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min_hftn.cpp
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min_hftn.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.
------------------------------------------------------------------------- */
/* ----------------------------------------------------------------------
Author: Todd Plantenga (SNL)
Sources: "Numerical Optimization", Nocedal and Wright, 2nd Ed, p170
"Parallel Unconstrained Min", Plantenga, SAND98-8201
------------------------------------------------------------------------- */
#include <math.h>
#include <string.h>
#include "atom.h"
#include "fix_minimize.h"
#include "min_hftn.h"
#include "modify.h"
#include "output.h"
#include "pair.h"
#include "update.h"
#include "timer.h"
using namespace LAMMPS_NS;
/* ----------------------------------------------------------------------
* This class performs Hessian-free truncated Newton minimization on an
* unconstrained molecular potential. The algorithm avoids computing the
* Hessian matrix, but obtains a near-quadratic rate of convergence.
------------------------------------------------------------------------- */
/* ----------------------------------------------------------------------
File local data
------------------------------------------------------------------------- */
//---- CONSTANTS MAP TO stopstrings DECLARED IN Min.run (min.cpp).
static const int STOP_MAX_ITER = 0; //-- MAX ITERATIONS EXCEEDED
static const int STOP_MAX_FORCE_EVALS = 1; //-- MAX FORCE EVALUATIONS EXCEEDED
static const int STOP_ENERGY_TOL = 2; //-- STEP DID NOT CHANGE ENERGY
static const int STOP_FORCE_TOL = 3; //-- CONVERGED TO DESIRED FORCE TOL
static const int STOP_TR_TOO_SMALL = 8; //-- TRUST REGION TOO SMALL
static const int STOP_ERROR = 9; //-- INTERNAL ERROR
static const int NO_CGSTEP_BECAUSE_F_TOL_SATISFIED = 0;
static const int CGSTEP_NEWTON = 1;
static const int CGSTEP_TO_TR = 2;
static const int CGSTEP_TO_DMAX = 3;
static const int CGSTEP_NEGATIVE_CURVATURE = 4;
static const int CGSTEP_MAX_INNER_ITERS = 5;
static const int CGSTEP_UNDETERMINED = 6;
//---- WHEN TESTING ENERGY_TOL, THE ENERGY MAGNITUDE MUST BE AT LEAST THIS BIG.
static const double MIN_ETOL_MAG = 1.0e-8;
//---- MACHINE PRECISION IS SOMETIMES DEFINED BY THE C RUNTIME.
#ifdef DBL_EPSILON
#define MACHINE_EPS DBL_EPSILON
#else
#define MACHINE_EPS 2.220446049250313e-16
#endif
/* ----------------------------------------------------------------------
Constructor
------------------------------------------------------------------------- */
MinHFTN::MinHFTN(LAMMPS *lmp) : Min(lmp)
{
searchflag = 1;
for (int i = 1; i < NUM_HFTN_ATOM_BASED_VECTORS; i++)
_daExtraGlobal[i] = NULL;
for (int i = 0; i < NUM_HFTN_ATOM_BASED_VECTORS; i++)
_daExtraAtom[i] = NULL;
_fpPrint = NULL;
return;
}
/* ----------------------------------------------------------------------
Destructor
------------------------------------------------------------------------- */
MinHFTN::~MinHFTN (void)
{
for (int i = 1; i < NUM_HFTN_ATOM_BASED_VECTORS; i++)
if (_daExtraGlobal[i] != NULL)
delete [] _daExtraGlobal[i];
for (int i = 0; i < NUM_HFTN_ATOM_BASED_VECTORS; i++)
if (_daExtraAtom[i] != NULL)
delete [] _daExtraAtom[i];
return;
}
/* ----------------------------------------------------------------------
Public method init
------------------------------------------------------------------------- */
void MinHFTN::init()
{
Min::init();
for (int i = 1; i < NUM_HFTN_ATOM_BASED_VECTORS; i++) {
if (_daExtraGlobal[i] != NULL)
delete [] _daExtraGlobal[i];
_daExtraGlobal[i] = NULL;
}
for (int i = 0; i < NUM_HFTN_ATOM_BASED_VECTORS; i++) {
if (_daExtraAtom[i] != NULL)
delete [] _daExtraAtom[i];
_daExtraAtom[i] = NULL;
}
return;
}
/* ----------------------------------------------------------------------
Public method setup_style
------------------------------------------------------------------------- */
void MinHFTN::setup_style()
{
//---- ALLOCATE MEMORY FOR ATOMIC DEGREES OF FREEDOM.
for (int i = 0; i < NUM_HFTN_ATOM_BASED_VECTORS; i++)
fix_minimize->add_vector(3);
//---- ALLOCATE MEMORY FOR EXTRA GLOBAL DEGREES OF FREEDOM.
//---- THE FIX MODULE TAKES CARE OF THE FIRST VECTOR, X0 (XK).
if (nextra_global) {
for (int i = 1; i < NUM_HFTN_ATOM_BASED_VECTORS; i++)
_daExtraGlobal[i] = new double[nextra_global];
}
//---- ALLOCATE MEMORY FOR EXTRA PER-ATOM DEGREES OF FREEDOM.
if (nextra_atom) {
for (int i = 0; i < NUM_HFTN_ATOM_BASED_VECTORS; i++)
_daExtraAtom[i] = new double*[nextra_atom];
for (int m = 0; m < nextra_atom; m++) {
for (int i = 0; i < NUM_HFTN_ATOM_BASED_VECTORS; i++)
fix_minimize->add_vector (extra_peratom[m]);
}
}
return;
}
/* ----------------------------------------------------------------------
Public method reset_vectors
After an energy/force calculation, atoms may migrate from one processor
to another. Any local vector correlated with atom positions or forces
must also be migrated. This is accomplished by a subclass of Fix.
This method updates local pointers to the latest Fix copies.
------------------------------------------------------------------------- */
void MinHFTN::reset_vectors()
{
nvec = 3 * atom->nlocal;
//---- ATOMIC DEGREES OF FREEDOM.
if (nvec > 0) {
xvec = atom->x[0];
fvec = atom->f[0];
}
for (int i = 0; i < NUM_HFTN_ATOM_BASED_VECTORS; i++)
_daAVectors[i] = fix_minimize->request_vector (i);
//---- EXTRA PER-ATOM DEGREES OF FREEDOM.
if (nextra_atom) {
int n = NUM_HFTN_ATOM_BASED_VECTORS;
for (int m = 0; m < nextra_atom; m++) {
extra_nlen[m] = extra_peratom[m] * atom->nlocal;
requestor[m]->min_xf_pointers(m,&xextra_atom[m],&fextra_atom[m]);
for (int i = 0; i < NUM_HFTN_ATOM_BASED_VECTORS; i++)
_daExtraAtom[i][m] = fix_minimize->request_vector (n++);
}
}
return;
}
/* ----------------------------------------------------------------------
Public method iterate
Upon entry, Min::setup() and Min::run have executed, and energy has
already been evaluated at the initial point. Return an integer code
that maps to a stop condition in min.cpp.
------------------------------------------------------------------------- */
int MinHFTN::iterate(int)
{
//---- TURN THIS ON TO GENERATE AN OPTIMIZATION PROGRESS FILE.
bool bPrintProgress = false;
if (bPrintProgress)
open_hftn_print_file_();
double dFinalEnergy = 0.0;
double dFinalFnorm2 = 0.0;
modify->min_clearstore();
int nStopCode = execute_hftn_ (bPrintProgress,
einitial,
fnorm2_init,
dFinalEnergy,
dFinalFnorm2);
modify->min_clearstore();
if (bPrintProgress)
close_hftn_print_file_();
return( nStopCode );
}
/* ----------------------------------------------------------------------
Private method execute_hftn_
@param[in] bPrintProgress - if true then print progress to a file
@param[in] dInitialEnergy - energy at input x
@param[in] dInitialForce2 - |F|_2 at input x
@param[out] dFinalEnergy - energy at output x
@param[out] dFinalForce2 - |F|_2 at output x
Return stop code described in the enumeration at the top of this file,
and the following:
atom->x - positions at output x
atom->f - forces evaluated at output x
------------------------------------------------------------------------- */
int MinHFTN::execute_hftn_(const bool bPrintProgress,
const double dInitialEnergy,
const double dInitialForce2,
double & dFinalEnergy,
double & dFinalForce2)
{
//---- DEFINE OUTPUTS PRINTED BY "Finish".
