one_flavor_rat_monomial_w.h

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// -*- C++ -*-
 
/*! @file
 * @brief One flavor monomials using RHMC
 */
 
#ifndef __one_flavor_rat_monomial_w_h__
#define __one_flavor_rat_monomial_w_h__
 
#include "unprec_wilstype_fermact_w.h"
#include "eoprec_constdet_wilstype_fermact_w.h"
#include "seoprec_constdet_wilstype_fermact_w.h"
#include "update/molecdyn/monomial/abs_monomial.h"
#include "update/molecdyn/monomial/force_monitors.h"
#include "update/molecdyn/monomial/remez_coeff.h"
#include <typeinfo>
 
namespace Chroma
{
  //-------------------------------------------------------------------------------------------
  //! Exact 1 flavor fermact monomial using rational polynomials
  /*! @ingroup monomial
   *
   * Exact 1 flavor fermact monomial using Rational Polynomial. 
   * Preconditioning is not specified yet.
   * Can supply a default dsdq and pseudoferm refresh algorithm
   */
  template<typename P, typename Q, typename Phi>
  class OneFlavorRatExactWilsonTypeFermMonomial : public ExactWilsonTypeFermMonomial<P,Q,Phi>
  {
  public:
     //! virtual destructor:
    ~OneFlavorRatExactWilsonTypeFermMonomial() {}
 
    //! Compute the total action
    virtual Double S(const AbsFieldState<P,Q>& s)  = 0;
 
    //! Compute dsdq for the system... 
    /*! Actions of the form  chi^dag*(M^dag*M)*chi */
    virtual void dsdq(P& F, const AbsFieldState<P,Q>& s)
    {
      START_CODE();
 
      // Self Description/Encapsulation Rule
      XMLWriter& xml_out = TheXMLLogWriter::Instance();
      push(xml_out, "OneFlavorRatExactWilsonTypeFermMonomial");
 
      /**** Identical code for unprec and even-odd prec case *****/
      
      /* The pseudofermionic action is of the form  S_pf = chi^dag N*D^(-1) chi
       * where N(Q) and D(Q) are polynomials in the rescaled kernel:
       *
       *     Q   = M^dag*M
       *     M   = is some operator
       *
       * The function x^(-alpha) is approximated by c*N(x)/D(x)
       * with c=FRatNorm. This has to be taken into account when comparing
       * the force with the standard HMC routine dsduf for alpha=1.  To solve
       * ( N(Q)/D(Q) )psi the rational function is reformed as a partial fraction
       * expansion and a multishift solver used to find the solution.
       *
       * Need
       * dS_f/dU = - \sum_i psi_i^dag * p_i * [d(M^dag)*M + M^dag*dM] * psi
       *    where    psi_i = (M^dag*M + q_i)^(-1)*chi
       *
       * In Balint's notation, the result is  
       * \dot{S} = -\sum_i p_i [ X_i^dag*\dot{M}^\dag*Y_i - Y_i^dag\dot{M}*X_i]
       * where
       *    X_i = (M^dag*M + q_i)^(-1)*chi   Y_i = M*X_i
       * In Robert's notation,  X_i -> psi_i .
       */
      const WilsonTypeFermAct<Phi,P,Q>& FA = getFermAct();
      
      // Create a state for linop
      Handle< FermState<Phi,P,Q> > state(FA.createState(s.getQ()));
        
      // Need way to get gauge state from AbsFieldState<P,Q>
      Handle< DiffLinearOperator<Phi,P,Q> > lin(FA.linOp(state));
 
      // Get multi-shift system solver
      Handle< MdagMMultiSystemSolver<Phi> > invMdagM(FA.mInvMdagM(state, getForceInvParams()));
 
      // Partial Fraction Expansion coeffs for force
      const RemezCoeff_t& fpfe = getFPFE();
 
      multi1d<Phi> X;
      Phi Y;
 
      P  F_1;
      F.resize(Nd);
      F = zero;
 
      // Loop over all the pseudoferms
      multi1d<int> n_count(getNPF());
      QDPIO::cout << "num_pf = " << getNPF() << std::endl;
 
      for(int n=0; n < getNPF(); ++n)
      {
        // The multi-shift inversion
        SystemSolverResults_t res = (*invMdagM)(X, fpfe.pole, getPhi()[n]);
        n_count[n] = res.n_count;
 
