fopr_CloverTerm_eo.cpp

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#include "fopr_CloverTerm_eo.h"

#include "threadManager_OpenMP.h"
#include "solver_CG.h"

#ifdef USE_PARAMETERS_FACTORY
#include "parameters_factory.h"
#endif

using std::valarray;


//====================================================================
//- parameter entry
namespace {
  void append_entry(Parameters& param)
  {
    param.Register_double("hopping_parameter", 0.0);
    param.Register_double("clover_coefficient", 0.0);
    param.Register_int_vector("boundary_condition", std::valarray<int>());

    param.Register_string("verbose_level", "NULL");
  }


#ifdef USE_PARAMETERS_FACTORY
  bool init_param = ParametersFactory::Register("Fopr.CloverTerm_eo",
                                                append_entry);
#endif
}
//- end

//- parameters class
Parameters_Fopr_CloverTerm_eo::Parameters_Fopr_CloverTerm_eo()
{ append_entry(*this); }
//- end

const std::string Fopr_CloverTerm_eo::class_name = "Fopr_CloverTerm_eo";

//====================================================================
void Fopr_CloverTerm_eo::init(std::string repr)
{
  m_repr = repr;

  m_Nc    = CommonParameters::Nc();
  m_Nd    = CommonParameters::Nd();
  m_Ndim  = CommonParameters::Ndim();
  m_NinF  = 2 * m_Nc * m_Nd;
  m_Nvol  = CommonParameters::Nvol();
  m_Nvol2 = m_Nvol / 2;

  m_boundary.resize(m_Ndim);

  m_Ueo = 0;

  m_GM.resize(m_Ndim + 1);
  m_SG.resize(m_Ndim * m_Ndim);

  GammaMatrixSet *gmset = GammaMatrixSet::New(m_repr);

  m_GM[0] = gmset->get_GM(gmset->GAMMA1);
  m_GM[1] = gmset->get_GM(gmset->GAMMA2);
  m_GM[2] = gmset->get_GM(gmset->GAMMA3);
  m_GM[3] = gmset->get_GM(gmset->GAMMA4);
  m_GM[4] = gmset->get_GM(gmset->GAMMA5);

  m_SG[sg_index(0, 1)] = gmset->get_GM(gmset->SIGMA12);
  m_SG[sg_index(1, 2)] = gmset->get_GM(gmset->SIGMA23);
  m_SG[sg_index(2, 0)] = gmset->get_GM(gmset->SIGMA31);
  m_SG[sg_index(3, 0)] = gmset->get_GM(gmset->SIGMA41);
  m_SG[sg_index(3, 1)] = gmset->get_GM(gmset->SIGMA42);
  m_SG[sg_index(3, 2)] = gmset->get_GM(gmset->SIGMA43);

  m_SG[sg_index(1, 0)] = m_SG[sg_index(0, 1)].mult(-1);
  m_SG[sg_index(2, 1)] = m_SG[sg_index(1, 2)].mult(-1);
  m_SG[sg_index(0, 2)] = m_SG[sg_index(2, 0)].mult(-1);
  m_SG[sg_index(0, 3)] = m_SG[sg_index(3, 0)].mult(-1);
  m_SG[sg_index(1, 3)] = m_SG[sg_index(3, 1)].mult(-1);
  m_SG[sg_index(2, 3)] = m_SG[sg_index(3, 2)].mult(-1);

  m_SG[sg_index(0, 0)] = gmset->get_GM(gmset->UNITY);
  m_SG[sg_index(1, 1)] = gmset->get_GM(gmset->UNITY);
  m_SG[sg_index(2, 2)] = gmset->get_GM(gmset->UNITY);
  m_SG[sg_index(3, 3)] = gmset->get_GM(gmset->UNITY);
  // these 4 gamma matrices are actually not used.

  delete gmset;

  m_fee_inv = new Field_F(m_Nvol2, m_Nc * m_Nd);
  m_foo_inv = new Field_F(m_Nvol2, m_Nc * m_Nd);

  m_vf.reset(m_Nvol2, 1);
  m_ff.reset(m_Nvol2, 1);

  int Nfst = 6;
  m_T2.resize(2);   // 0: even, 1: odd.
  m_T2[0].reset(m_Nvol2, Nfst);
  m_T2[1].reset(m_Nvol2, Nfst);
}


//====================================================================
void Fopr_CloverTerm_eo::tidyup()
{
  delete m_foo_inv;
  delete m_fee_inv;
}


//====================================================================
void Fopr_CloverTerm_eo::set_parameters(const Parameters& params)
{
  const string str_vlevel = params.get_string("verbose_level");

  m_vl = vout.set_verbose_level(str_vlevel);

