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;

#if defined USE_GROUP_SU3
#include "fopr_Wilson_impl_SU3.inc"
#elif defined USE_GROUP_SU2
#include "fopr_Wilson_impl_SU2.inc"
#elif defined USE_GROUP_SU_N
#include "fopr_Wilson_impl_SU_N.inc"
#endif

//====================================================================
//- 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);
}


//====================================================================
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 {
        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)
{
  if (m_repr == "Dirac") {
    mult_csw_inv_dirac(v, f, ieo);
  } else if (m_repr == "Chiral") {
    mult_csw_inv_chiral(v, f, ieo);
  }
}


//====================================================================
void Fopr_CloverTerm_eo::mult_csw_inv_dirac(Field& v,
                                            const Field& f, const int ieo)
{
  int Nvc = 2 * m_Nc;

  double *v1 = const_cast<Field *>(&f)->ptr(0);
  double *v2 = v.ptr(0);
  double *csw_inv;

  if (ieo == 0) {
    csw_inv = m_fee_inv->ptr(0);
  } else if (ieo == 1) {
    csw_inv = m_foo_inv->ptr(0);

    /*
  } else {
    vout.crucial(m_vl, "%s: wrong parameter, ieo = %d.\n",
                                          class_name.c_str(), ieo);
    abort();
    */
  }

  // threadding applied.
  int nth = ThreadManager_OpenMP::get_num_threads();
  int ith = ThreadManager_OpenMP::get_thread_id();
  int is  = m_Nvol2 * ith / nth;
  int ns  = m_Nvol2 * (ith + 1) / nth;

  int Nd2 = m_Nd / 2;
  for (int site = is; site < ns; ++site) {
    for (int icd = 0; icd < m_Nc * Nd2; ++icd) {
      int iv2 = 2 * icd + m_NinF * site;
      v2[iv2]     = 0.0;
      v2[iv2 + 1] = 0.0;
      for (int jd = 0; jd < m_Nd; ++jd) {
        int jcd = Nvc * jd;
        int iv  = jcd + m_NinF * site;
        int ig  = jcd + m_NinF * (site + m_Nvol2 * icd);
        v2[iv2]     += mult_uv_r(&csw_inv[ig], &v1[iv], m_Nc);
        v2[iv2 + 1] += mult_uv_i(&csw_inv[ig], &v1[iv], m_Nc);
      }
    }

    for (int icd = 0; icd < m_Nc * Nd2; ++icd) {
      int iv2 = 2 * (icd + m_Nc * Nd2) + m_NinF * site;
      v2[iv2]     = 0.0;
      v2[iv2 + 1] = 0.0;
      for (int jd = 0; jd < m_Nd; ++jd) {
        int jd2 = (jd + Nd2) % m_Nd;
        int iv  = Nvc * jd + m_NinF * site;
        int ig  = Nvc * jd2 + m_NinF * (site + m_Nvol2 * icd);
        v2[iv2]     += mult_uv_r(&csw_inv[ig], &v1[iv], m_Nc);
        v2[iv2 + 1] += mult_uv_i(&csw_inv[ig], &v1[iv], m_Nc);
      }
    }
  }
#pragma omp barrier
}


//====================================================================
void Fopr_CloverTerm_eo::mult_csw_inv_chiral(Field& v,
                                             const Field& f, const int ieo)
{
  int Nvc = 2 * m_Nc;

  double *v1 = const_cast<Field *>(&f)->ptr(0);
  double *v2 = v.ptr(0);
  double *csw_inv;

  if (ieo == 0) {
    csw_inv = m_fee_inv->ptr(0);
  } else if (ieo == 1) {
    csw_inv = m_foo_inv->ptr(0);

    /*
  } else {
    vout.crucial(m_vl, "%s: wrong parameter, ieo = %d.\n",
                                          class_name.c_str(), ieo);
    abort();
    */
  }