        // Loop over solns and accumulate force contributions
 
 
#if 0 
 
        P F_2;
        P F_tmp(Nd);
 
        F_tmp = zero;
        for(int i=0; i < X.size(); ++i)
        {
          (*lin)(Y, X[i], PLUS);
 
          // The  d(M^dag)*M  term
          lin->deriv(F_1, X[i], Y, MINUS);
      
          // The  M^dag*d(M)  term
          lin->deriv(F_2, Y, X[i], PLUS);
          F_1 += F_2;
 
          // Reweight each contribution in partial fraction
          for(int mu=0; mu < F.size(); mu++) {
            F_tmp[mu] -= fpfe.res[i] * F_1[mu];
          }
        }
        F += F_tmp;
#else
        // New code with new force term
        multi1d<Phi> Y(X.size());
        for(int i=0; i < X.size(); i++) {
          (*lin)(Y[i], X[i], PLUS);
          Y[i]*= -fpfe.res[i];
        }
 
        lin->derivMultipole(F_1, X, Y, MINUS);
        F += F_1;
        lin->derivMultipole(F_1, Y, X, PLUS);
        F += F_1;
#endif
        // Concious choice. Don't monitor forces by pole 
        // Just accumulate it
        
      }
 
      state->deriv(F);
      write(xml_out, "n_count", n_count);
      monitorForces(xml_out, "Forces", F);
      pop(xml_out);
 
      END_CODE();
    }
 
  
    //! Refresh pseudofermions
    /*!
     * This routine calculates the pseudofermion field (chi) for the case
     * of rational evolution
     *
     *           chi =  n(Q)*[d(Q)]^(-1) * eta
     * Where:    Q   = M^dag*M
     *           d(Q) = (Q+q_1)*(Q+q_2)*...*(Q+q_m)
     *           n(Q) = (Q+p_1)*(Q+p_2)*...  *(Q+p_m)
     *           m  = HBRatDeg
     *                                                          
     * The rational function n(x)/d(x) is the optimal rational
     * approximation to the inverse square root of N(x)/D(x) which in
     * turn is the optimal rational approximation to x^(-alpha).
     * Here, alpha = 1/2
     *
     * To solve {n(Q)*[d(Q)]^(-1) * eta} the partial fraction expansion is
     * used in combination with a multishift solver.
     */
    virtual void refreshInternalFields(const AbsFieldState<P,Q>& s) 
    {
      START_CODE();
 
      // Heatbath all the fields
      
      // Self Description/Encapsulation Rule
      XMLWriter& xml_out = TheXMLLogWriter::Instance();
      push(xml_out, "OneFlavorRatExactWilsonTypeFermMonomial");
 
      // Get at the ferion action for piece i
      const WilsonTypeFermAct<Phi,P,Q>& FA = getFermAct();
      
      // Create a Connect State, apply fermionic boundaries
      Handle< FermState<Phi,P,Q> > f_state(FA.createState(s.getQ()));
      
      // Create a linear operator
      Handle< DiffLinearOperator<Phi,P,Q> > M(FA.linOp(f_state));
      
      // Get multi-shift system solver
#if 1
      Handle< MdagMMultiSystemSolver<Phi> > invMdagM(FA.mInvMdagM(f_state, getActionInvParams()));
#else
      Handle< MdagMMultiSystemSolverAccumulate<Phi> > invMdagM(FA.mInvMdagMAcc(f_state, getActionInvParams()));
#endif
      // Partial Fraction Expansion coeffs for heat-bath
      const RemezCoeff_t& sipfe = getSIPFE();
 
      // Loop over pseudoferms
      getPhi().resize(getNPF());
      multi1d<int> n_count(getNPF());
      Phi eta;
 
      for(int n=0; n < getNPF(); ++n)
      {
        // Fill the eta field with gaussian noise
        eta = zero;
        gaussian(eta, M->subset());
      
        // Account for fermion BC by modifying the proposed field
        FA.getFermBC().modifyF(eta);
 
        // Temporary: Move to correct normalisation
        eta *= sqrt(0.5);
      