eprevious = dInitialEnergy;
alpha_final = 0.0;
dFinalEnergy = dInitialEnergy;
dFinalForce2 = dInitialForce2;
if (dInitialForce2 < update->ftol)
return( STOP_FORCE_TOL );
//---- SAVE ATOM POSITIONS BEFORE AN ITERATION.
fix_minimize->store_box();
for (int i = 0; i < nvec; i++)
_daAVectors[VEC_XK][i] = xvec[i];
if (nextra_atom) {
for (int m = 0; m < nextra_atom; m++) {
double * xatom = xextra_atom[m];
double * xkAtom = _daExtraAtom[VEC_XK][m];
int n = extra_nlen[m];
for (int i = 0; i < n; i++)
xkAtom[i] = xatom[i];
}
}
if (nextra_global)
modify->min_store();
double dXInf = calc_xinf_using_mpi_();
//---- FIND THE NUMBER OF UNKNOWNS.
int nLocalNumUnknowns = nvec + nextra_atom;
MPI_Allreduce (&nLocalNumUnknowns, &_nNumUnknowns,
1, MPI_INT, MPI_SUM, world);
//---- INITIALIZE THE TRUST RADIUS BASED ON THE GRADIENT.
double dTrustRadius = 1.5 * dInitialForce2;
//---- TRUST RADIUS MUST KEEP STEPS FROM LETTING ATOMS MOVE SO FAR THEY
//---- VIOLATE PHYSICS OR JUMP BEYOND A PARALLEL PROCESSING DOMAIN.
//---- LINE SEARCH METHODS DO THIS BY RESTRICTING THE LARGEST CHANGE
//---- OF ANY ATOM'S COMPONENT TO dmax. AN EXACT CHECK IS MADE LATER,
//---- BUT THIS GUIDES DETERMINATION OF A MAX TRUST RADIUS.
double dMaxTrustRadius = dmax * sqrt((double) _nNumUnknowns);
dTrustRadius = MIN (dTrustRadius, dMaxTrustRadius);
double dLastNewtonStep2 = dMaxTrustRadius;
if (bPrintProgress)
hftn_print_line_ (false, -1, neval, dInitialEnergy, dInitialForce2,
-1, dTrustRadius, 0.0, 0.0, 0.0);
bool bHaveEvaluatedAtX = true;
double dCurrentEnergy = dInitialEnergy;
double dCurrentForce2 = dInitialForce2;
for (niter = 0; niter < update->nsteps; niter++) {
(update->ntimestep)++;
//---- CALL THE INNER LOOP TO GET THE NEXT TRUST REGION STEP.
double dCgForce2StopTol = MIN ((dCurrentForce2 / 2.0), 0.1 / (niter+1));
dCgForce2StopTol = MAX (dCgForce2StopTol, update->ftol);
double dNewEnergy;
double dNewForce2;
int nStepType;
double dStepLength2;
double dStepLengthInf;
if (compute_inner_cg_step_ (dTrustRadius,
dCgForce2StopTol,
update->max_eval,
bHaveEvaluatedAtX,
dCurrentEnergy, dCurrentForce2,
dNewEnergy, dNewForce2,
nStepType,
dStepLength2, dStepLengthInf) == false) {
//---- THERE WAS AN ERROR. RESTORE TO LAST ACCEPTED STEP.
if (nextra_global)
modify->min_step (0.0, _daExtraGlobal[VEC_CG_P]);
for (int i = 0; i < nvec; i++)
xvec[i] = _daAVectors[VEC_XK][i];
if (nextra_atom) {
for (int m = 0; m < nextra_atom; m++) {
double * xatom = xextra_atom[m];
double * xkAtom = _daExtraAtom[VEC_XK][m];
int n = extra_nlen[m];
for (int i = 0; i < n; i++)
xatom[i] = xkAtom[i];
requestor[m]->min_x_set(m);
}
}
dFinalEnergy = energy_force (0);
neval++;
dFinalForce2 = sqrt (fnorm_sqr());
return( STOP_ERROR );
}
//---- STOP IF THE CURRENT POSITION WAS FOUND TO BE ALREADY GOOD ENOUGH.
//---- IN THIS CASE THE ENERGY AND FORCES ARE ALREADY COMPUTED.
if (nStepType == NO_CGSTEP_BECAUSE_F_TOL_SATISFIED) {
if (bPrintProgress)
hftn_print_line_ (true, niter+1, neval, dNewEnergy, dNewForce2,
nStepType, dTrustRadius, dStepLength2,
0.0, 0.0);
dFinalEnergy = dNewEnergy;
dFinalForce2 = dNewForce2;
return( STOP_FORCE_TOL );
}
//---- COMPUTE THE DIRECTIONAL DERIVATIVE H(x_k) p.
bool bUseForwardDiffs = (dCurrentForce2 > 1000.0 * sqrt (MACHINE_EPS));
evaluate_dir_der_ (bUseForwardDiffs,
VEC_CG_P,
VEC_CG_HD,
true,
dCurrentEnergy);
//---- COMPUTE p^T grad(x_k) AND SAVE IT FOR PRED.
double dGradDotP = calc_grad_dot_v_using_mpi_ (VEC_CG_P);
//---- MOVE TO THE NEW POINT AND EVALUATE ENERGY AND FORCES.
//---- THIS IS THE PLACE WHERE energy_force IS ALLOWED TO RESET.
for (int i = 0; i < nvec; i++)
xvec[i] = _daAVectors[VEC_XK][i] + _daAVectors[VEC_CG_P][i];
if (nextra_atom) {
for (int m = 0; m < nextra_atom; m++) {
double * xatom = xextra_atom[m];
double * xkAtom = _daExtraAtom[VEC_XK][m];
double * pAtom = _daExtraAtom[VEC_CG_P][m];
int n = extra_nlen[m];
for (int i = 0; i < n; i++)
xatom[i] = xkAtom[i] + pAtom[i];
requestor[m]->min_x_set(m);
}
}
if (nextra_global)
modify->min_step (1.0, _daExtraGlobal[VEC_CG_P]);
dNewEnergy = energy_force (1);
neval++;
dNewForce2 = sqrt (fnorm_sqr());
double dAred = dCurrentEnergy - dNewEnergy;
//---- STOP IF THE FORCE TOLERANCE IS MET.
if (dNewForce2 < update->ftol) {
if (bPrintProgress)
hftn_print_line_ (true, niter+1, neval, dNewEnergy, dNewForce2,
nStepType, dTrustRadius, dStepLength2,
dAred, -1.0);
//---- (IMPLICITLY ACCEPT THE LAST STEP TO THE NEW POINT.)
dFinalEnergy = dNewEnergy;
dFinalForce2 = dNewForce2;
return( STOP_FORCE_TOL );
}
//---- STOP IF THE ACTUAL ENERGY REDUCTION IS TINY.
if (nStepType != CGSTEP_TO_DMAX) {
double dMag = 0.5 * (fabs (dCurrentEnergy) + fabs (dNewEnergy));
dMag = MAX (dMag, MIN_ETOL_MAG);
if ( (fabs (dAred) < (update->etol * dMag))
|| (dStepLengthInf == 0.0) ) {
if (bPrintProgress)
hftn_print_line_ (true, niter+1, neval,
dNewEnergy, dNewForce2,
nStepType, dTrustRadius, dStepLength2,
dAred, -1.0);
//---- (IMPLICITLY ACCEPT THE LAST STEP TO THE NEW POINT.)
dFinalEnergy = dNewEnergy;
dFinalForce2 = dNewForce2;
return( STOP_ENERGY_TOL );
}
}
//---- COMPUTE THE PREDICTED REDUCTION - p^T grad - 0.5 p^T Hp
double dPHP = calc_dot_prod_using_mpi_ (VEC_CG_P, VEC_CG_HD);
double dPred = - dGradDotP - (0.5 * dPHP);
//---- ACCEPT OR REJECT THE STEP PROPOSED BY THE INNER CG LOOP.