  // threadding applied.
  int nth = ThreadManager_OpenMP::get_num_threads();
  int ith = ThreadManager_OpenMP::get_thread_id();
  int is  = m_Nvol2 * ith / nth;
  int ns  = m_Nvol2 * (ith + 1) / nth;

  for (int site = is; site < ns; ++site) {
    for (int icd = 0; icd < m_Nc * m_Nd / 2; ++icd) {
      int iv2 = 2 * icd + m_NinF * site;
      v2[iv2]     = 0.0;
      v2[iv2 + 1] = 0.0;

      for (int jd = 0; jd < m_Nd / 2; ++jd) {
        int jcd = Nvc * jd;
        int iv  = jcd + m_NinF * site;
        int ig  = jcd + m_NinF * (site + m_Nvol2 * icd);
        v2[iv2]     += mult_uv_r(&csw_inv[ig], &v1[iv], m_Nc);
        v2[iv2 + 1] += mult_uv_i(&csw_inv[ig], &v1[iv], m_Nc);
      }
    }

    for (int icd = m_Nc * m_Nd / 2; icd < m_Nc * m_Nd; ++icd) {
      int iv2 = 2 * icd + m_NinF * site;
      v2[iv2]     = 0.0;
      v2[iv2 + 1] = 0.0;

      for (int jd = m_Nd / 2; jd < m_Nd; ++jd) {
        int jcd = Nvc * jd;
        int iv  = jcd + m_NinF * site;
        int ig  = jcd + m_NinF * (site + m_Nvol2 * icd);
        v2[iv2]     += mult_uv_r(&csw_inv[ig], &v1[iv], m_Nc);
        v2[iv2 + 1] += mult_uv_i(&csw_inv[ig], &v1[iv], m_Nc);
      }
    }
  }
#pragma omp barrier
}


//====================================================================
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)
{
  if (m_repr == "Dirac") {
    D_dirac(v, f, ieo);
  } else if (m_repr == "Chiral") {
    D_chiral(v, f, ieo);
  }
}


//====================================================================
void Fopr_CloverTerm_eo::D_dirac(Field& v, const Field& f, const int ieo)
{
  //  assert(f.nvol() == m_Nvol2);
  //  assert(f.nex()  == 1);
  //  assert(v.nvol() == m_Nvol2);
  //  assert(v.nex()  == 1);

  double *fp = const_cast<Field *>(&f)->ptr(0);
  double *vp = v.ptr(0);
  double *tp = m_T.ptr(0, m_Nvol2 * ieo, 0);

  int nth = ThreadManager_OpenMP::get_num_threads();
  int ith = ThreadManager_OpenMP::get_thread_id();
  int is  = m_Nvol2 * ith / nth;
  int ns  = m_Nvol2 * (ith + 1) / nth;

  int Nvc  = 2 * m_Nc;
  int Nd2  = m_Nd / 2;
  int NinF = 2 * m_Nc * m_Nd;
  int NinG = 2 * m_Nc * m_Nc;

  for (int site = is; site < ns; ++site) {
    for (int id = 0; id < Nd2; ++id) {
      for (int ic = 0; ic < m_Nc; ++ic) {
        int icd = ic + m_Nc * id;

        int iv2 = 2 * icd + NinF * site;
        vp[iv2]     = 0.0;
        vp[iv2 + 1] = 0.0;
        for (int jd = 0; jd < m_Nd; ++jd) {
          int iv = Nvc * jd + NinF * site;
          int ig = Nvc * ic + NinG * (site + m_Nvol * (id * m_Nd + jd));
          vp[iv2]     += mult_uv_r(&tp[ig], &fp[iv], m_Nc);
          vp[iv2 + 1] += mult_uv_i(&tp[ig], &fp[iv], m_Nc);
        }

        iv2        += Nvc * Nd2;
        vp[iv2]     = 0.0;
        vp[iv2 + 1] = 0.0;
        for (int jd = 0; jd < m_Nd; ++jd) {
          int jd2 = (2 + jd) % m_Nd;
          int iv  = Nvc * jd + NinF * site;
          int ig  = Nvc * ic + NinG * (site + m_Nvol * (id * m_Nd + jd2));
          vp[iv2]     += mult_uv_r(&tp[ig], &fp[iv], m_Nc);
          vp[iv2 + 1] += mult_uv_i(&tp[ig], &fp[iv], m_Nc);
        }
      }
    }
  }
#pragma omp barrier
}