        // The multi-shift inversion
#if 1
        multi1d<Phi> X;
        SystemSolverResults_t res = (*invMdagM)(X, sipfe.pole, eta);
#else
        SystemSolverResults_t res = (*invMdagM)(getPhi()[n], sipfe.norm, sipfe.res,sipfe.pole, eta);
#endif
        n_count[n] = res.n_count;
 
        // Weight solns to make final PF field
#if 1
        getPhi()[n][M->subset()] = sipfe.norm * eta;
        for(int i=0; i < X.size(); ++i)
          getPhi()[n][M->subset()] += sipfe.res[i] * X[i];
#endif
      }
 
      write(xml_out, "n_count", n_count);
      pop(xml_out);
 
      END_CODE();
    }                               
  
    //! Copy pseudofermions if any
    virtual void setInternalFields(const Monomial<P,Q>& m) 
    {
      START_CODE();
 
      try {
        const OneFlavorRatExactWilsonTypeFermMonomial<P,Q,Phi>& fm = dynamic_cast<  const OneFlavorRatExactWilsonTypeFermMonomial<P,Q,Phi>& >(m);
 
        getPhi() = fm.getPhi();
      }
      catch(std::bad_cast) { 
        QDPIO::cerr << "Failed to cast input Monomial to OneFlavorRatExactWilsonTypeFermMonomial " << std::endl;
        QDP_abort(1);
      }
 
      END_CODE();
    }
 
 
    //! Compute the action on the appropriate subset
    /*!
     * This measures the pseudofermion contribution to the Hamiltonian
     * for the case of rational evolution (with polynomials n(x) and d(x),
     * of degree SRatDeg
     *
     * S_f = chi_dag * (n(A)*d(A)^(-1))^2* chi
     *
     * where A is M^dag*M
     *
     * The rational function n(x)/d(x) is the optimal rational
     * approximation to the square root of N(x)/D(x) which in
     * turn is the optimal rational approximation to x^(-alpha).
     * Here, alpha = 1/2
     */
    virtual Double S_subset(const AbsFieldState<P,Q>& s) const
    {
      START_CODE();
 
      XMLWriter& xml_out = TheXMLLogWriter::Instance();
      push(xml_out, "S_subset");
 
      const WilsonTypeFermAct<Phi,P,Q>& FA = getFermAct();
 
      Handle< FermState<Phi,P,Q> > bc_g_state = FA.createState(s.getQ());
 
      // Need way to get gauge state from AbsFieldState<P,Q>
      Handle< DiffLinearOperator<Phi,P,Q> > lin(FA.linOp(bc_g_state));
 
      // Get multi-shift system solver
#if 0
      Handle< MdagMMultiSystemSolverAccumulate<Phi> > invMdagM(FA.mInvMdagMAcc(bc_g_state, getActionInvParams()));
#else
     Handle< MdagMMultiSystemSolver<Phi> > invMdagM(FA.mInvMdagM(bc_g_state, getActionInvParams()));
#endif
 
      // Partial Fraction Expansion coeffs for action
      const RemezCoeff_t& spfe = getSPFE();
 
      // Compute energy
      // Get X out here via multisolver
#if 1
      multi1d<Phi> X;
#endif
      // Loop over all the pseudoferms
      multi1d<int> n_count(getNPF());
      Double action = zero;
      Phi psi;
 
      for(int n=0; n < getNPF(); ++n)
      {
#if 0
        // The multi-shift inversion
        SystemSolverResults_t res = (*invMdagM)(psi, spfe.norm, spfe.res,spfe.pole, getPhi()[n]);
#else
        // The multi-shift inversion
        SystemSolverResults_t res = (*invMdagM)(X, spfe.pole, getPhi()[n]);
#endif
        n_count[n] = res.n_count;
        LatticeDouble site_S=zero;
 
        // Take a volume factor out - redefine zero point energy
        // this constant should have no physical effect, but by
        // making S fluctuate around 0, it should remove a volume
        // factor from the energies
        site_S[ lin->subset() ] = -Double(12);
#if 1   
        psi[lin->subset()] = spfe.norm * getPhi()[n];
        for(int i=0; i < X.size(); ++i) {
          psi[lin->subset()] += spfe.res[i] * X[i];
        }
#endif
        // Accumulate locally 
        site_S[ lin->subset()] += localNorm2(psi);
 
        // action += norm2(psi, lin->subset());
 