//---- WHEN NEAR A SOLUTION, THE FORCE NORM IS PROBABLY MORE ACCURATE,
//---- SO DON'T ACCEPT A STEP THAT REDUCES ENERGY SOME TINY AMOUNT
//---- WHILE INCREASING THE FORCE NORM.
bool bStepAccepted = (dAred > 0.0)
&& ( (dNewForce2 < dCurrentForce2)
|| (dCurrentForce2 > 1.0e-6));
if (bStepAccepted) {
//---- THE STEP IS ACCEPTED.
if (bPrintProgress)
hftn_print_line_ (true, niter+1, neval, dNewEnergy, dNewForce2,
nStepType, dTrustRadius, dStepLength2,
dAred, dPred);
fix_minimize->store_box();
modify->min_clearstore();
for (int i = 0; i < nvec; i++)
_daAVectors[VEC_XK][i] = xvec[i];
if (nextra_atom) {
for (int m = 0; m < nextra_atom; m++) {
double * xatom = xextra_atom[m];
double * xkAtom = _daExtraAtom[VEC_XK][m];
int n = extra_nlen[m];
for (int i = 0; i < n; i++)
xkAtom[i] = xatom[i];
}
}
if (nextra_global)
modify->min_store();
if (niter > 0)
eprevious = dCurrentEnergy;
dCurrentEnergy = dNewEnergy;
dCurrentForce2 = dNewForce2;
bHaveEvaluatedAtX = true;
if (nStepType == CGSTEP_NEWTON)
dLastNewtonStep2 = dStepLength2;
//---- UPDATE THE TRUST REGION BASED ON AGREEMENT BETWEEN
//---- THE ACTUAL REDUCTION AND THE PREDICTED MODEL REDUCTION.
if ((dAred > 0.75 * dPred) && (dStepLength2 >= 0.99 * dTrustRadius))
dTrustRadius = 2.0 * dTrustRadius;
dTrustRadius = MIN (dTrustRadius, dMaxTrustRadius);
//---- DMAX VIOLATIONS TRUNCATE THE CG STEP WITHOUT COMPARISONS;
//---- BETTER TO ADJUST THE TRUST REGION SO DMAX STOPS HAPPENING.
if (nStepType == CGSTEP_TO_DMAX) {
if (dStepLength2 <= MACHINE_EPS)
dTrustRadius = 0.1 * dTrustRadius;
else
dTrustRadius = MIN (dTrustRadius, 2.0 * dStepLength2);
}
}
else {
//---- THE STEP IS REJECTED.
if (bPrintProgress)
hftn_print_line_ (false, niter+1, neval,
dCurrentEnergy, dCurrentForce2,
nStepType, dTrustRadius, dStepLength2,
dAred, dPred);
//---- RESTORE THE LAST X_K POSITION.
if (nextra_global)
modify->min_step (0.0, _daExtraGlobal[VEC_CG_P]);
for (int i = 0; i < nvec; i++)
xvec[i] = _daAVectors[VEC_XK][i];
if (nextra_atom) {
for (int m = 0; m < nextra_atom; m++) {
double * xatom = xextra_atom[m];
double * xkAtom = _daExtraAtom[VEC_XK][m];
int n = extra_nlen[m];
for (int i = 0; i < n; i++)
xatom[i] = xkAtom[i];
requestor[m]->min_x_set(m);
}
}
modify->min_clearstore();
bHaveEvaluatedAtX = false;
//---- UPDATE THE TRUST REGION.
//---- EXPERIMENTS INDICATE NEGATIVE CURVATURE CAN TAKE A BAD
//---- STEP A LONG WAY, SO BE MORE AGGRESSIVE IN THIS CASE.
//---- ALSO, IF NEAR A SOLUTION AND DONE WITH NEWTON STEPS,
//---- THEN REDUCE TO SOMETHING NEAR THE LAST GOOD NEWTON STEP.
if ((nStepType == CGSTEP_NEGATIVE_CURVATURE) && (-dAred > dPred))
dTrustRadius = 0.10 * MIN (dTrustRadius, dStepLength2);
else if ( (nStepType == CGSTEP_TO_DMAX)
&& (dStepLength2 <= MACHINE_EPS))
dTrustRadius = 0.10 * dTrustRadius;
else if (-dAred > dPred)
dTrustRadius = 0.20 * MIN (dTrustRadius, dStepLength2);
else
dTrustRadius = 0.25 * MIN (dTrustRadius, dStepLength2);
if ( (nStepType != CGSTEP_NEWTON)
&& (dCurrentForce2 < sqrt (MACHINE_EPS)))
dTrustRadius = MIN (dTrustRadius, 2.0 * dLastNewtonStep2);
dLastNewtonStep2 = dMaxTrustRadius;
//---- STOP IF THE TRUST RADIUS IS TOO SMALL TO CONTINUE.
if ( (dTrustRadius <= 0.0)
|| (dTrustRadius <= MACHINE_EPS * MAX (1.0, dXInf))) {
dFinalEnergy = dCurrentEnergy;
dFinalForce2 = dCurrentForce2;
return( STOP_TR_TOO_SMALL );
}
}
//---- OUTPUT FOR thermo, dump, restart FILES.
if (output->next == update->ntimestep) {
//---- IF THE LAST STEP WAS REJECTED, THEN REEVALUATE ENERGY AND
//---- FORCES AT THE OLD POINT SO THE OUTPUT DOES NOT DISPLAY
//---- THE INCREASED ENERGY OF THE REJECTED STEP.
if (bStepAccepted == false) {
dCurrentEnergy = energy_force (1);
neval++;
}
timer->stamp();
output->write (update->ntimestep);
timer->stamp (Timer::OUTPUT);
}
//---- RETURN IF NUMBER OF EVALUATIONS EXCEEDED.
if (neval >= update->max_eval) {
dFinalEnergy = dCurrentEnergy;
dFinalForce2 = dCurrentForce2;
return( STOP_MAX_FORCE_EVALS );
}
} //-- END for LOOP OVER niter
dFinalEnergy = dCurrentEnergy;
dFinalForce2 = dCurrentForce2;
return( STOP_MAX_ITER );
}
/* ----------------------------------------------------------------------
Private method compute_inner_cg_step_
Execute CG using Hessian-vector products approximated by finite difference
directional derivatives.
On input these must be defined:
atom->x - positions at x
atom->f - ignored
VEC_XK - positions at x
On output these are defined:
atom->x - unchanged
atom->f - forces evaluated at x, but only if nStepType == NO_CGSTEP
VEC_XK - unchanged
VEC_CG_P - step from VEC_XK to new positions
During processing these are modified:
VEC_CG_D - conjugate gradient inner loop step
VEC_CG_HD - Hessian-vector product
VEC_CG_R - residual of inner loop step
VEC_DIF1 - temp storage
VEC_DIF2 - temp storage
@param[in] dTrustRadius - trust region radius for this subiteration
@param[in] dForceTol - stop tolerance on |F|_2 for this subiteration
@param[in] nMaxEvals - total energy/force evaluations allowed
@param[in] bHaveEvalAtXin - true if forces are valid at input x
@param[in] dEnergyAtXin - energy at input x, if bHaveEvalAtXin is true
@param[in] dForce2AtXin - |F|_2 at input x, if bHaveEvalAtXin is true
@param[out] dEnergyAtXout - energy at output x, if NO_CGSTEP (see below)
@param[out] dForce2AtXout - |F|_2 at output x, if NO_CGSTEP (see below)
@param[out] nStepType - step type for hftn_print_line_()
@param[out] dStepLength2 - |step|_2
@param[out] dStepLengthInf - |step|_inf
Return false if there was a fatal error.
If nStepType equals NO_CGSTEP_BECAUSE_F_TOL_SATISFIED, then the energy
and forces are evaluated and returned in dEnergyAtXout, dForce2AtXout;
else energy and forces are not evaluated.
------------------------------------------------------------------------- */
bool MinHFTN::compute_inner_cg_step_(const double dTrustRadius,
const double dForceTol,
const int nMaxEvals,
const bool bHaveEvalAtXin,
const double dEnergyAtXin,
const double dForce2AtXin,
double & dEnergyAtXout,
double & dForce2AtXout,
int & nStepType,
double & dStepLength2,
double & dStepLengthInf)
{
//---- SET p_0 = 0.
if (nextra_global) {
for (int i = 0; i < nextra_global; i++)
_daExtraGlobal[VEC_CG_P][i] = 0.0;
}
for (int i = 0; i < nvec; i++)
_daAVectors[VEC_CG_P][i] = 0.0;
if (nextra_atom) {
for (int m = 0; m < nextra_atom; m++) {
double * pAtom = _daExtraAtom[VEC_CG_P][m];
int n = extra_nlen[m];
for (int i = 0; i < n; i++)
pAtom[i] = 0.0;
}
}
double dPP = 0.0;
//---- OBTAIN THE ENERGY AND FORCES AT THE INPUT POSITION.
double dEnergyAtX = dEnergyAtXin;
double dForce2AtX = dForce2AtXin;
if (bHaveEvalAtXin == false) {
dEnergyAtX = energy_force (0);
neval++;
dForce2AtX = sqrt (fnorm_sqr());
}
//---- RETURN IMMEDIATELY IF THE FORCE TOLERANCE IS ALREADY MET.
