Minimize.h

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/*-------------------------------------------------------------------
Copyright 2011 Ravishankar Sundararaman, Kendra Letchworth Weaver

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_H
#define JDFTX_CORE_MINIMIZE_H

#include <cmath>
#include <algorithm>
#include <core/Util.h>
#include <core/MinimizeParams.h>


template<typename Vector> struct Minimizable
{
        virtual void step(const Vector& dir, double alpha)=0;
        
        virtual double compute(Vector* grad)=0; 
        
        virtual Vector precondition(const Vector& grad) { return clone(grad); }
        
        virtual bool report(int iter) { return false; }
        
        virtual void constrain(Vector&) {}
        
        virtual double sync(double x) const { return x; }
        
        double minimize(const MinimizeParams& params);
        
        void fdTest(const MinimizeParams& params);
        
private:
        typedef bool (*Linmin)(Minimizable<Vector>&, const MinimizeParams&, const Vector&, double, double&, double&, Vector&);
        Linmin getLinmin(const MinimizeParams& params) const;
        double lBFGS(const MinimizeParams& params); //limited memory BFGS implementation (differs sufficiently from CG to be justify a separate implementation)
};

template<typename Vector> struct LinearSolvable
{
        Vector state; 
        
        virtual Vector hessian(const Vector&) const=0;
        
        virtual Vector precondition(const Vector& v) const { return clone(v); }
        
        virtual double sync(double x) const { return x; }
        
        int solve(const Vector& rhs, const MinimizeParams& params);
};

//---------------------- Implementation ----------------------------

#include <core/Minimize_linmin.h>
#include <core/Minimize_lBFGS.h>

template<typename Vector> double Minimizable<Vector>::minimize(const MinimizeParams& p)
{       if(p.fdTest) fdTest(p); // finite difference test
        if(p.dirUpdateScheme == MinimizeParams::LBFGS) return lBFGS(p);
        
        Vector g, gPrev; //current and previous gradient
        double E = sync(compute(&g)); //get initial energy and gradient
        EdiffCheck ediffCheck(p.nEnergyDiff, p.energyDiffThreshold); //list of past energies
        
        Vector d = clone(g); //step direction (will be reset in first iteration)
        bool forceGradDirection = true; //whether current direction is along the gradient
        MinimizeParams::DirectionUpdateScheme currentDirUpdateScheme = p.dirUpdateScheme; //initially use the specified scheme, may switch to SD on trouble
        
        double alphaT = p.alphaTstart; //test step size
        double alpha = alphaT; //actual step size
        double beta = 0.0; //CG prev search direction mix factor
        double gKNorm = 0.0, gKNormPrev = 0.0; //current and previous norms of the preconditioned gradient

        //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
                        fprintf(p.fpLog, "%s\tState modified externally: resetting search direction.\n", p.linePrefix);
                        fflush(p.fpLog);
                        forceGradDirection = true; //reset search direction
                }
                
                Vector Kg = precondition(g);
                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  alpha: %10.3le", sqrt(gKNorm/p.nDim), alpha);

                //Print prev step stats and set CG direction parameter if necessary
                beta = 0.0;
                if(!forceGradDirection)
                {       double dotgd = sync(dot(g,d));
                        double dotgPrevKg = sync(dot(gPrev, Kg));

                        double linmin = dotgd/sqrt(sync(dot(g,g))*sync(dot(d,d)));
                        double cgtest = dotgPrevKg/sqrt(gKNorm*gKNormPrev);
                        fprintf(p.fpLog, "  linmin: %10.3le", linmin);
                        fprintf(p.fpLog, "  cgtest: %10.3le", cgtest);

                        //Update beta:
                        switch(currentDirUpdateScheme)
                        {       case MinimizeParams::FletcherReeves:  beta = gKNorm/gKNormPrev; break;
                                case MinimizeParams::PolakRibiere:    beta = (gKNorm-dotgPrevKg)/gKNormPrev; break;
                                case MinimizeParams::HestenesStiefel: beta = (gKNorm-dotgPrevKg)/(dotgd-sync(dot(d,gPrev))); break;
                                case MinimizeParams::SteepestDescent: beta = 0.0; break;
                                case MinimizeParams::LBFGS: break; //Should never encounter since LBFGS handled separately; just to eliminate compiler warnings
                        }
                        if(beta<0.0)
                        {       fprintf(p.fpLog, "\n%sEncountered beta<0, resetting CG.", p.linePrefix);
                                beta=0.0;
                        }
                }
                forceGradDirection = false;
                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;
                gPrev = g;
                gKNormPrev = gKNorm;

                //Update search direction
                d *= beta; axpy(-1.0, Kg, d);  // d = beta*d - Kg

