsrot = MY_2PI / (100.0); + +} + +/* ---------------------------------------------------------------------- */ + +MinSpinOSO_CG2::~MinSpinOSO_CG2() +{ + memory->destroy(g_old); + memory->destroy(g_cur); + memory->destroy(p_s); + if (use_line_search) + memory->destroy(sp_copy); +} + +/* ---------------------------------------------------------------------- */ + +void MinSpinOSO_CG2::init() +{ + local_iter = 0; + der_e_cur = 0.0; + der_e_pr = 0.0; + + Min::init(); + + last_negative = update->ntimestep; + + // allocate tables + + nlocal_max = atom->nlocal; + memory->grow(g_old,3*nlocal_max,"min/spin/oso/cg2:g_old"); + memory->grow(g_cur,3*nlocal_max,"min/spin/oso/cg2:g_cur"); + memory->grow(p_s,3*nlocal_max,"min/spin/oso/cg2:p_s"); + if (use_line_search) + memory->grow(sp_copy,nlocal_max,3,"min/spin/oso/cg2:sp_copy"); +} + +/* ---------------------------------------------------------------------- */ + +void MinSpinOSO_CG2::setup_style() +{ + double **v = atom->v; + int nlocal = atom->nlocal; + + // check if the atom/spin style is defined + + if (!atom->sp_flag) + error->all(FLERR,"min/spin_oso_cg2 requires atom/spin style"); + + for (int i = 0; i < nlocal; i++) + v[i][0] = v[i][1] = v[i][2] = 0.0; +} + +/* ---------------------------------------------------------------------- */ + +int MinSpinOSO_CG2::modify_param(int narg, char **arg) +{ + + if (strcmp(arg[0],"line_search") == 0) { + if (narg < 2) error->all(FLERR,"Illegal fix_modify command"); + use_line_search = force->numeric(FLERR,arg[1]); + return 2; + } + if (strcmp(arg[0],"discrete_factor") == 0) { + if (narg < 2) error->all(FLERR,"Illegal fix_modify command"); + double discrete_factor; + discrete_factor = force->numeric(FLERR,arg[1]); + maxepsrot = MY_2PI / discrete_factor; + return 2; + } + return 0; +} + +/* ---------------------------------------------------------------------- + set current vector lengths and pointers + called after atoms have migrated +------------------------------------------------------------------------- */ + +void MinSpinOSO_CG2::reset_vectors() +{ + // atomic dof + + // size sp is 4N vector + nvec = 4 * atom->nlocal; + if (nvec) spvec = atom->sp[0]; + + nvec = 3 * atom->nlocal; + if (nvec) fmvec = atom->fm[0]; + + if (nvec) xvec = atom->x[0]; + if (nvec) fvec = atom->f[0]; +} + +/* ---------------------------------------------------------------------- + minimization via damped spin dynamics +------------------------------------------------------------------------- */ + +int MinSpinOSO_CG2::iterate(int maxiter) +{ + int nlocal = atom->nlocal; + bigint ntimestep; + double fmdotfm; + int flag, flagall; + double **sp = atom->sp; + double der_e_cur_tmp = 0.0; + + if (nlocal_max < nlocal) { + nlocal_max = nlocal; + local_iter = 0; + nlocal_max = nlocal; + memory->grow(g_old,3*nlocal_max,"min/spin/oso/cg2:g_old"); + memory->grow(g_cur,3*nlocal_max,"min/spin/oso/cg2:g_cur"); + memory->grow(p_s,3*nlocal_max,"min/spin/oso/cg2:p_s"); + if (use_line_search) + memory->grow(sp_copy,nlocal_max,3,"min/spin/oso/cg2:sp_copy"); + } + + for (int iter = 0; iter < maxiter; iter++) { + + if (timer->check_timeout(niter)) + return TIMEOUT; + + ntimestep = ++update->ntimestep; + niter++; + + // optimize timestep accross processes / replicas + // need a force calculation for timestep optimization + + if (use_line_search) { + + // here we need to do line search + if (local_iter == 0) + calc_gradient(); + + calc_search_direction(); + der_e_cur = 