  //- fetch and check input parameters
  double        kappa, cSW;
  valarray<int> bc;

  int err = 0;
  err += params.fetch_double("hopping_parameter", kappa);
  err += params.fetch_double("clover_coefficient", cSW);
  err += params.fetch_int_vector("boundary_condition", bc);

  if (err) {
    vout.crucial(m_vl, "%s: fetch error, input parameter not found.\n", class_name.c_str());
    abort();
  }

  set_parameters(kappa, cSW, bc);
}


//====================================================================
void Fopr_CloverTerm_eo::set_parameters(const double kappa, const double cSW,
                                        const std::valarray<int> bc)
{
  //- print input parameters
  vout.general(m_vl, "Parameters of %s:\n", class_name.c_str());
  vout.general(m_vl, "  kappa = %8.4f\n", kappa);
  vout.general(m_vl, "  cSW   = %8.4f\n", cSW);
  for (int mu = 0; mu < m_Ndim; ++mu) {
    vout.general(m_vl, "  boundary[%d] = %2d\n", mu, bc[mu]);
  }

  //- range check
  // NB. kappa,cSW == 0 is allowed.
  assert(bc.size() == m_Ndim);

  //- store values
  m_kappa = kappa;
  m_cSW   = cSW;
  assert(bc.size() == m_Ndim);
  for (int mu = 0; mu < m_Ndim; ++mu) {
    m_boundary[mu] = bc[mu];
  }
}


//====================================================================
void Fopr_CloverTerm_eo::set_config(Field *Ueo)
{
  m_Ueo = (Field_G *)Ueo;

  set_csw();
  solve_csw_inv();
}


//====================================================================
void Fopr_CloverTerm_eo::solve_csw_inv()
{
  double eps2 = CommonParameters::epsilon_criterion2();

  Parameters *params_solver = ParametersFactory::New("Solver");

  params_solver->set_string("solver_type", "CG");
  params_solver->set_int("maximum_number_of_iteration", 1000);
  params_solver->set_double("convergence_criterion_squared", 1.0e-30);
  //- NB. set VerboseLevel to CRUCIAL to suppress frequent messages.
  params_solver->set_string("verbose_level", "Crucial");

  int    Nconv;
  double diff;

  Solver *solver = new Solver_CG(this);
  solver->set_parameters(*params_solver);

  Field_F w(m_Nvol2);
  Field_F w2(m_Nvol2);

  for (int ispin = 0; ispin < m_Nd; ++ispin) {
    for (int icolor = 0; icolor < m_Nc; ++icolor) {
      int spin_color = icolor + m_Nc * ispin;
      w = 0.0;
      for (int isite = 0; isite < m_Nvol2; ++isite) {
        w.set_ri(icolor, ispin, isite, 0, 1, 0);
      }

      if (m_cSW * m_cSW < eps2) {
        m_fee_inv->setpart_ex(spin_color, w, 0);
        m_foo_inv->setpart_ex(spin_color, w, 0);
      } else {
        //        m_fopr_csw->set_mode("even");
        set_mode("even");
        solver->solve(w2, w, Nconv, diff);
        m_fee_inv->setpart_ex(spin_color, w2, 0);

        vout.detailed(m_vl, "  Nconv,diff = %d %12.4e\n", Nconv, diff);

        set_mode("odd");
        solver->solve(w2, w, Nconv, diff);
        m_foo_inv->setpart_ex(spin_color, w2, 0);

        vout.detailed(m_vl, "  Nconv,diff = %d %12.4e\n", Nconv, diff);
      }
    }
  }

  delete params_solver;
  delete solver;

  // redefine the inverse matrix with its dagger.
  double re, im;
  for (int ics = 0; ics < m_Nc * m_Nd; ++ics) {
    for (int site = 0; site < m_Nvol2; ++site) {
      for (int id = 0; id < m_Nd; ++id) {
        for (int ic = 0; ic < m_Nc; ++ic) {
          re = m_foo_inv->cmp_r(ic, id, site, ics);
          im = m_foo_inv->cmp_i(ic, id, site, ics);
          m_foo_inv->set_ri(ic, id, site, ics, re, -im);
          re = m_fee_inv->cmp_r(ic, id, site, ics);
          im = m_fee_inv->cmp_i(ic, id, site, ics);
          m_fee_inv->set_ri(ic, id, site, ics, re, -im);
        }
      }
    }
  }
}