                //Line minimization
                if(linmin(*this, p, d, alphaT, alpha, E, g))
                {       //linmin succeeded:
                        if(p.updateTestStepSize)
                        {       alphaT = alpha;
                                if(alphaT<p.alphaTmin) //bad step size
                                        alphaT = p.alphaTstart; //make sure next test step size is not too bad
                        }
                }
                else
                {       //linmin failed:
                        fprintf(p.fpLog, "%s\tUndoing step.\n", p.linePrefix);
                        step(d, -alpha);
                        E = sync(compute(&g));
                        if(beta)
                        {       //Failed, but not along the gradient direction:
                                fprintf(p.fpLog, "%s\tStep failed: resetting search direction.\n", p.linePrefix);
                                fflush(p.fpLog);
                                forceGradDirection = true; //reset search direction
                        }
                        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;
                        }
                }
        }
        fprintf(p.fpLog, "%sNone of the convergence criteria satisfied after %d iterations.\n", p.linePrefix, iter);
        return E;
}


template<typename Vector> void Minimizable<Vector>::fdTest(const MinimizeParams& p)
{       
        const double deltaMin = 1e-9;
        const double deltaMax = 1e+1;
        const double deltaScale = 1e+1;
        string fdPrefixString = p.linePrefix + string("fdTest: ");
        const char* fdPrefix = fdPrefixString.c_str();
        fprintf(p.fpLog, "%s--------------------------------------\n", fdPrefix);
        Vector g;
        double E0 = sync(compute(&g));
        
        Vector dx;
        {       // Set the direction to be a random vector of the same norm
                // as the preconditioned gradient times the initial test step size
                Vector Kg = precondition(g);
                dx = clone(Kg);
                randomize(dx);
                constrain(dx);
                dx *= p.alphaTstart * sqrt(sync(dot(Kg,Kg))/sync(dot(dx,dx)));
        }
        double dE_ddelta = sync(dot(dx, g)); //directional derivative at delta=0

        double deltaPrev=0;
        for(double delta=deltaMin; delta<=deltaMax; delta*=deltaScale)
        {       double dE = dE_ddelta*delta;
                step(dx, delta-deltaPrev); deltaPrev=delta;
                double deltaE = sync(compute(0)) - E0;
                fprintf(p.fpLog, "%s   delta=%le:\n", fdPrefix, delta);
                fprintf(p.fpLog, "%s      d%s Ratio: %19.16lf\n", fdPrefix, p.energyLabel, deltaE/dE);
                fprintf(p.fpLog, "%s      d%s Error: %19.16lf\n", fdPrefix, p.energyLabel, sqrt(p.nDim)*1.1e-16/fabs(dE));
        }
        fprintf(p.fpLog, "%s--------------------------------------\n", fdPrefix);
        step(dx, -deltaPrev); //restore state to original value
}


template<typename Vector> int LinearSolvable<Vector>::solve(const Vector& rhs, const MinimizeParams& p)
{       //Initialize:
        Vector r = clone(rhs); axpy(-1.0, hessian(state), r); //residual r = rhs - A.state;
        Vector z = precondition(r), d = r; //the preconditioned residual and search direction
        double beta=0.0, rdotzPrev=0.0, rdotz = sync(dot(r, z));

        //Check initial residual
        double rzNorm = sqrt(fabs(rdotz)/p.nDim);
        fprintf(p.fpLog, "%sInitial:  sqrt(|r.z|): %12.6le\n", p.linePrefix, rzNorm); fflush(p.fpLog);
        if(rzNorm<p.knormThreshold) { fprintf(p.fpLog, "%sConverged sqrt(r.z)<%le\n", p.linePrefix, p.knormThreshold); fflush(p.fpLog); return 0; }

        //Main loop:
        int iter;
        for(iter=0; iter<p.nIterations && !killFlag; iter++)
        {       //Update search direction:
                if(rdotzPrev)
                {       beta = rdotz/rdotzPrev;
                        d *= beta; axpy(1.0, z, d); // d = z + beta*d
                }
                else d = clone(z); //fresh search direction (along gradient)
                //Step:
                Vector w = hessian(d);
                double alpha = rdotz/sync(dot(w,d));
                axpy(alpha, d, state);
                axpy(-alpha, w, r);
                z = precondition(r);
                rdotzPrev = rdotz;
                rdotz = sync(dot(r, z));
                //Print info:
                double rzNorm = sqrt(fabs(rdotz)/p.nDim);
                fprintf(p.fpLog, "%sIter: %3d  sqrt(|r.z|): %12.6le  alpha: %12.6le  beta: %13.6le\n",
                        p.linePrefix, iter, rzNorm, alpha, beta); fflush(p.fpLog);
                //Check convergence:
                if(rzNorm<p.knormThreshold) { fprintf(p.fpLog, "%sConverged sqrt(r.z)<%le\n", p.linePrefix, p.knormThreshold); fflush(p.fpLog); return iter; }
        }
        fprintf(p.fpLog, "%sGradient did not converge within threshold in %d iterations\n", p.linePrefix, iter); fflush(p.fpLog);
        return iter;
}

#endif // JDFTX_CORE_MINIMIZE_H