        // Sum
        action += sum(site_S, lin->subset());
      }
 
      write(xml_out, "n_count", n_count);
      write(xml_out, "S", action);
      pop(xml_out);
 
      END_CODE();
 
      return action;
    }
 
 
  protected:
    //! Get at fermion action
    virtual const WilsonTypeFermAct<Phi,P,Q>& getFermAct(void) const = 0;
 
    //! Get inverter params
    virtual const GroupXML_t& getActionInvParams(void) const = 0;
 
    //! Get inverter params
    virtual const GroupXML_t& getForceInvParams(void) const = 0;
 
    //! Return number of roots in used
    virtual int getNPF() const = 0;
 
    //! Return the partial fraction expansion for the force calc
    virtual const RemezCoeff_t& getFPFE() const = 0;
 
    //! Return the partial fraction expansion for the action calc
    virtual const RemezCoeff_t& getSPFE() const = 0;
 
    //! Return the partial fraction expansion for the heat-bath
    virtual const RemezCoeff_t& getSIPFE() const = 0;
 
    //! Accessor for pseudofermion (read only)
    virtual const multi1d<Phi>& getPhi(void) const = 0;
 
    //! mutator for pseudofermion
    virtual multi1d<Phi>& getPhi(void) = 0;    
 
  };
 
 
  //-------------------------------------------------------------------------------------------
  //! Exact 1 flavor unpreconditioned fermact monomial
  /*! @ingroup monomial
   *
   * Exact 1 flavor unpreconditioned fermact monomial.
   */
  template<typename P, typename Q, typename Phi>
  class OneFlavorRatExactUnprecWilsonTypeFermMonomial : public OneFlavorRatExactWilsonTypeFermMonomial<P,Q,Phi>
  {
  public:
     //! virtual destructor:
    ~OneFlavorRatExactUnprecWilsonTypeFermMonomial() {}
 
    //! Compute the total action
    virtual Double S(const AbsFieldState<P,Q>& s)
    {
      START_CODE();
 
      // Self identification/encapsulation Rule
      XMLWriter& xml_out = TheXMLLogWriter::Instance();
      push(xml_out, "OneFlavorRatExactUnprecWilsonTypeFermMonomial");
 
      Double action = this->S_subset(s);
 
      write(xml_out, "S", action);
      pop(xml_out);
 
      END_CODE();
 
      return action;
    }
 
  protected:
    //! Get at fermion action
    virtual const WilsonTypeFermAct<Phi,P,Q>& getFermAct(void) const = 0;
 
    //! Get inverter params
    virtual const GroupXML_t& getActionInvParams(void) const = 0;
 
    //! Get inverter params
    virtual const GroupXML_t& getForceInvParams(void) const = 0;
 
    //! Return number of roots in used
    virtual int getNPF() const = 0;
 
    //! Return the partial fraction expansion for the force calc
    virtual const RemezCoeff_t& getFPFE() const = 0;
 
    //! Return the partial fraction expansion for the action calc
    virtual const RemezCoeff_t& getSPFE() const = 0;
 
    //! Return the partial fraction expansion for the heat-bath
    virtual const RemezCoeff_t& getSIPFE() const = 0;
 
    //! Accessor for pseudofermion (read only)
    virtual const multi1d<Phi>& getPhi(void) const = 0;
 
    //! mutator for pseudofermion
    virtual multi1d<Phi>& getPhi(void) = 0;    
  };
 
 
  //-------------------------------------------------------------------------------------------
  //! Exact 1 flavor even-odd preconditioned fermact monomial
  /*! @ingroup monomial
   *
   * Exact 1 flavor even-odd preconditioned fermact monomial.
   * Can supply a default dsdq algorithm
   */
  template<typename P, typename Q, typename Phi,
          template<class, class,class> class EOFermActT>
  class OneFlavorRatExactEOPrecWilsonTypeFermMonomialT : public OneFlavorRatExactWilsonTypeFermMonomial<P,Q,Phi>
  {
  public:
     //! virtual destructor:
    virtual  ~OneFlavorRatExactEOPrecWilsonTypeFermMonomialT() {}
 
    //! Even even contribution (eg ln det Clover)
    virtual Double S_even_even(const AbsFieldState<P,Q>& s) = 0;
 
