Minimize_lBFGS.h

/*-------------------------------------------------------------------
Copyright 2014 Ravishankar Sundararaman

This file is part of JDFTx.

JDFTx 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, either version 3 of the License, or
(at your option) any later version.

JDFTx is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
GNU General Public License for more details.

You should have received a copy of the GNU General Public License
along with JDFTx.  If not, see <http://www.gnu.org/licenses/>.
-------------------------------------------------------------------*/

#ifndef JDFTX_CORE_MINIMIZE_LBFGS_H
#define JDFTX_CORE_MINIMIZE_LBFGS_H

#include <core/Minimize_linmin.h>
#include <core/Minimize.h> //this include is present only to aid IDE's autocompletion (does nothing since this file is always used via Minimize.h)
#include <memory>
#include <list>
#include <stack>

//Following Nocedal and Liu, Math Prog 45, 503 (1989)
template<typename Vector> double Minimizable<Vector>::lBFGS(const MinimizeParams& p)
{       
        Vector g; //gradient
        double E = sync(compute(&g)); //get initial energy and gradient
        Vector Kg = precondition(g); //preconditioned gradient
        
        EdiffCheck ediffCheck(p.nEnergyDiff, p.energyDiffThreshold); //list of past energies

        double alpha = 0.; //step size (note BFGS always tries alpha=alphaTstart first, which is recommended to be 1)
        double linminTest = 0.;
        
        //History of variable and residual changes:
        struct History
        {       Vector s; //change in variable (= alpha d)
                Vector Ky; //change in preconditioned residual (= Kg - KgPrev)
                double rho; //= 1/dot(s,y)
        };
        std::list< std::shared_ptr<History> > history;
        double gamma = 0.; //scaling: set to dot(s,y)/dot(y,Ky) each iteration
        
        //Select the linmin method:
        Linmin linmin = getLinmin(p);
        
        //Iterate until convergence, max iteration count or kill signal
        int iter=0;
        for(iter=0; !killFlag; iter++)
        {       
                if(report(iter)) //optional reporting/processing
                {       E = sync(compute(&g)); //update energy and gradient if state was modified
                        Kg = precondition(g);
                        fprintf(p.fpLog, "%s\tState modified externally: resetting history.\n", p.linePrefix);
                        fflush(p.fpLog);
                        history.clear();
                }
                
                double gKnorm = sync(dot(g,Kg));
                fprintf(p.fpLog, "%sIter: %3d  %s: ", p.linePrefix, iter, p.energyLabel);
                fprintf(p.fpLog, p.energyFormat, E);
                fprintf(p.fpLog, "  |grad|_K: %10.3le", sqrt(gKnorm/p.nDim));
                if(alpha) fprintf(p.fpLog, "  alpha: %10.3le", alpha);
                if(linminTest) fprintf(p.fpLog, "  linmin: %10.3le", linminTest);
                
                //Check stopping conditions:
                fprintf(p.fpLog, "\n"); fflush(p.fpLog);
                if(sqrt(gKnorm/p.nDim) < p.knormThreshold)
                {       fprintf(p.fpLog, "%sConverged (|grad|_K<%le).\n", p.linePrefix, p.knormThreshold);
                        fflush(p.fpLog); return E;
                }
                if(ediffCheck.checkConvergence(E))
                {       fprintf(p.fpLog, "%sConverged (|Delta %s|<%le for %d iters).\n",
                                p.linePrefix, p.energyLabel, p.energyDiffThreshold, p.nEnergyDiff);
                        fflush(p.fpLog); return E;
                }
                if(!std::isfinite(gKnorm))
                {       fprintf(p.fpLog, "%s|grad|_K=%le. Stopping ...\n", p.linePrefix, gKnorm);
                        fflush(p.fpLog); return E;
                }
                if(!std::isfinite(E))
                {       fprintf(p.fpLog, "%sE=%le. Stopping ...\n", p.linePrefix, E);
                        fflush(p.fpLog); return E;
                }
                if(iter>=p.nIterations) break;
                
                //Prepare container that will be committed to history below: (and avoid copies)
                auto h = std::make_shared<History>();
                Vector& d = h->s;
                
                //Compute search direction:
                d = clone(Kg);
                std::stack<double> a; //alpha in the reference renamed to 'a' here to not clash with step size
                for(auto h=history.rbegin(); h!=history.rend(); h++)
                {       a.push( (*h)->rho * sync(dot((*h)->s, d)) );
                        axpy(-a.top(), (*h)->Ky, d);
                }
                if(gamma) d *= gamma; //scaling (available after first iteration)
                for(auto h=history.begin(); h!=history.end(); h++)
                {       double b = (*h)->rho * sync(dot((*h)->Ky, d));
                        axpy(a.top()-b, (*h)->s, d);
                        a.pop();
                }
                d *= -1;
                if((int)history.size() == p.history) history.pop_front(); //if full, make room for the upcoming history entry (do this here to free memory earlier)
                
                //Line minimization
                Vector y = clone(g); //store previous gradient before linmin changes it (this will later be converted to y = g-gPrev)
                if(!linmin(*this, p, d, p.alphaTstart, alpha, E, g))
                {       //linmin failed:
                        fprintf(p.fpLog, "%s\tUndoing step.\n", p.linePrefix);
                        step(d, -alpha);
                        E = sync(compute(&g));
                        Kg = precondition(g);
                        if(history.size())
                        {       //Failed, but not along the gradient direction:
                                fprintf(p.fpLog, "%s\tStep failed: resetting history.\n", p.linePrefix);
                                fflush(p.fpLog);
                                history.clear();
                                gamma = 0.;
                                linminTest = 0.;
                                continue;
                        }
                        else
                        {       //Failed along the gradient direction
                                fprintf(p.fpLog, "%s\tStep failed along negative gradient direction.\n", p.linePrefix);
                                fprintf(p.fpLog, "%sProbably at roundoff error limit. (Stopping)\n", p.linePrefix);
                                fflush(p.fpLog);
                                return E;
                        }
                }
                
                //Update history:
                linminTest = sync(dot(g,d))/sqrt(sync(dot(g,g))*sync(dot(d,d)));
                d *= alpha; //d -> alpha * d, which is change of state, and it resides in h->s
                h->Ky = Kg; Kg = precondition(g); //store previous preconditioned gradient, and compute new one
                h->Ky *= -1; axpy(1., Kg, h->Ky); //Ky = K(g-gPrev)
                y *= -1; axpy(1., g, y); //y = g-gPrev
                double ydots = sync(dot(y, h->s));
                h->rho = 1./ydots;
                gamma = ydots / sync(dot(y, h->Ky));
                history.push_back(h);
        }
        fprintf(p.fpLog, "%sNone of the convergence criteria satisfied after %d iterations.\n", p.linePrefix, iter);
        return E;
}

#endif //JDFTX_CORE_MINIMIZE_LBFGS_H