//====================================================================
const Field_F Fopr_CloverTerm_eo::mult_csw_inv(const Field_F& f, const int ieo)
{
  int     nex = f.nex();
  Field_F w(m_Nvol2, nex);

  mult_csw_inv(w, f, ieo);

  return w;
}


//====================================================================
void Fopr_CloverTerm_eo::mult_csw_inv(Field& v,
                                      const Field& f, const int ieo)
{
  int     nex = f.nex();
  Field_F v2(m_Nvol2, nex), f2(m_Nvol2, nex);
  Field_F *csw_inv;

  copy(f2, f);
  v2.set(0.0);

  if (ieo == 0) {
    csw_inv = m_fee_inv;
  } else if (ieo == 1) {
    csw_inv = m_foo_inv;
  } else {
    vout.crucial(m_vl, "%s: wrong parameter, ieo=%d.\n",
                 class_name.c_str(), ieo);
    abort();
  }

  for (int iex = 0; iex < nex; ++iex) {
    for (int isite = 0; isite < m_Nvol2; ++isite) {
      for (int ispin = 0; ispin < m_Nd; ++ispin) {
        for (int icolor = 0; icolor < m_Nc; ++icolor) {
          double re = 0.0;
          double im = 0.0;

          for (int jspin = 0; jspin < m_Nd; ++jspin) {
            for (int jcolor = 0; jcolor < m_Nc; ++jcolor) {
              int spin_color = jcolor + m_Nc * jspin;
              // Hermiteness of clover term is used here.
              re += csw_inv->cmp_r(icolor, ispin, isite, spin_color) *
                    f2.cmp_r(jcolor, jspin, isite, iex);
              re += csw_inv->cmp_i(icolor, ispin, isite, spin_color) *
                    f2.cmp_i(jcolor, jspin, isite, iex);

              im += csw_inv->cmp_r(icolor, ispin, isite, spin_color) *
                    f2.cmp_i(jcolor, jspin, isite, iex);
              im -= csw_inv->cmp_i(icolor, ispin, isite, spin_color) *
                    f2.cmp_r(jcolor, jspin, isite, iex);
            }
          }

          v2.set_ri(icolor, ispin, isite, iex, re, im);
        }
      }
    }
  }
  copy(v, v2);
}


//====================================================================
std::vector<double> Fopr_CloverTerm_eo::csmatrix(const int& site)
{
  std::vector<double> matrix(m_Nc * m_Nc * m_Nd * m_Nd * 2);

  for (int ispin = 0; ispin < m_Nd / 2; ++ispin) {
    for (int icolor = 0; icolor < m_Nc; ++icolor) {
      int ics = icolor + ispin * m_Nc;
      for (int jspin = 0; jspin < m_Nd; ++jspin) {
        int js2 = (jspin + m_Nd / 2) % m_Nd;
        for (int jcolor = 0; jcolor < m_Nc; ++jcolor) {
          int cs1 = jcolor + m_Nc * (jspin + m_Nd * ics);
          int cs2 = jcolor + m_Nc * (jspin + m_Nd * (ics + m_Nc * m_Nd / 2));
          int cc  = jcolor + icolor * m_Nc;
          int ss1 = jspin + ispin * m_Nd;
          int ss2 = js2 + ispin * m_Nd;

          matrix[2 * cs1]     = m_T.cmp_r(cc, site, ss1);
          matrix[2 * cs1 + 1] = m_T.cmp_i(cc, site, ss1);

          matrix[2 * cs2]     = m_T.cmp_r(cc, site, ss2);
          matrix[2 * cs2 + 1] = m_T.cmp_i(cc, site, ss2);
        }
      }
    }
  }

  return matrix;
}


//====================================================================
void Fopr_CloverTerm_eo::D(Field& v, const Field& f, const int ieo)
{
  Field_F vf(v.nvol(), v.nex());
  Field_F ff(f.nvol(), f.nex());
  Field_F wt(f.nvol(), f.nex());

  int     Nfst = 6;
  Field_G T2(m_Nvol2, Nfst);
  int     NinG = T2.nin();

  /*
  for(int ex = 0; ex < Nfst; ++ex){
    for(int isite = 0; isite < m_Nvol2; ++isite){
      for(int in = 0; in < NinG; ++in){
      T2.set(in, isite, ex, m_T.cmp(in, idx.site(isite, ieo), ex));
    }
   }
  }
  */

  copy(ff, f);   //  ff = (Field_F)f;
  copy(vf, ff);
  double coeff = -m_kappa * m_cSW;

  // i s_23 F_23
  mult_iGM(wt, m_SG[sg_index(1, 2)], ff);
  multadd_Field_Gn(vf, 0, m_T2[ieo], 0, wt, 0, coeff);