//---- THE STEP TYPE INFORMS THE CALLER THAT ENERGY AND FORCES HAVE
//---- BEEN EVALUATED.
if (dForce2AtX <= dForceTol) {
dEnergyAtXout = dEnergyAtX;
dForce2AtXout = dForce2AtX;
nStepType = NO_CGSTEP_BECAUSE_F_TOL_SATISFIED;
dStepLength2 = 0.0;
dStepLengthInf = 0.0;
return( true );
}
//---- r_0 = -grad (FIRST SEARCH DIRECTION IS STEEPEST DESCENT)
//---- d_0 = r_0
//---- REMEMBER THAT FORCES = -GRADIENT.
if (nextra_global) {
for (int i = 0; i < nextra_global; i++) {
_daExtraGlobal[VEC_CG_R][i] = fextra[i];
_daExtraGlobal[VEC_CG_D][i] = fextra[i];
}
}
for (int i = 0; i < nvec; i++) {
_daAVectors[VEC_CG_R][i] = fvec[i];
_daAVectors[VEC_CG_D][i] = fvec[i];
}
if (nextra_atom) {
for (int m = 0; m < nextra_atom; m++) {
double * fatom = fextra_atom[m];
double * rAtom = _daExtraAtom[VEC_CG_R][m];
double * dAtom = _daExtraAtom[VEC_CG_D][m];
int n = extra_nlen[m];
for (int i = 0; i < n; i++) {
rAtom[i] = fatom[i];
dAtom[i] = fatom[i];
}
}
}
double dRR = dForce2AtX * dForce2AtX;
double dR0norm2 = sqrt (dRR);
//---- LIMIT THE NUMBER OF INNER CG ITERATIONS.
//---- BASE IT ON THE NUMBER OF UNKNOWNS, OR MAXIMUM EVALUATIONS ASSUMING
//---- FORWARD DIFFERENCES ARE USED.
//---- NOTE THAT SETTING MAX=1 GIVES STEEPEST DESCENT.
int nLimit1 = _nNumUnknowns / 5;
if (nLimit1 < 100)
nLimit1 = MIN (_nNumUnknowns, 100);
int nLimit2 = (nMaxEvals - neval) / 2;
int nMaxInnerIters = MIN (nLimit1, nLimit2);
//---- FURTHER LIMIT ITERATIONS IF NEAR MACHINE ROUNDOFF.
//---- THE METHOD CAN WASTE A LOT EVALUATIONS WITH LITTLE PAYOFF PROSPECT.
if (dForce2AtX < (sqrt (MACHINE_EPS) * MAX (1.0, fabs (dEnergyAtX))) )
nMaxInnerIters = MIN (nMaxInnerIters, _nNumUnknowns / 20);
bool bUseForwardDiffs = (dForce2AtX > 1000.0 * sqrt (MACHINE_EPS));
//---- MAIN CG LOOP.
for (int nInnerIter = 0; nInnerIter < nMaxInnerIters; nInnerIter++) {
//---- COMPUTE HESSIAN-VECTOR PRODUCT: H(x_k) d_i.
double dDummyEnergy;
evaluate_dir_der_ (bUseForwardDiffs,
VEC_CG_D,
VEC_CG_HD,
false,
dDummyEnergy);
//---- CALCULATE d_i^T H d_i AND d_i^T d_i.
double dDHD;
double dDD;
calc_dhd_dd_using_mpi_ (dDHD, dDD);
//---- HANDLE NEGATIVE CURVATURE.
if (dDHD <= (MACHINE_EPS * dDD)) {
//---- PROJECT BOTH DIRECTIONS TO THE TRUST RADIUS AND DECIDE
//---- WHICH MAKES A BETTER PREDICTED REDUCTION.
//---- p_i^T H(x_k) d_i AND grad_i^T d_i.
double dPdotD = calc_dot_prod_using_mpi_ (VEC_CG_P, VEC_CG_D);
double dPdotHD = calc_dot_prod_using_mpi_ (VEC_CG_P, VEC_CG_HD);
//---- MOVE TO X_K AND COMPUTE ENERGY AND FORCES.
if (nextra_global)
modify->min_step (0.0, _daExtraGlobal[VEC_CG_P]);
for (int i = 0; i < nvec; i++)
xvec[i] = _daAVectors[VEC_XK][i];
if (nextra_atom) {
for (int m = 0; m < nextra_atom; m++) {
double * xatom = xextra_atom[m];
double * xkAtom = _daExtraAtom[VEC_XK][m];
int n = extra_nlen[m];
for (int i = 0; i < n; i++)
xatom[i] = xkAtom[i];
requestor[m]->min_x_set(m);
}
}
dEnergyAtX = energy_force (0);
neval++;
double dGradDotD = calc_grad_dot_v_using_mpi_ (VEC_CG_D);
double tau = compute_to_tr_ (dPP, dPdotD, dDD, dTrustRadius,
true, dDHD, dPdotHD, dGradDotD);
//---- MOVE THE POINT.
if (nextra_global) {
double * pGlobal = _daExtraGlobal[VEC_CG_P];
double * dGlobal = _daExtraGlobal[VEC_CG_D];
for (int i = 0; i < nextra_global; i++) {
pGlobal[i] += tau * dGlobal[i];
}
}
for (int i = 0; i < nvec; i++)
_daAVectors[VEC_CG_P][i] += tau * _daAVectors[VEC_CG_D][i];
if (nextra_atom) {
for (int m = 0; m < nextra_atom; m++) {
double * pAtom = _daExtraAtom[VEC_CG_P][m];
double * dAtom = _daExtraAtom[VEC_CG_D][m];
int n = extra_nlen[m];
for (int i = 0; i < n; i++)
pAtom[i] += tau * dAtom[i];
}
}
nStepType = CGSTEP_NEGATIVE_CURVATURE;
calc_plengths_using_mpi_ (dStepLength2, dStepLengthInf);
return( true );
}
//---- COMPUTE THE OPTIMAL STEP LENGTH BASED ON THE QUADRATIC CG MODEL.
double dAlpha = dRR / dDHD;
//---- MIGHT WANT TO ENABLE THIS TO DEBUG INTERNAL CG STEPS.
//fprintf (_fpPrint, " alpha = %11.8f neval=%4d\n", dAlpha, neval);
//---- p_i+1 = p_i + alpha_i d_i
//---- (SAVE THE CURRENT p_i IN CASE THE STEP HAS TO BE SHORTENED.)
if (nextra_global) {
double * pGlobal = _daExtraGlobal[VEC_CG_P];
double * dGlobal = _daExtraGlobal[VEC_CG_D];
double * d1Global = _daExtraGlobal[VEC_DIF1];
for (int i = 0; i < nextra_global; i++) {
d1Global[i] = pGlobal[i];
pGlobal[i] += dAlpha * dGlobal[i];
}
}
for (int i = 0; i < nvec; i++) {
_daAVectors[VEC_DIF1][i] = _daAVectors[VEC_CG_P][i];
_daAVectors[VEC_CG_P][i] += dAlpha * _daAVectors[VEC_CG_D][i];
}
if (nextra_atom) {
for (int m = 0; m < nextra_atom; m++) {
double * pAtom = _daExtraAtom[VEC_CG_P][m];
double * dAtom = _daExtraAtom[VEC_CG_D][m];
double * d1Atom = _daExtraAtom[VEC_DIF1][m];
int n = extra_nlen[m];
for (int i = 0; i < n; i++) {
d1Atom[i] = pAtom[i];
pAtom[i] += dAlpha * dAtom[i];
}
}
}
//---- COMPUTE VECTOR PRODUCTS p_i+1^T p_i+1 AND p_i^T d_i.
double dPnewDotPnew;
double dPoldDotD;
calc_ppnew_pdold_using_mpi_ (dPnewDotPnew, dPoldDotD);
nStepType = CGSTEP_UNDETERMINED;
//---- IF STEP LENGTH IS TOO LARGE, THEN REDUCE IT AND RETURN.