    //! Compute the odd odd contribution (eg
    virtual Double S_odd_odd(const AbsFieldState<P,Q>& s)
    {
      return this->S_subset(s);
    }
 
    //! Compute the total action
    Double S(const AbsFieldState<P,Q>& s)
    {
      START_CODE();
 
      XMLWriter& xml_out = TheXMLLogWriter::Instance();
      push(xml_out, "OneFlavorRatExactEvenOddPrecWilsonTypeFermMonomial");
 
      Double action_e = S_even_even(s);
      Double action_o = S_odd_odd(s);
      Double action   = action_e + action_o;
 
      write(xml_out, "S_even_even", action_e);
      write(xml_out, "S_odd_odd", action_o);
      write(xml_out, "S", action);
      pop(xml_out);
 
      END_CODE();
 
      return action;
    }
 
  protected:
    //! Get at fermion action
    virtual const EOFermActT<Phi,P,Q>& getFermAct() const = 0;
 
    //! Get inverter params
    virtual const GroupXML_t& getActionInvParams(void) const = 0;
 
    //! Get inverter params
    virtual const GroupXML_t& getForceInvParams(void) const = 0;
 
    //! Return number of roots in used
    virtual int getNPF() const = 0;
 
    //! Return the partial fraction expansion for the force calc
    virtual const RemezCoeff_t& getFPFE() const = 0;
 
    //! Return the partial fraction expansion for the action calc
    virtual const RemezCoeff_t& getSPFE() const = 0;
 
    //! Return the partial fraction expansion for the heat-bath
    virtual const RemezCoeff_t& getSIPFE() const = 0;
 
    //! Accessor for pseudofermion (read only)
    virtual const multi1d<Phi>& getPhi(void) const = 0;
 
    //! mutator for pseudofermion
    virtual multi1d<Phi>& getPhi(void) = 0;    
  };
 
  template<typename P, typename Q, typename Phi>
  using OneFlavorRatExactEvenOddPrecWilsonTypeFermMonomial =
                  OneFlavorRatExactEOPrecWilsonTypeFermMonomialT<P,Q,Phi,EvenOddPrecWilsonTypeFermAct>;
 
  template<typename P, typename Q, typename Phi>
    using OneFlavorRatExactSymEvenOddPrecWilsonTypeFermMonomial =
                  OneFlavorRatExactEOPrecWilsonTypeFermMonomialT<P,Q,Phi,SymEvenOddPrecWilsonTypeFermAct>;
 
  //-------------------------------------------------------------------------------------------
  //! Exact 1 flavor even-odd preconditioned fermact monomial constant determinant
  //  Can fill out the S_odd_odd piece
 
  /*! @ingroup monomial
   *
   * Exact 1 flavor even-odd preconditioned fermact monomial.
   * Can supply a default dsdq algorithm
   */
  template<typename P, typename Q, typename Phi,
          template<class,class,class> class EOFermActT>
  class OneFlavorRatExactEOPrecConstDetWilsonTypeFermMonomialT :
    public OneFlavorRatExactEOPrecWilsonTypeFermMonomialT<P,Q,Phi,EOFermActT>
  {
  public:
     //! virtual destructor:
    virtual ~OneFlavorRatExactEOPrecConstDetWilsonTypeFermMonomialT() {}
 
    //! Even even contribution (eg ln det Clover)
    virtual Double S_even_even(const AbsFieldState<P,Q>& s) {
      return Double(0);
    }
 
  protected:
    //!  Replace thiw with PrecConstDet
    virtual const EOFermActT<Phi,P,Q>& getFermAct() const = 0;
  };
 
  template<typename P, typename Q, typename Phi>
  using OneFlavorRatExactEvenOddPrecConstDetWilsonTypeFermMonomial =
                  OneFlavorRatExactEOPrecConstDetWilsonTypeFermMonomialT<P,Q,Phi,EvenOddPrecWilsonTypeFermAct>;
 
  template<typename P, typename Q, typename Phi>
    using OneFlavorRatExactSymEvenOddPrecConstDetWilsonTypeFermMonomial =
                  OneFlavorRatExactEOPrecConstDetWilsonTypeFermMonomialT<P,Q,Phi,SymEvenOddPrecWilsonTypeFermAct>;
}
 
 
#endif