  // i s_31 F_31
  mult_iGM(wt, m_SG[sg_index(2, 0)], ff);
  multadd_Field_Gn(vf, 0, m_T2[ieo], 1, wt, 0, coeff);

  // i s_12 F_12
  mult_iGM(wt, m_SG[sg_index(0, 1)], ff);
  multadd_Field_Gn(vf, 0, m_T2[ieo], 2, wt, 0, coeff);

  // i s_41 F_41
  mult_iGM(wt, m_SG[sg_index(3, 0)], ff);
  multadd_Field_Gn(vf, 0, m_T2[ieo], 3, wt, 0, coeff);

  // i s_42 F_42
  mult_iGM(wt, m_SG[sg_index(3, 1)], ff);
  multadd_Field_Gn(vf, 0, m_T2[ieo], 4, wt, 0, coeff);

  // i s_43 F_43
  mult_iGM(wt, m_SG[sg_index(3, 2)], ff);
  multadd_Field_Gn(vf, 0, m_T2[ieo], 5, wt, 0, coeff);

  copy(v, vf);

  /*
  Field_F vf(v.nvol(), v.nex());
  Field_F ff(f.nvol(), f.nex());

  ff = (Field_F)f;

  int n_ex = f.nex();

  Vec_SU_N u_vec, d_vec;
  for (int iex = 0; iex < n_ex; ++iex) {
    for (int isite = 0; isite < m_Nvol2; ++isite) {
      for (int ispin = 0; ispin < m_Nd / 2; ++ispin) {
        u_vec.zero();
        d_vec.zero();
        for (int jspin = 0; jspin < m_Nd; ++jspin) {
          int u_spin = jspin + ispin * m_Nd;
          u_vec += m_T.mat(idx.site(isite, ieo), u_spin)
                   * ff.vec(jspin, isite, iex);
          int d_spin = (jspin + m_Nd / 2) % m_Nd + ispin * m_Nd;
          d_vec += m_T.mat(idx.site(isite, ieo), d_spin)
                   * ff.vec(jspin, isite, iex);
        }
        vf.set_vec(ispin, isite, iex, u_vec);
        vf.set_vec(ispin + m_Nd / 2, isite, iex, d_vec);
      }
    }
  }

  v = (Field)vf;
  */
}


//====================================================================
void Fopr_CloverTerm_eo::mult_isigma(Field_F& v, const Field_F& w,
                                     const int mu, const int nu)
{
  assert(mu != nu);
  mult_iGM(v, m_SG[sg_index(mu, nu)], w);
}


//====================================================================
void Fopr_CloverTerm_eo::set_csw()
{
  m_T.set(0.0);

  Field_G F;

  //- F_23
  set_fieldstrength(F, 1, 2);
  copy(m_T, 0, F, 0);

  //- F_31
  set_fieldstrength(F, 2, 0);
  copy(m_T, 1, F, 0);

  //- F_12
  set_fieldstrength(F, 0, 1);
  copy(m_T, 2, F, 0);

  //- F_41
  set_fieldstrength(F, 3, 0);
  copy(m_T, 3, F, 0);

  //- F_42
  set_fieldstrength(F, 3, 1);
  copy(m_T, 4, F, 0);

  //- F_43
  set_fieldstrength(F, 3, 2);
  copy(m_T, 5, F, 0);

  int Nfst = 6;
  int NinG = m_T2[0].nin();
  for (int ieo = 0; ieo < 2; ++ieo) {
    for (int ex = 0; ex < Nfst; ++ex) {
      for (int isite = 0; isite < m_Nvol2; ++isite) {
        for (int in = 0; in < NinG; ++in) {
          m_T2[ieo].set(in, isite, ex, m_T.cmp(in, idx.site(isite, ieo), ex));
        }
      }
    }
  }


  /*
  //- sigma23
  Field_G F;
  set_fieldstrength(F, 1, 2);
  F.xI();
  m_T.addpart_ex(1, F, 0);
  m_T.addpart_ex(4, F, 0);

  //- sigma31
  set_fieldstrength(F, 2, 0);
  m_T.addpart_ex(1, F, 0);
  scal(F, -1.0);
  m_T.addpart_ex(4, F, 0);

  //- sigma12
  set_fieldstrength(F, 0, 1);
  F.xI();
  m_T.addpart_ex(0, F, 0);
  scal(F, -1.0);
  m_T.addpart_ex(5, F, 0);

  //- sigma41
  set_fieldstrength(F, 3, 0);
  F.xI();
  scal(F, -1.0);  //  F *= -1.0;
  m_T.addpart_ex(3, F, 0);
  m_T.addpart_ex(6, F, 0);