double tau;
if (step_exceeds_TR_ (dTrustRadius, dPP, dPoldDotD, dDD, tau)) {
adjust_step_to_tau_ (tau);
nStepType = CGSTEP_TO_TR;
}
if (step_exceeds_DMAX_()) {
adjust_step_to_tau_ (0.0);
nStepType = CGSTEP_TO_DMAX;
}
if ((nStepType == CGSTEP_TO_TR) || (nStepType == CGSTEP_TO_DMAX)) {
calc_plengths_using_mpi_ (dStepLength2, dStepLengthInf);
return( true );
}
dStepLength2 = sqrt (dPnewDotPnew);
//---- r_i+1 = r_i - alpha * H d_i
if (nextra_global) {
double * rGlobal = _daExtraGlobal[VEC_CG_R];
double * hdGlobal = _daExtraGlobal[VEC_CG_HD];
for (int i = 0; i < nextra_global; i++)
rGlobal[i] -= dAlpha * hdGlobal[i];
}
for (int i = 0; i < nvec; i++)
_daAVectors[VEC_CG_R][i] -= dAlpha * _daAVectors[VEC_CG_HD][i];
if (nextra_atom) {
for (int m = 0; m < nextra_atom; m++) {
double * rAtom = _daExtraAtom[VEC_CG_R][m];
double * hdAtom = _daExtraAtom[VEC_CG_HD][m];
int n = extra_nlen[m];
for (int i = 0; i < n; i++)
rAtom[i] -= dAlpha * hdAtom[i];
}
}
double dRnewDotRnew = calc_dot_prod_using_mpi_ (VEC_CG_R, VEC_CG_R);
//---- IF RESIDUAL IS SMALL ENOUGH, THEN RETURN THE CURRENT STEP.
if (sqrt (dRnewDotRnew) < dForceTol * dR0norm2) {
nStepType = CGSTEP_NEWTON;
calc_plengths_using_mpi_ (dStepLength2, dStepLengthInf);
return( true );
}
//---- beta = r_i+1^T r_i+1 / r_i^T r_i
//---- d_i+1 = r_i+1 + beta d_i
double dBeta = dRnewDotRnew / dRR;
if (nextra_global) {
double * rGlobal = _daExtraGlobal[VEC_CG_R];
double * dGlobal = _daExtraGlobal[VEC_CG_D];
for (int i = 0; i < nextra_global; i++)
dGlobal[i] = rGlobal[i] + dBeta * dGlobal[i];
}
for (int i = 0; i < nvec; i++)
_daAVectors[VEC_CG_D][i] = _daAVectors[VEC_CG_R][i]
+ dBeta * _daAVectors[VEC_CG_D][i];
if (nextra_atom) {
for (int m = 0; m < nextra_atom; m++) {
double * rAtom = _daExtraAtom[VEC_CG_R][m];
double * dAtom = _daExtraAtom[VEC_CG_D][m];
int n = extra_nlen[m];
for (int i = 0; i < n; i++)
dAtom[i] = rAtom[i] + dBeta * dAtom[i];
}
}
//---- CONTINUE THE LOOP.
dRR = dRnewDotRnew;
dPP = dPnewDotPnew;
}
nStepType = CGSTEP_MAX_INNER_ITERS;
calc_plengths_using_mpi_ (dStepLength2, dStepLengthInf);
return( true );
}
/* ----------------------------------------------------------------------
Private method calc_xinf_using_mpi_
------------------------------------------------------------------------- */
double MinHFTN::calc_xinf_using_mpi_(void) const
{
double dXInfLocal = 0.0;
for (int i = 0; i < nvec; i++)
dXInfLocal = MAX(dXInfLocal,fabs(xvec[i]));
double dXInf;
MPI_Allreduce (&dXInfLocal, &dXInf, 1, MPI_DOUBLE, MPI_MAX, world);
if (nextra_atom) {
for (int m = 0; m < nextra_atom; m++) {
double * xatom = xextra_atom[m];
int n = extra_nlen[m];
double dXInfLocalExtra = 0.0;
for (int i = 0; i < n; i++)
dXInfLocalExtra = MAX (dXInfLocalExtra, fabs (xatom[i]));
double dXInfExtra;
MPI_Allreduce (&dXInfLocalExtra, &dXInfExtra,
1, MPI_DOUBLE, MPI_MAX, world);
dXInf = MAX (dXInf, dXInfExtra);
}
}
return( dXInf );
}
/* ----------------------------------------------------------------------
Private method calc_dot_prod_using_mpi_
------------------------------------------------------------------------- */
double MinHFTN::calc_dot_prod_using_mpi_(const int nIx1,
const int nIx2) const
{
double dDotLocal = 0.0;
for (int i = 0; i < nvec; i++)
dDotLocal += _daAVectors[nIx1][i] * _daAVectors[nIx2][i];
if (nextra_atom) {
for (int m = 0; m < nextra_atom; m++) {
double * i1Atom = _daExtraAtom[nIx1][m];
double * i2Atom = _daExtraAtom[nIx2][m];
int n = extra_nlen[m];
for (int i = 0; i < n; i++)
dDotLocal += i1Atom[i] * i2Atom[i];
}
}
double dDot;
MPI_Allreduce (&dDotLocal, &dDot, 1, MPI_DOUBLE, MPI_SUM, world);
if (nextra_global) {
for (int i = 0; i < nextra_global; i++) {
double * i1Global = _daExtraGlobal[nIx1];
double * i2Global = _daExtraGlobal[nIx2];
dDot += i1Global[i] * i2Global[i];
}
}
return( dDot );
}
/* ----------------------------------------------------------------------
Private method calc_grad_dot_v_using_mpi_
------------------------------------------------------------------------- */
double MinHFTN::calc_grad_dot_v_using_mpi_(const int nIx) const
{
//---- ASSUME THAT FORCES HAVE BEEN EVALUATED AT DESIRED ATOM POSITIONS.
//---- REMEMBER THAT FORCES = -GRADIENT.
double dGradDotVLocal = 0.0;
for (int i = 0; i < nvec; i++)
dGradDotVLocal += - _daAVectors[nIx][i] * fvec[i];
if (nextra_atom) {
for (int m = 0; m < nextra_atom; m++) {
double * fatom = fextra_atom[m];
double * iAtom = _daExtraAtom[nIx][m];
int n = extra_nlen[m];
for (int i = 0; i < n; i++)
dGradDotVLocal += - iAtom[i] * fatom[i];
}
}
double dGradDotV;
MPI_Allreduce (&dGradDotVLocal, &dGradDotV, 1, MPI_DOUBLE, MPI_SUM, world);
if (nextra_global) {
for (int i = 0; i < nextra_global; i++) {
double * iGlobal = _daExtraGlobal[nIx];
dGradDotV += - iGlobal[i] * fextra[i];
}
}
return( dGradDotV );
}
/* ----------------------------------------------------------------------
Private method calc_dhd_dd_using_mpi_
------------------------------------------------------------------------- */
void MinHFTN::calc_dhd_dd_using_mpi_(double & dDHD,
double & dDD) const
{
double dDHDLocal = 0.0;
double dDDLocal = 0.0;
for (int i = 0; i < nvec; i++) {
dDHDLocal += _daAVectors[VEC_CG_D][i] * _daAVectors[VEC_CG_HD][i];
dDDLocal += _daAVectors[VEC_CG_D][i] * _daAVectors[VEC_CG_D][i];
}
if (nextra_atom) {
for (int m = 0; m < nextra_atom; m++) {
double * dAtom = _daExtraAtom[VEC_CG_D][m];
double * hdAtom = _daExtraAtom[VEC_CG_HD][m];
int n = extra_nlen[m];
for (int i = 0; i < n; i++) {
dDHDLocal += dAtom[i] * hdAtom[i];
dDDLocal += dAtom[i] * dAtom[i];
}
}
}
double daDotsLocal[2];
daDotsLocal[0] = dDHDLocal;
daDotsLocal[1] = dDDLocal;
double daDots[2];
MPI_Allreduce (daDotsLocal, daDots, 2, MPI_DOUBLE, MPI_SUM, world);
if (nextra_global) {
double * dGlobal = _daExtraGlobal[VEC_CG_D];
double * hdGlobal = _daExtraGlobal[VEC_CG_HD];
for (int i = 0; i < nextra_global; i++) {
daDots[0] += dGlobal[i] * hdGlobal[i];
daDots[1] += dGlobal[i] * dGlobal[i];
}
}
dDHD = daDots[0];
dDD = daDots[1];
return;
}
/* ----------------------------------------------------------------------
Private method calc_ppnew_pdold_using_mpi_
------------------------------------------------------------------------- */
void MinHFTN::calc_ppnew_pdold_using_mpi_(double & dPnewDotPnew,
double & dPoldDotD) const
{
double dPnewDotPnewLocal = 0.0;