//====================================================================
void Fopr_CloverTerm_eo::D_chiral(Field& v, const Field& f, const int ieo)
{
  double *fp = const_cast<Field *>(&f)->ptr(0);
  double *vp = v.ptr(0);
  double *tp = m_T.ptr(0, m_Nvol2 * ieo, 0);

  int nth = ThreadManager_OpenMP::get_num_threads();
  int ith = ThreadManager_OpenMP::get_thread_id();
  int is  = m_Nvol2 * ith / nth;
  int ns  = m_Nvol2 * (ith + 1) / nth;

  int Nvc  = 2 * m_Nc;
  int Nd2  = m_Nd / 2;
  int NinF = 2 * m_Nc * m_Nd;
  int NinG = 2 * m_Nc * m_Nc;

  for (int site = is; site < ns; ++site) {
    for (int id = 0; id < Nd2; ++id) {
      for (int ic = 0; ic < m_Nc; ++ic) {
        int icd = ic + m_Nc * id;

        int iv2 = 2 * icd + NinF * site;
        vp[iv2]     = 0.0;
        vp[iv2 + 1] = 0.0;
        for (int jd = 0; jd < Nd2; ++jd) {
          int iv = Nvc * jd + NinF * site;
          int ig = Nvc * ic + NinG * (site + m_Nvol * (id * Nd2 + jd));
          vp[iv2]     += mult_uv_r(&tp[ig], &fp[iv], m_Nc);
          vp[iv2 + 1] += mult_uv_i(&tp[ig], &fp[iv], m_Nc);
        }

        iv2        += Nvc * Nd2;
        vp[iv2]     = 0.0;
        vp[iv2 + 1] = 0.0;
        for (int jd = 0; jd < Nd2; ++jd) {
          int iv = Nvc * (Nd2 + jd) + NinF * site;
          int ig = Nvc * ic + NinG * (site + m_Nvol * (m_Nd + id * Nd2 + jd));
          vp[iv2]     += mult_uv_r(&tp[ig], &fp[iv], m_Nc);
          vp[iv2 + 1] += mult_uv_i(&tp[ig], &fp[iv], m_Nc);
        }
      }
    }
  }
#pragma omp barrier
}


//====================================================================
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()
{
  if (m_repr == "Dirac") {
    set_csw_dirac();
  } else if (m_repr == "Chiral") {
    set_csw_chiral();
  } else {
    vout.crucial(m_vl, "%s: unsupported gamma matrix repr. %s.\n",
                 class_name.c_str(), m_repr.c_str());
    abort();
  }
}


//====================================================================
void Fopr_CloverTerm_eo::set_csw_dirac()
{
  // The clover term in the Dirac representation is as spin-space
  // matrix
  //   [ P Q ]
  //   [ Q P ],
  // where P and Q are 2x2 block matrices as
  //   P =  [          iF(1,2)   F(3,1) + iF(2,3) ]
  //        [-F(3,1) + iF(2,3)          - iF(1,2) ]
  // and
  //   Q =  [        - iF(4,3)  -F(4,2) - iF(4,1) ]
  //        [ F(4,2) - iF(4,1)            iF(4,3) ]
  // up to the coefficient.
  // in the following what defined is
  // [ P Q ] = [ T(0) T(1)  T(2) T(3) ]
  //           [ T(4) T(5)  T(6) T(7) ].

  m_T.set(0.0);

  //- sigma23
  Field_G F;
  set_fieldstrength(F, 1, 2);
  F.xI();
  axpy(m_T, 1, 1.0, F, 0);
  axpy(m_T, 4, 1.0, F, 0);

  //- sigma31
  set_fieldstrength(F, 2, 0);
  axpy(m_T, 1, 1.0, F, 0);
  axpy(m_T, 4, -1.0, F, 0);

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

  //- sigma41
  set_fieldstrength(F, 3, 0);
  F.xI();
  axpy(m_T, 3, -1.0, F, 0);
  axpy(m_T, 6, -1.0, F, 0);