  //- sigma42
  set_fieldstrength(F, 3, 1);
  m_T.addpart_ex(6, F, 0);
  scal(F, -1.0);
  m_T.addpart_ex(3, F, 0);

  //- sigma43
  set_fieldstrength(F, 3, 2);
  F.xI();
  m_T.addpart_ex(7, F, 0);
  scal(F, -1.0);
  m_T.addpart_ex(2, F, 0);

  scal(m_T, -m_kappa*m_cSW);

  //- add unit color matrix for diag part of dirac matrix;
  for (int ispin = 0; ispin < m_Nd / 2; ++ispin) {
    int spin_diag = ispin + m_Nd * ispin;
    for (int isite = 0; isite < m_Nvol; ++isite) {
      for (int icolor = 0; icolor < m_Nc; ++icolor) {
        int cc2 = 2 * (icolor * m_Nc + icolor);
        m_T.add(cc2, isite, spin_diag, 1.0);
      }
    }
  }
  */
}


//====================================================================
void Fopr_CloverTerm_eo::set_fieldstrength(Field_G& Fst,
                                           const int mu, const int nu)
{
  Staples_eo staple;

  Field_G Cup(m_Nvol, 1), Cdn(m_Nvol, 1);
  Field_G Umu(m_Nvol, 1);
  Field_G w(m_Nvol, 1), v(m_Nvol, 1), v2(m_Nvol, 1);

  Cup = staple.upper(m_Ueo, mu, nu);
  Cdn = staple.lower(m_Ueo, mu, nu);
  Umu.setpart_ex(0, *m_Ueo, mu);

  for (int site = 0; site < m_Nvol; ++site) {
    w.set_mat(site, 0, Umu.mat(site) * Cup.mat_dag(site));
  }

  for (int site = 0; site < m_Nvol; ++site) {
    v2.set_mat(site, 0, Umu.mat(site) * Cdn.mat_dag(site));
  }

  w -= v2;

  for (int site = 0; site < m_Nvol; ++site) {
    v.set_mat(site, 0, Cup.mat_dag(site) * Umu.mat(site));
  }

  for (int site = 0; site < m_Nvol; ++site) {
    v2.set_mat(site, 0, Cdn.mat_dag(site) * Umu.mat(site));
  }

  v -= v2;

  m_shift_eo.forward(v2, v, mu);

  w += v2;

  for (int site = 0; site < m_Nvol; ++site) {
    Fst.set_mat(site, 0, w.mat(site).ah());
  }

  Fst *= 0.25;
}


//====================================================================
const Field_G Fopr_CloverTerm_eo::trSigmaInv(const int mu, const int nu)
{
  int      nex_finv = m_fee_inv->nex();
  Vec_SU_N v;
  Field_F  sigma_inv(m_Nvol, nex_finv);
  Field_G  tr_sigma_inv(m_Nvol, 1);

  {
    Field_F sigma_eo_inv(m_Nvol2, nex_finv);
    mult_isigma(sigma_eo_inv, *m_fee_inv, mu, nu);
    m_idx.reverseField(sigma_inv, sigma_eo_inv, 0);
    mult_isigma(sigma_eo_inv, *m_foo_inv, mu, nu);
    m_idx.reverseField(sigma_inv, sigma_eo_inv, 1);
  }

  for (int isite = 0; isite < m_Nvol; ++isite) {
    for (int ispin = 0; ispin < m_Nd; ++ispin) {
      for (int icolor = 0; icolor < m_Nc; ++icolor) {
        v = sigma_inv.vec(ispin, isite, icolor + m_Nc * ispin);
        for (int jcolor = 0; jcolor < m_Nc; ++jcolor) {
          int cc = icolor + m_Nc * jcolor;
          tr_sigma_inv.set_r(cc, isite, 0, v.r(jcolor));
          tr_sigma_inv.set_i(cc, isite, 0, v.i(jcolor));
        }
      }
    }
  }
  return tr_sigma_inv;
}


//====================================================================
double Fopr_CloverTerm_eo::flop_count()
{
  // The following counting explicitly depends on the implementation
  // and to be recalculated when the code is modified.
  // Present counting is based on rev.1107. [24 Aug 2014 H.Matsufuru]

  int    Lvol      = CommonParameters::Lvol();
  double flop_site =
    static_cast<double>(8 * m_Nc * m_Nc * m_Nd * m_Nd);

  double flop = flop_site * static_cast<double>(Lvol / 2);

  return flop;
}


//====================================================================
//============================================================END=====