0.0; + for (int i = 0; i < 3 * nlocal; i++) + der_e_cur += g_cur[i] * p_s[i]; + MPI_Allreduce(&der_e_cur,&der_e_cur_tmp,1,MPI_DOUBLE,MPI_SUM,world); + der_e_cur = der_e_cur_tmp; + if (update->multireplica == 1) { + MPI_Allreduce(&der_e_cur_tmp,&der_e_cur,1,MPI_DOUBLE,MPI_SUM,universe->uworld); + } + for (int i = 0; i < nlocal; i++) + for (int j = 0; j < 3; j++) + sp_copy[i][j] = sp[i][j]; + + eprevious = ecurrent; + der_e_pr = der_e_cur; + calc_and_make_step(0.0, 1.0, 0); + } + else{ + + // here we don't do line search + // but use cutoff rotation angle + // if gneb calc., nreplica > 1 + // then calculate gradients and advance spins + // of intermediate replicas only + + if (nreplica > 1) { + if(ireplica != 0 && ireplica != nreplica-1) + calc_gradient(); + calc_search_direction(); + advance_spins(); + } else{ + calc_gradient(); + calc_search_direction(); + advance_spins(); + } + eprevious = ecurrent; + ecurrent = energy_force(0); + neval++; + } + + //// energy tolerance criterion + //// only check after DELAYSTEP elapsed since velocties reset to 0 + //// sync across replicas if running multi-replica minimization + + if (update->etol > 0.0 && ntimestep-last_negative > DELAYSTEP) { + if (update->multireplica == 0) { + if (fabs(ecurrent-eprevious) < + update->etol * 0.5*(fabs(ecurrent) + fabs(eprevious) + EPS_ENERGY)) + return ETOL; + } else { + if (fabs(ecurrent-eprevious) < + update->etol * 0.5*(fabs(ecurrent) + fabs(eprevious) + EPS_ENERGY)) + flag = 0; + else flag = 1; + MPI_Allreduce(&flag,&flagall,1,MPI_INT,MPI_SUM,universe->uworld); + if (flagall == 0) return ETOL; + } + } + + // magnetic torque tolerance criterion + // sync across replicas if running multi-replica minimization + + if (update->ftol > 0.0) { + fmdotfm = max_torque(); + if (update->multireplica == 0) { + if (fmdotfm < update->ftol*update->ftol) return FTOL; + } else { + if (fmdotfm < update->ftol*update->ftol) flag = 0; + else flag = 1; + MPI_Allreduce(&flag,&flagall,1,MPI_INT,MPI_SUM,universe->uworld); + if (flagall == 0) return FTOL; + } + } + + // output for thermo, dump, restart files + + if (output->next == ntimestep) { + timer->stamp(); + output->write(ntimestep); + timer->stamp(Timer::OUTPUT); + } + } + + return MAXITER; +} + +/* ---------------------------------------------------------------------- + calculate gradients +---------------------------------------------------------------------- */ + +void MinSpinOSO_CG2::calc_gradient() +{ + int nlocal = atom->nlocal; + double **sp = atom->sp; + double **fm = atom->fm; + double hbar = force->hplanck/MY_2PI; + + // loop on all spins on proc. + + for (int i = 0; i < nlocal; i++) { + + // calculate gradients + + g_cur[3 * i + 0] = (fm[i][0]*sp[i][1] - fm[i][1]*sp[i][0]) * hbar; + g_cur[3 * i + 1] = -(fm[i][2]*sp[i][0] - fm[i][0]*sp[i][2]) * hbar; + g_cur[3 * i + 2] = (fm[i][1]*sp[i][2] - fm[i][2]*sp[i][1]) * hbar; + } +} + + +/* ---------------------------------------------------------------------- + search direction: + The Fletcher-Reeves conj. grad. method + See Jorge Nocedal and Stephen J. Wright 'Numerical + Optimization' Second Edition, 2006 (p. 121) +---------------------------------------------------------------------- */ + +void MinSpinOSO_CG2::calc_search_direction() +{ + int nlocal = atom->nlocal; + double g2old = 0.0; + double g2 = 0.0; + double beta = 0.0; + + double g2_global = 0.0; + double g2old_global = 0.0; + double scaling = 1.0; + + if (use_line_search == 0) + scaling = maximum_rotation(g_cur); + + if (local_iter == 0 || local_iter % 5 == 0){ // steepest descent direction + for (int i = 0; i < 3 * nlocal; i++) { + p_s[i] = -g_cur[i] * scaling; + g_old[i] = g_cur[i]; + } + } else { // conjugate direction + for (int i = 0; i < 3 * nlocal; i++) { + g2old += g_old[i] * g_old[i]; + g2 += g_cur[i] * g_cur[i]; + } + + // now we need to collect/broadcast beta on this replica + // different replica can have different beta for now. + // need to check what is beta for GNEB + + MPI_Allreduce(&g2, &g2_global, 1, MPI_DOUBLE, MPI_SUM, world); + MPI_Allreduce(&g2old, &g2old_global, 1, MPI_DOUBLE, MPI_SUM, world); + + // Sum over all replicas. Good for GNEB. + if (update->multireplica == 1) { + g2 = g2_global; + g2old = g2old_global; + MPI_Allreduce(&g2,&g2_global,1,MPI_DOUBLE,MPI_SUM,universe->uworld); + MPI_Allreduce(&g2old,&g2old_global,1,MPI_DOUBLE,MPI_SUM,universe->uworld); + } + + if (fabs(g2_global) < 1.0e-60) beta = 0.0; + else beta = g2_global / g2old_global; + // calculate conjugate direction + for (int i = 0; i < 3 * nlocal; i++) { + p_s[i] = (beta * p_s[i] - g_cur[i])*scaling; + g_old[i] = g_cur[i]; + } + } + + local_iter++; +} + +/* ---------------------------------------------------------------------- + rotation of spins along the search direction +---------------------------------------------------------------------- */ + +void MinSpinOSO_CG2::advance_spins() +{ + int nlocal = atom->nlocal; + double **sp = atom->sp; + double **fm = atom->fm; + double tdampx, tdampy, tdampz; + double rot_mat[9]; // exponential of matrix made of search direction + double s_new[3]; + + // loop on all spins on proc. + + for (int i = 0; i < nlocal; i++) { + rodrigues_rotation(p_s + 3 * i, rot_mat); + + // rotate spins + + vm3(rot_mat, sp[i], s_new); + for (int j = 0; j < 3; j++) sp[i][j] = s_new[j]; + } +} + +/* ---------------------------------------------------------------------- + compute and return max_i||mag. torque_i||_2 +------------------------------------------------------------------------- */ + +double MinSpinOSO_CG2::max_torque() +{ + double fmsq,fmaxsqone,fmaxsqloc,fmaxsqall; + int nlocal = atom->nlocal; + + // finding max fm on this proc. + + fmsq = fmaxsqone = fmaxsqloc = fmaxsqall = 0.0; + for (int i = 0; i < nlocal; i++) { + fmsq = 0.0; + for (int j = 0; j < 3; j++) + fmsq += g_cur[3 * i + j] * g_cur[3 * i + j]; + fmaxsqone = MAX(fmaxsqone,fmsq); + } + + // finding max fm on this replica + + fmaxsqloc = fmaxsqone; + MPI_Allreduce(&fmaxsqone,&fmaxsqloc,1,MPI_DOUBLE,MPI_MAX,world); + + // finding max fm over all replicas, if necessary + // this communicator would be invalid for multiprocess replicas + + fmaxsqall = fmaxsqloc; + if (update->multireplica == 1) { + fmaxsqall = fmaxsqloc; + MPI_Allreduce(&fmaxsqloc,&fmaxsqall,1,MPI_DOUBLE,MPI_MAX,universe->uworld); + } + + return sqrt(fmaxsqall); +} + +/* ---------------------------------------------------------------------- + calculate 3x3 matrix exponential using Rodrigues' formula + (R. Murray, Z. Li, and S. Shankar Sastry, + A Mathematical Introduction to + Robotic Manipulation (1994), p. 28 and 30). + + upp_tr - vector x, y, z so that one calculate + U = exp(A) with A= [[0, x, y], + [-x, 0, z], + [-y, -z, 0]] +------------------------------------------------------------------------- */ + +void MinSpinOSO_CG2::rodrigues_rotation(const double *upp_tr, double *out) +{ + double theta,A,B,D,x,y,z; + double s1,s2,s3,a1,a2,a3; + + if (fabs(upp_tr[0]) < 1.0e-40 && + fabs(upp_tr[1]) < 1.0e-40 && + fabs(upp_tr[2]) < 1.0e-40){ + + // if upp_tr is zero, return unity matrix + for(int k = 0; k < 3; k++){ + for(int m = 0; m < 3; m++){ + if (m == k) out[3 * k + m] = 1.0; + else out[3 * k + m] = 0.0; + } + } + return; + } + + theta = sqrt(upp_tr[0] * upp_tr[0] + + upp_tr[1] * upp_tr[1] + + upp_tr[2] * upp_tr[2]); + + A = cos(theta); + B = sin(theta); + D = 1 - A; + x = upp_tr[0]/theta; + y = upp_tr[1]/theta; + z = upp_tr[2]/theta; + + // diagonal elements of U + + out[0] = A + z * z * D; + out[4] = A + y * y * D; + out[8] = A + x * x * D; + + // off diagonal of U + + s1 = -y * z *D; + s2 = x * z * D; + s3 = -x * y * D; + + a1 = x * B; + a2 = y * B; + a3 = z * B; + + out[1] = s1 + a1; + out[3] = s1 - a1; + out[2] = s2 + a2; + out[6] = s2 - a2; + out[5] = s3 + a3; + out[7] = s3 - a3; + +} + +/* ---------------------------------------------------------------------- + out = vector^T x m, + m -- 3x3 matrix , v -- 3-d vector +------------------------------------------------------------------------- */ + +void MinSpinOSO_CG2::vm3(const double *m, const double *v, double *out) +{ + for(int i = 0; i < 3; i++){ + out[i] *= 0.0; + for(int j = 0; j < 3; j++) + out[i] += *(m + 3 * j + i) * v[j]; + } +} + + +void MinSpinOSO_CG2::make_step(double c, double *energy_and_der) +{ + double p_scaled[3]; + int nlocal = atom->nlocal; + double rot_mat[9]; // exponential of matrix made of search direction + double s_new[3]; + double **sp = atom->sp; + double der_e_cur_tmp = 0.0;; + + for (int i = 0; i < nlocal; i++) { + + // scale the search direction + + for (int j = 0; j < 3; j++) p_scaled[j] = c * p_s[3 * i + j]; + + // calculate rotation matrix + + rodrigues_rotation(p_scaled, rot_mat); + + // rotate spins + + vm3(rot_mat, sp[i], s_new); + for (int j = 0; j < 3; j++) sp[i][j] = s_new[j]; + } + + ecurrent = energy_force(0); + calc_gradient(); + neval++; + der_e_cur = 0.0; + for (int i = 0; i < 3 * nlocal; i++) { + der_e_cur += g_cur[i] * p_s[i]; + } + MPI_Allreduce(&der_e_cur,&der_e_cur_tmp,1,MPI_DOUBLE,MPI_SUM,world); + der_e_cur = der_e_cur_tmp; + if (update->multireplica == 1) { + MPI_Allreduce(&der_e_cur_tmp,&der_e_cur,1,MPI_DOUBLE,MPI_SUM,universe->uworld); + } + + energy_and_der[0] = ecurrent; + energy_and_der[1] = der_e_cur; +} + +/* ---------------------------------------------------------------------- + Calculate step length which satisfies approximate Wolfe conditions + using the cubic interpolation +------------------------------------------------------------------------- */ + +int MinSpinOSO_CG2::calc_and_make_step(double a, double b, int index) +{ + double e_and_d[2] = {0.0,0.0}; + double alpha,c1,c2,c3; + double **sp = atom->sp; + int nlocal = atom->nlocal; + + make_step(b,e_and_d); + ecurrent = e_and_d[0]; + der_e_cur = e_and_d[1]; + index++; + + if (awc(der_e_pr,eprevious,e_and_d[1],e_and_d[0]) || index == 10){ + MPI_Bcast(&b,1,MPI_DOUBLE,0,world); + for (int i = 0; i < 3 * nlocal; i++) { + p_s[i] = b * p_s[i]; + } + return 1; + } + else{ + double r,f0,f1,df0,df1; + r = b - a; + f0 = eprevious; + f1 = ecurrent; + df0 = der_e_pr; + df1 = der_e_cur; + + c1 = -2.0*(f1-f0)/(r*r*r)+(df1+df0)/(r*r); + c2 = 3.0*(f1-f0)/(r*r)-(df1+2.0*df0)/(r); + c3 = df0; + + // f(x) = c1 x^3 + c2 x^2 + c3 x^1 + c4 + // has minimum at alpha below. We do not check boundaries. + + alpha = (-c2 + sqrt(c2*c2 - 3.0*c1*c3))/(3.0*c1); + MPI_Bcast(&alpha,1,MPI_DOUBLE,0,world); + + if (alpha < 0.0) alpha = r/2.0; + + std::cout << alpha << "\n"; + + for (int i = 0; i < nlocal; i++) { + for (int j = 0; j < 3; j++) sp[i][j] = sp_copy[i][j]; + } + calc_and_make_step(0.0, alpha, index); + } + + return 0; +} + +/* ---------------------------------------------------------------------- + Approximate Wolfe conditions: + William W. Hager and Hongchao Zhang + SIAM J. optim., 16(1), 170-192. (23 pages) +------------------------------------------------------------------------- */ + +int MinSpinOSO_CG2::awc(double der_phi_0, double phi_0, double der_phi_j, double phi_j){ + + double eps = 1.0e-6; + double delta = 0.1; + double sigma = 0.9; + + if ((phi_j<=phi_0+eps*fabs(phi_0)) && ((2.0*delta-1.0) * der_phi_0>=der_phi_j>=sigma*der_phi_0)) + return 1; + else + return 0; +} + +double MinSpinOSO_CG2::maximum_rotation(double *p) +{ + double norm2,norm2_global,scaling,alpha; + int nlocal = atom->nlocal; + int ntotal = 0; + + norm2 = 0.0; + for (int i = 0; i < 3 * nlocal; i++) norm2 += p[i] * p[i]; + + MPI_Allreduce(&norm2,&norm2_global,1,MPI_DOUBLE,MPI_SUM,world); + if (update->multireplica == 1) { + norm2 = norm2_global; + MPI_Allreduce(&norm2,&norm2_global,1,MPI_DOUBLE,MPI_SUM,universe->uworld); + } + MPI_Allreduce(&nlocal,&ntotal,1,MPI_INT,MPI_SUM,world); + if (update->multireplica == 1) { + nlocal = ntotal; + MPI_Allreduce(&nlocal,&ntotal,1,MPI_INT,MPI_SUM,universe->uworld); + } + + scaling = (maxepsrot * sqrt((double) ntotal / norm2_global)); + + if (scaling < 1.0) alpha = scaling; + else alpha = 1.0; + + return alpha; +} \ No newline at end of file diff --git a/src/SPIN/min_spin_oso_cg2.h b/src/SPIN/min_spin_oso_cg2.h new file mode 100644 index 0000000000..c96e82ca8e --- /dev/null +++ b/src/SPIN/min_spin_oso_cg2.h @@ -0,0 +1,68 @@ +/* -*- c++ -*- ---------------------------------------------------------- + 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. +------------------------------------------------------------------------- */ + +#ifdef MINIMIZE_CLASS + +MinimizeStyle(spin/oso_cg2, MinSpinOSO_CG2) + +#else + +#ifndef LMP_MIN_SPIN_OSO_CG2_H +#define LMP_MIN_SPIN_OSO_CG2_H + +#include "min.h" + +namespace LAMMPS_NS { + +class MinSpinOSO_CG2: public Min { + public: + MinSpinOSO_CG2(class LAMMPS *); + virtual ~MinSpinOSO_CG2(); + void init(); + void setup_style(); + int modify_param(int, char **); + void reset_vectors(); + int iterate(int); + private: + int ireplica,nreplica; // for neb + double *spvec; // variables for atomic dof, as 1d vector + double *fmvec; // variables for atomic dof, as 1d vector + double *g_cur; // current gradient vector + double *g_old; // gradient vector at previous step + double *p_s; // search direction vector + double **sp_copy; // copy of the spins + int local_iter; // for neb + int nlocal_max; // max value of nlocal (for size of lists) + + void advance_spins(); + void calc_gradient(); + void calc_search_direction(); + double maximum_rotation(double *); + void vm3(const double *, const double *, double *); + void rodrigues_rotation(const double *, double *); + int calc_and_make_step(double, double, int); + int awc(double, double, double, double); + void make_step(double, double *); + double max_torque(); + double der_e_cur; // current derivative along search dir. + double der_e_pr; // previous derivative along search dir. + int use_line_search; // use line search or not. + double maxepsrot; + + bigint last_negative; +}; + +} + +#endif +#endif