double dPoldDotDLocal = 0.0;
for (int i = 0; i < nvec; i++) {
dPnewDotPnewLocal
+= _daAVectors[VEC_CG_P][i] * _daAVectors[VEC_CG_P][i];
dPoldDotDLocal
+= _daAVectors[VEC_DIF1][i] * _daAVectors[VEC_CG_D][i];
}
if (nextra_atom) {
for (int m = 0; m < nextra_atom; m++) {
double * dAtom = _daExtraAtom[VEC_CG_D][m];
double * pAtom = _daExtraAtom[VEC_CG_P][m];
double * d1Atom = _daExtraAtom[VEC_DIF1][m];
int n = extra_nlen[m];
for (int i = 0; i < n; i++) {
dPnewDotPnewLocal += pAtom[i] * pAtom[i];
dPoldDotDLocal += d1Atom[i] * dAtom[i];
}
}
}
double daDotsLocal[2];
daDotsLocal[0] = dPnewDotPnewLocal;
daDotsLocal[1] = dPoldDotDLocal;
double daDots[2];
MPI_Allreduce (daDotsLocal, daDots, 2, MPI_DOUBLE, MPI_SUM, world);
if (nextra_global) {
for (int i = 0; i < nextra_global; i++) {
double * dGlobal = _daExtraGlobal[VEC_CG_D];
double * pGlobal = _daExtraGlobal[VEC_CG_P];
double * d1Global = _daExtraGlobal[VEC_DIF1];
daDots[0] += pGlobal[i] * pGlobal[i];
daDots[1] += d1Global[i] * dGlobal[i];
}
}
dPnewDotPnew = daDots[0];
dPoldDotD = daDots[1];
return;
}
/* ----------------------------------------------------------------------
Private method calc_plengths_using_mpi_
------------------------------------------------------------------------- */
void MinHFTN::calc_plengths_using_mpi_(double & dStepLength2,
double & dStepLengthInf) const
{
double dPPLocal = 0.0;
double dPInfLocal = 0.0;
for (int i = 0; i < nvec; i++) {
dPPLocal += _daAVectors[VEC_CG_P][i] * _daAVectors[VEC_CG_P][i];
dPInfLocal = MAX (dPInfLocal, fabs (_daAVectors[VEC_CG_P][i]));
}
if (nextra_atom) {
for (int m = 0; m < nextra_atom; m++) {
double * pAtom = _daExtraAtom[VEC_CG_P][m];
int n = extra_nlen[m];
for (int i = 0; i < n; i++) {
dPPLocal += pAtom[i] * pAtom[i];
dPInfLocal = MAX (dPInfLocal, fabs (pAtom[i]));
}
}
}
double dPP;
MPI_Allreduce (&dPPLocal, &dPP, 1, MPI_DOUBLE, MPI_SUM, world);
double dPInf;
MPI_Allreduce (&dPInfLocal, &dPInf, 1, MPI_DOUBLE, MPI_MAX, world);
if (nextra_global) {
for (int i = 0; i < nextra_global; i++) {
double * pGlobal = _daExtraGlobal[VEC_CG_P];
dPP += pGlobal[i] * pGlobal[i];
dPInf = MAX (dPInf, fabs (pGlobal[i]));
}
}
dStepLength2 = sqrt (dPP);
dStepLengthInf = dPInf;
return;
}
/* ----------------------------------------------------------------------
Private method step_exceeds_TR_
------------------------------------------------------------------------- */
bool MinHFTN::step_exceeds_TR_(const double dTrustRadius,
const double dPP,
const double dPD,
const double dDD,
double & dTau) const
{
double dPnewNorm2;
double dPnewNormInf;
calc_plengths_using_mpi_ (dPnewNorm2, dPnewNormInf);
if (dPnewNorm2 > dTrustRadius) {
dTau = compute_to_tr_ (dPP, dPD, dDD, dTrustRadius,
false, 0.0, 0.0, 0.0);
return( true );
}
//---- STEP LENGTH IS NOT TOO LONG.
dTau = 0.0;
return( false );
}
/* ----------------------------------------------------------------------
Private method step_exceeds_DMAX_
Check that atoms do not move too far:
for atom coordinates: limit is dmax
for extra per-atom DOF: limit is extra_max[]
for extra global DOF: limit is set by modify->max_alpha,
which calls fix_box_relax->max_alpha
------------------------------------------------------------------------- */
bool MinHFTN::step_exceeds_DMAX_(void) const
{
double dAlpha = dmax * sqrt((double) _nNumUnknowns);
double dPInfLocal = 0.0;
for (int i = 0; i < nvec; i++)
dPInfLocal = MAX (dPInfLocal, fabs (_daAVectors[VEC_CG_P][i]));
double dPInf;
MPI_Allreduce (&dPInfLocal, &dPInf, 1, MPI_DOUBLE, MPI_MAX, world);
if (dPInf > dmax)
return( true );
if (dPInf > MACHINE_EPS)
dAlpha = MIN (dAlpha, dmax / dPInf);
if (nextra_atom) {
for (int m = 0; m < nextra_atom; m++) {
double * pAtom = _daExtraAtom[VEC_CG_P][m];
dPInfLocal = 0.0;
int n = extra_nlen[m];
for (int i = 0; i < n; i++)
dPInfLocal = MAX (dPInfLocal, fabs (pAtom[i]));
MPI_Allreduce (&dPInfLocal, &dPInf, 1, MPI_DOUBLE, MPI_MAX, world);
if (dPInf > extra_max[m])
return( true );
if (dPInf > MACHINE_EPS)
dAlpha = MIN (dAlpha, extra_max[m] / dPInf);
}
}
if (nextra_global) {
//---- IF THE MAXIMUM DISTANCE THAT THE GLOBAL BOX CONSTRAINT WILL
//---- ALLOW IS SMALLER THAN THE PROPOSED DISTANCE, THEN THE STEP
//---- IS TOO LONG. PROPOSED DISTANCE IS ESTIMATED BY |P|_INF.
double dAlphaExtra = modify->max_alpha (_daExtraGlobal[VEC_CG_P]);
if (dAlphaExtra < dAlpha)
return( true );
}
//---- STEP LENGTH IS NOT TOO LONG.
return( false );
}
/* ----------------------------------------------------------------------
Private method adjust_step_to_tau_
Adjust the step so that VEC_CG_P = VEC_DIF1 + tau * VEC_CG_D.
------------------------------------------------------------------------- */
void MinHFTN::adjust_step_to_tau_(const double tau)
{
if (nextra_global) {
double * pGlobal = _daExtraGlobal[VEC_CG_P];
double * dGlobal = _daExtraGlobal[VEC_CG_D];
double * d1Global = _daExtraGlobal[VEC_DIF1];
for (int i = 0; i < nextra_global; i++)
pGlobal[i] = d1Global[i] + (tau * dGlobal[i]);
}
for (int i = 0; i < nvec; i++) {
_daAVectors[VEC_CG_P][i] = _daAVectors[VEC_DIF1][i]
+ (tau * _daAVectors[VEC_CG_D][i]);
}
if (nextra_atom) {
for (int m = 0; m < nextra_atom; m++) {
double * pAtom = _daExtraAtom[VEC_CG_P][m];
double * dAtom = _daExtraAtom[VEC_CG_D][m];
double * d1Atom = _daExtraAtom[VEC_DIF1][m];
int n = extra_nlen[m];
for (int i = 0; i < n; i++)
pAtom[i] = d1Atom[i] + (tau * dAtom[i]);
}
}
return;
}
/* ----------------------------------------------------------------------
Private method compute_to_tr_
Return the value tau that solves
|| p + tau*d ||_2 = dTrustRadius
If both roots are considered, the TR method chooses the one that minimizes
grad^T (p + tau*d) + 0.5 (p + tau*d)^T H (p + tau*d)
@param[in] dPP - p^T p
@param[in] dPD - p^T d
@param[in] dDD - d^T d
@param[in] dTrustRadius - distance to match
@param[in] bConsiderBothRoots - evaluate both roots, or return the positive
@param[in] dDHD - d^T H d
@param[in] dPdotHD - p^T H d
@param[in] dGradDotD - grad(x_k)^T d
------------------------------------------------------------------------- */
double MinHFTN::compute_to_tr_(const double dPP,
const double dPD,
const double dDD,
const double dTrustRadius,
const bool bConsiderBothRoots,
const double dDHD,
const double dPdotHD,
const double dGradDotD) const
{
//---- SOLVE A QUADRATIC EQUATION FOR TAU.
