nonlinsol.h

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/*
  This file is part of MADNESS.

  Copyright (C) 2007,2010 Oak Ridge National Laboratory

  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; either version 2 of the License, or
  (at your option) any later version.

  This program 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 this program; if not, write to the Free Software
  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA

  For more information please contact:

  Robert J. Harrison
  Oak Ridge National Laboratory
  One Bethel Valley Road
  P.O. Box 2008, MS-6367

  email: harrisonrj@ornl.gov
  tel:   865-241-3937
  fax:   865-572-0680

  $Id$
*/

#ifndef MADNESS_EXAMPLES_NONLINSOL_H__INCLUDED
#define MADNESS_EXAMPLES_NONLINSOL_H__INCLUDED

#include <madness/mra/mra.h>
#include <madness/tensor/solvers.h>

namespace madness {



        template<typename C>
        void check_linear_dependence(const Tensor<C>& Q, Tensor<C>& c, const double rcondtol, const double cabsmax) {
                double rcond = 1e-12;
                int m = c.dim(0);

                while(1){
                        c = KAIN(Q, rcond);
                        //if (world.rank() == 0) print("kain c:", c);
//                      if(std::abs(c[m - 1]) < 3.0){
                        if (c.absmax()<cabsmax) {
                                break;
                        } else  if(rcond < rcondtol){
                                print("Increasing subspace singular value threshold ", c[m - 1], rcond);
                                rcond *= 100;
                        } else {
                                print("Forcing full step due to subspace malfunction");
                                c = 0.0;
                                c[m - 1] = 1.0;
                                break;
                        }
                }
        }


        template<size_t NDIM>
        class NonlinearSolverND {
                const unsigned int maxsub; //< Maximum size of subspace dimension
                std::vector<Function<double,NDIM> > ulist, rlist;
                real_tensor Q;

        public:
                bool do_print;

                NonlinearSolverND(unsigned int maxsub = 10) : maxsub(maxsub), do_print(false) {}


                Function<double,NDIM> update(const Function<double,NDIM>& u, const Function<double,NDIM>& r,
                                const double rcondtol=1e-8, const double cabsmax=1000.0) {
                        if (maxsub==1) return u-r;
                        int iter = ulist.size();
                        ulist.push_back(u);
                        rlist.push_back(r);

                        // Solve subspace equations
                        real_tensor Qnew(iter+1,iter+1);
                        if (iter>0) Qnew(Slice(0,-2),Slice(0,-2)) = Q;
                        for (int i=0; i<=iter; i++) {
                                Qnew(i,iter) = inner(ulist[i],rlist[iter]);
                                Qnew(iter,i) = inner(ulist[iter],rlist[i]);
                        }
                        Q = Qnew;
                        real_tensor c = KAIN(Q);
                        check_linear_dependence(Q,c,rcondtol,cabsmax);
                        if (do_print) print("subspace solution",c);

                        // Form new solution in u
                        Function<double,NDIM> unew = FunctionFactory<double,NDIM>(u.world());
                        if (ulist[0].is_compressed()) unew.compress();
                        for (int i=0; i<=iter; i++) {
                                unew.gaxpy(1.0,ulist[i], c[i]);
                                unew.gaxpy(1.0,rlist[i],-c[i]);
                        }
                        unew.truncate();

                        if (ulist.size() == maxsub) {
                                ulist.erase(ulist.begin());
                                rlist.erase(rlist.begin());
                                Q = copy(Q(Slice(1,-1),Slice(1,-1)));
                        }
                        return unew;
                }
        };

        // backwards compatibility
        typedef NonlinearSolverND<3> NonlinearSolver;


        template <class T>
        struct default_allocator {
        T operator()() {return T();}
    };
    

    template <class T, class C = double, class Alloc = default_allocator<T> >
    class XNonlinearSolver {
        unsigned int maxsub; //< Maximum size of subspace dimension
        Alloc alloc;
        std::vector<T> ulist, rlist; 
        Tensor<C> Q;
    public:
        bool do_print;

        XNonlinearSolver(const Alloc& alloc = Alloc())
            : maxsub(10)
            , alloc(alloc)
                , do_print(false)
        {}

        XNonlinearSolver(const XNonlinearSolver& other)
            : maxsub(other.maxsub)
            , alloc(other.alloc)
                        , do_print(false)
        {}


        std::vector<T>& get_ulist() {return ulist;}
        std::vector<T>& get_rlist() {return rlist;}

        void set_maxsub(int maxsub) {this->maxsub = maxsub;}


        T update(const T& u, const T& r, const double rcondtol=1e-8, const double cabsmax=1000.0) {
                if (maxsub==1) return u-r;
                int iter = ulist.size();
                ulist.push_back(u);
                rlist.push_back(r);

                // Solve subspace equations
                Tensor<C> Qnew(iter+1,iter+1);
                if (iter>0) Qnew(Slice(0,-2),Slice(0,-2)) = Q;
                for (int i=0; i<=iter; i++) {
                        Qnew(i,iter) = inner(ulist[i],rlist[iter]);
                        Qnew(iter,i) = inner(ulist[iter],rlist[i]);
                }
                Q = Qnew;
                Tensor<C> c = KAIN(Q);

                check_linear_dependence(Q,c,rcondtol,cabsmax);
                if (do_print) print("subspace solution",c);

                // Form new solution in u
                T unew = alloc();
                for (int i=0; i<=iter; i++) {
                        unew += (ulist[i] - rlist[i])*c[i];
                }

                if (ulist.size() == maxsub) {
                        ulist.erase(ulist.begin());
                        rlist.erase(rlist.begin());
                        Q = copy(Q(Slice(1,-1),Slice(1,-1)));
                }
                return unew;
        }

    };



}
#endif