//---- THE COEFFICIENTS ARE SUCH THAT THERE ARE ALWAYS TWO REAL ROOTS,
//---- ONE POSITIVE AND ONE NEGATIVE.
//---- CHECK FOR ERRONEOUS DATA.
if ( (dDD <= 0.0) || (dPP < 0.0) || (dTrustRadius < 0.0)
|| (dTrustRadius * dTrustRadius < dPP) ) {
printf ("HFTN internal error - bad data given to compute_to_tr_()\n");
return( 0.0 );
}
double dTRsqrd = dTrustRadius * dTrustRadius;
double dDiscr = (dPD * dPD) - (dDD * (dPP - dTRsqrd));
dDiscr = MAX (0.0, dDiscr); //-- SHOULD NEVER BE NEGATIVE
dDiscr = sqrt (dDiscr);
double dRootPos = (-dPD + dDiscr) / dDD;
double dRootNeg = (-dPD - dDiscr) / dDD;
if (bConsiderBothRoots == false)
return( dRootPos );
//---- EVALUATE THE CG OBJECTIVE FUNCTION FOR EACH ROOT.
double dTmpTerm = dGradDotD + dPdotHD;
double dCgRedPos = (dRootPos * dTmpTerm) + (0.5 * dRootPos*dRootPos * dDHD);
double dCgRedNeg = (dRootNeg * dTmpTerm) + (0.5 * dRootNeg*dRootNeg * dDHD);
if ((-dCgRedPos) > (-dCgRedNeg))
return( dRootPos );
else
return( dRootNeg );
}
/* ----------------------------------------------------------------------
Private method evaluate_dir_der_
Compute the directional derivative using a finite difference approximation.
This is equivalent to the Hessian times direction vector p.
As a side effect, the method computes the energy and forces at x.
On input these must be defined:
atom->x - positions at x
atom->f - ignored
nIxDir - VEC_ index of the direction p
nIxResult - ignored
On output these are defined:
atom->x - unchanged
atom->f - forces evaluated at x, only if bEvaluateAtX is true
nIxDir - unchanged
nIxResult - directional derivative Hp
During processing these are modified:
VEC_DIF1
VEC_DIF2
@param[in] bUseForwardDiffs - if true use forward difference approximation,
else use central difference
@param[in] nIxDir - VEC_ index of the direction
@param[in] nIxResult - VEC_ index to place the result
(it is acceptable for nIxDir = nIxResult)
@param[in] bEvaluateAtX - if true, then evaluate at x before returning
@param[out] dNewEnergy - energy at x, if bEvaluateAtX is true
@param[out] dNewForce2 - |F|_2 at x, if bEvaluateAtX is true
------------------------------------------------------------------------- */
void MinHFTN::evaluate_dir_der_(const bool bUseForwardDiffs,
const int nIxDir,
const int nIxResult,
const bool bEvaluateAtX,
double & dNewEnergy)
{
//---- COMPUTE THE MAGNITUDE OF THE DIRECTION VECTOR: |p|_2.
double dDirNorm2SqrdLocal = 0.0;
for (int i = 0; i < nvec; i++)
dDirNorm2SqrdLocal
+= _daAVectors[nIxDir][i] * _daAVectors[nIxDir][i];
if (nextra_atom) {
for (int m = 0; m < nextra_atom; m++) {
double * iAtom = _daExtraAtom[nIxDir][m];
int n = extra_nlen[m];
for (int i = 0; i < n; i++)
dDirNorm2SqrdLocal += iAtom[i] * iAtom[i];
}
}
double dDirNorm2Sqrd = 0.0;
MPI_Allreduce (&dDirNorm2SqrdLocal, &dDirNorm2Sqrd,
1, MPI_DOUBLE, MPI_SUM, world);
if (nextra_global) {
for (int i = 0; i < nextra_global; i++) {
double * iGlobal = _daExtraGlobal[nIxDir];
dDirNorm2Sqrd += iGlobal[i] * iGlobal[i];
}
}
double dDirNorm2 = sqrt (dDirNorm2Sqrd);
//---- IF THE STEP IS TOO SMALL, RETURN ZERO FOR THE DERIVATIVE.
if (dDirNorm2 == 0.0) {
for (int i = 0; i < nvec; i++)
_daAVectors[nIxResult][i] = 0.0;
if (nextra_atom) {
for (int m = 0; m < nextra_atom; m++) {
double * iAtom = _daExtraAtom[nIxDir][m];
int n = extra_nlen[m];
for (int i = 0; i < n; i++)
iAtom[i] = 0;
}
}
if (nextra_global) {
for (int i = 0; i < nextra_global; i++)
_daExtraGlobal[nIxDir][i] = 0.0;
}
if (bEvaluateAtX) {
dNewEnergy = energy_force (0);
neval++;
}
return;
}
//---- FORWARD DIFFERENCES ARE LESS ACCURATE THAN CENTRAL DIFFERENCES,
//---- BUT REQUIRE ONLY 2 ENERGY+FORCE EVALUATIONS VERSUS 3 EVALUATIONS.
//---- STORAGE REQUIREMENTS ARE THE SAME.
if (bUseForwardDiffs) {
//---- EQUATION IS FROM THE OLD LAMMPS VERSION, SAND98-8201.
double dEps = 2.0 * sqrt (1000.0 * MACHINE_EPS) / dDirNorm2;
//---- SAVE A COPY OF x.
fix_minimize->store_box();
for (int i = 0; i < nvec; i++)
_daAVectors[VEC_DIF1][i] = xvec[i];
if (nextra_atom) {
for (int m = 0; m < nextra_atom; m++) {
double * xatom = xextra_atom[m];
double * d1Atom = _daExtraAtom[VEC_DIF1][m];
int n = extra_nlen[m];
for (int i = 0; i < n; i++)
d1Atom[i] = xatom[i];
}
}
if (nextra_global) {
modify->min_pushstore();
modify->min_store();
}
//---- EVALUATE FORCES AT x + eps*p.
if (nextra_global)
modify->min_step (dEps, _daExtraGlobal[nIxDir]);
for (int i = 0; i < nvec; i++)
xvec[i] += dEps * _daAVectors[nIxDir][i];
if (nextra_atom) {
for (int m = 0; m < nextra_atom; m++) {
double * xatom = xextra_atom[m];
double * iAtom = _daExtraAtom[nIxDir][m];
int n = extra_nlen[m];
for (int i = 0; i < n; i++)
xatom[i] += dEps * iAtom[i];
requestor[m]->min_x_set(m);
}
}
energy_force (0);
neval++;
//---- STORE THE FORCE IN DIF2.
if (nextra_global) {
for (int i = 0; i < nextra_global; i++)
_daExtraGlobal[VEC_DIF2][i] = fextra[i];
}
for (int i = 0; i < nvec; i++)
_daAVectors[VEC_DIF2][i] = fvec[i];
if (nextra_atom) {
for (int m = 0; m < nextra_atom; m++) {
double * fatom = fextra_atom[m];
double * d2Atom = _daExtraAtom[VEC_DIF2][m];
int n = extra_nlen[m];
for (int i = 0; i < n; i++)
d2Atom[i] = fatom[i];
}
}
//---- MOVE BACK TO x AND EVALUATE FORCES.
if (nextra_global) {
modify->min_step (0.0, _daExtraGlobal[VEC_DIF1]);
modify->min_popstore();
}
for (int i = 0; i < nvec; i++)
xvec[i] = _daAVectors[VEC_DIF1][i];
if (nextra_atom) {
for (int m = 0; m < nextra_atom; m++) {
double * xatom = xextra_atom[m];
double * d1Atom = _daExtraAtom[VEC_DIF1][m];
int n = extra_nlen[m];
for (int i = 0; i < n; i++)
xatom[i] += d1Atom[i];
requestor[m]->min_x_set(m);
}
}
dNewEnergy = energy_force (0);
neval++;
//---- COMPUTE THE DIFFERENCE VECTOR: [grad(x + eps*p) - grad(x)] / eps.
//---- REMEMBER THAT FORCES = -GRADIENT.
for (int i = 0; i < nvec; i++)
_daAVectors[nIxResult][i] = (fvec[i] - _daAVectors[VEC_DIF2][i]) / dEps;
if (nextra_atom) {
for (int m = 0; m < nextra_atom; m++) {
double * iAtom = _daExtraAtom[nIxResult][m];
double * d2Atom = _daExtraAtom[VEC_DIF2][m];
int n = extra_nlen[m];
for (int i = 0; i < n; i++)
iAtom[i] = (fextra_atom[m][i] - d2Atom[i]) / dEps;
}
}
if (nextra_global) {
for (int i = 0; i < nextra_global; i++)
_daExtraGlobal[nIxResult][i]
= (fextra[i] - _daExtraGlobal[VEC_DIF2][i]) / dEps;
}
}
else { //-- bUseForwardDiffs == false
//---- EQUATION IS FROM THE OLD LAMMPS VERSION, SAND98-8201.
double dEps = pow (3000.0 * MACHINE_EPS, 0.33333333) / dDirNorm2;
//---- SAVE A COPY OF x.
fix_minimize->store_box();
for (int i = 0; i < nvec; i++)
_daAVectors[VEC_DIF1][i] = xvec[i];
if (nextra_atom) {
for (int m = 0; m < nextra_atom; m++) {
double * xatom = xextra_atom[m];
double * d1Atom = _daExtraAtom[VEC_DIF1][m];
int n = extra_nlen[m];
for (int i = 0; i < n; i++)
d1Atom[i] = xatom[i];
}
}
if (nextra_global) {
modify->min_pushstore();
modify->min_store();
}
//---- EVALUATE FORCES AT x + eps*p.
if (nextra_global)
modify->min_step (dEps, _daExtraGlobal[nIxDir]);
for (int i = 0; i < nvec; i++)
xvec[i] += dEps * _daAVectors[nIxDir][i];
if (nextra_atom) {
for (int m = 0; m < nextra_atom; m++) {
double * xatom = xextra_atom[m];
double * iAtom = _daExtraAtom[nIxDir][m];
int n = extra_nlen[m];
for (int i = 0; i < n; i++)
xatom[i] += dEps * iAtom[i];
requestor[m]->min_x_set(m);
}
}
energy_force (0);
neval++;
//---- STORE THE FORCE IN DIF2.
if (nextra_global) {
for (int i = 0; i < nextra_global; i++)
_daExtraGlobal[VEC_DIF2][i] = fextra[i];
}
for (int i = 0; i < nvec; i++)
_daAVectors[VEC_DIF2][i] = fvec[i];
if (nextra_atom) {
for (int m = 0; m < nextra_atom; m++) {
double * fatom = fextra_atom[m];
double * d2Atom = _daExtraAtom[VEC_DIF2][m];
int n = extra_nlen[m];
for (int i = 0; i < n; i++)
d2Atom[i] = fatom[i];
}
}
//---- EVALUATE FORCES AT x - eps*p.
if (nextra_global)
modify->min_step (-dEps, _daExtraGlobal[nIxDir]);
for (int i = 0; i < nvec; i++)
xvec[i] = _daAVectors[VEC_DIF1][i]
- dEps * _daAVectors[nIxDir][i];
if (nextra_atom) {
for (int m = 0; m < nextra_atom; m++) {
double * xatom = xextra_atom[m];
double * iAtom = _daExtraAtom[nIxDir][m];
double * d1Atom = _daExtraAtom[VEC_DIF1][m];
int n = extra_nlen[m];
for (int i = 0; i < n; i++)
xatom[i] = d1Atom[i] - dEps * iAtom[i];
requestor[m]->min_x_set(m);
}
}
energy_force (0);
neval++;
//---- COMPUTE THE DIFFERENCE VECTOR:
//---- [grad(x + eps*p) - grad(x - eps*p)] / 2*eps.
//---- REMEMBER THAT FORCES = -GRADIENT.
if (nextra_global) {
double * iGlobal = _daExtraGlobal[nIxResult];
double * d2Global = _daExtraGlobal[VEC_DIF2];
for (int i = 0; i < nextra_global; i++)
iGlobal[i] = (fextra[i] - d2Global[i]) / (2.0 + dEps);
}
for (int i = 0; i < nvec; i++)
_daAVectors[nIxResult][i] =
(fvec[i] - _daAVectors[VEC_DIF2][i]) / (2.0 * dEps);
if (nextra_atom) {
for (int m = 0; m < nextra_atom; m++) {
double * fatom = fextra_atom[m];
double * iAtom = _daExtraAtom[nIxResult][m];
double * d2Atom = _daExtraAtom[VEC_DIF2][m];
int n = extra_nlen[m];
for (int i = 0; i < n; i++)
iAtom[i] = (fatom[i] - d2Atom[i]) / (2.0 + dEps);
}
}
if (bEvaluateAtX) {
//---- EVALUATE FORCES AT x.
if (nextra_global) {
modify->min_step (0.0, _daExtraGlobal[VEC_DIF1]);
modify->min_popstore();
}
for (int i = 0; i < nvec; i++)
xvec[i] = _daAVectors[VEC_DIF1][i];
if (nextra_atom) {
for (int m = 0; m < nextra_atom; m++) {
double * xatom = xextra_atom[m];
double * d1Atom = _daExtraAtom[VEC_DIF1][m];
int n = extra_nlen[m];
for (int i = 0; i < n; i++)
xatom[i] = d1Atom[i];
requestor[m]->min_x_set(m);
}
}
dNewEnergy = energy_force (0);
neval++;
}
}
return;
}
/* ----------------------------------------------------------------------
Private method open_hftn_print_file_
------------------------------------------------------------------------- */
void MinHFTN::open_hftn_print_file_(void)
{
int nMyRank;
MPI_Comm_rank (world, &nMyRank);
char szTmp[50];
sprintf (szTmp, "progress_MinHFTN_%d.txt", nMyRank);
_fpPrint = fopen (szTmp, "w");
if (_fpPrint == NULL) {
printf ("*** MinHFTN cannot open file '%s'\n", szTmp);
printf ("*** continuing...\n");
return;
}
fprintf (_fpPrint, " Iter Evals Energy |F|_2"
" Step TR used |step|_2 ared pred\n");
return;
}
/* ----------------------------------------------------------------------
Private method hftn_print_line_
Step types:
1 - Nw (inner iteration converged like a Newton step)
2 - TR (inner iteration reached the trust region boundary)
3 - Neg (inner iteration ended with negative curvature)
------------------------------------------------------------------------- */
void MinHFTN::hftn_print_line_(const bool bIsStepAccepted,
const int nIteration,
const int nTotalEvals,
const double dEnergy,
const double dForce2,
const int nStepType,
const double dTrustRadius,
const double dStepLength2,
const double dActualRed,
const double dPredictedRed) const
{
const char sFormat1[]
= " %4d %5d %14.8f %11.5e\n";
const char sFormatA[]
= " %4d %5d %14.8f %11.5e %3s %9.3e %8.2e %10.3e %10.3e\n";
const char sFormatR[]
= "r %4d %5d %14.8f %11.5e %3s %9.3e %8.2e %10.3e %10.3e\n";
if (_fpPrint == NULL)
return;
char sStepType[4];
if (nStepType == NO_CGSTEP_BECAUSE_F_TOL_SATISFIED)
strcpy (sStepType, " - ");
else if (nStepType == CGSTEP_NEWTON)
strcpy (sStepType, "Nw ");
else if (nStepType == CGSTEP_TO_TR)
strcpy (sStepType, "TR ");
else if (nStepType == CGSTEP_TO_DMAX)
strcpy (sStepType, "dmx");
else if (nStepType == CGSTEP_NEGATIVE_CURVATURE)
strcpy (sStepType, "Neg");
else if (nStepType == CGSTEP_MAX_INNER_ITERS)
strcpy (sStepType, "its");
else
strcpy (sStepType, "???");
if (nIteration == -1) {
fprintf (_fpPrint, sFormat1,
0, nTotalEvals, dEnergy, dForce2);
}
else {
if (bIsStepAccepted)
fprintf (_fpPrint, sFormatA,
nIteration, nTotalEvals, dEnergy, dForce2,
sStepType, dTrustRadius, dStepLength2,
dActualRed, dPredictedRed);
else
fprintf (_fpPrint, sFormatR,
nIteration, nTotalEvals, dEnergy, dForce2,
sStepType, dTrustRadius, dStepLength2,
dActualRed, dPredictedRed);
}
fflush (_fpPrint);
return;
}
/* ----------------------------------------------------------------------
Private method close_hftn_print_file_
------------------------------------------------------------------------- */
void MinHFTN::close_hftn_print_file_(void)
{
if (_fpPrint != NULL) fclose (_fpPrint);
return;
}

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