  //- sigma42
  set_fieldstrength(F, 3, 1);
  axpy(m_T, 3, -1.0, F, 0);
  axpy(m_T, 6, 1.0, F, 0);

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

  scal(m_T, -m_kappa * m_cSW);

  Field_G Unity(m_Nvol, 1);
  Unity.set_unit();
  axpy(m_T, 0, 1.0, Unity, 0);
  axpy(m_T, 5, 1.0, Unity, 0);
}


//====================================================================
void Fopr_CloverTerm_eo::set_csw_chiral()
{
  // The clover term in the Dirac representation is
  // as spin-space matrix
  //  [ P+Q  0  ]
  //  [ 0   P-Q ],
  // where P and Q are 2x2 block matrices as
  //        [          iF(1,2) |  F(3,1) + iF(2,3) ]
  //   P =  [ -----------------+------------------ ]
  //        [-F(3,1) + iF(2,3) |         - iF(1,2) ]
  // and
  //        [        - iF(4,3) | -F(4,2) - iF(4,1) ]
  //   Q =  [ -----------------+------------------ ]
  //        [ F(4,2) - iF(4,1) |           iF(4,3) ]
  // up to the coefficient.
  // in the following what defined is
  //        [ T(0) | T(1) ]          [ T(4) | T(5) ]
  //  P+Q = [ -----+----- ]  P - Q = [ -----+----- ]
  //        [ T(2) | T(3) ]          [ T(6) | T(7) ]

  m_T.set(0.0);

  Field_G F;

  //- sigma23
  set_fieldstrength(F, 1, 2);
  F.xI();
  axpy(m_T, 1, 1.0, F, 0);
  axpy(m_T, 2, 1.0, F, 0);
  axpy(m_T, 5, 1.0, F, 0);
  axpy(m_T, 6, 1.0, F, 0);

  //- sigma31
  set_fieldstrength(F, 2, 0);
  axpy(m_T, 1, 1.0, F, 0);
  axpy(m_T, 2, -1.0, F, 0);
  axpy(m_T, 5, 1.0, F, 0);
  axpy(m_T, 6, -1.0, F, 0);

  //- sigma12
  set_fieldstrength(F, 0, 1);
  F.xI();
  axpy(m_T, 0, 1.0, F, 0);
  axpy(m_T, 3, -1.0, F, 0);
  axpy(m_T, 4, 1.0, F, 0);
  axpy(m_T, 7, -1.0, F, 0);

  //- sigma41
  set_fieldstrength(F, 3, 0);
  F.xI();
  axpy(m_T, 1, -1.0, F, 0);
  axpy(m_T, 2, -1.0, F, 0);
  axpy(m_T, 5, 1.0, F, 0);
  axpy(m_T, 6, 1.0, F, 0);

  //- sigma42
  set_fieldstrength(F, 3, 1);
  axpy(m_T, 1, -1.0, F, 0);
  axpy(m_T, 2, 1.0, F, 0);
  axpy(m_T, 5, 1.0, F, 0);
  axpy(m_T, 6, -1.0, F, 0);

  //- sigma43
  set_fieldstrength(F, 3, 2);
  F.xI();
  axpy(m_T, 0, -1.0, F, 0);
  axpy(m_T, 3, 1.0, F, 0);
  axpy(m_T, 4, 1.0, F, 0);
  axpy(m_T, 7, -1.0, F, 0);

  scal(m_T, -m_kappa * m_cSW);

  Field_G Unity(m_Nvol, 1);
  Unity.set_unit();
  axpy(m_T, 0, 1.0, Unity, 0);
  axpy(m_T, 3, 1.0, Unity, 0);
  axpy(m_T, 4, 1.0, Unity, 0);
  axpy(m_T, 7, 1.0, Unity, 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 = 0.0;

  if (m_repr == "Dirac") {
    flop_site = static_cast<double>(8 * m_Nc * m_Nc * m_Nd * m_Nd);
  } else if (m_repr == "Chiral") {
    flop_site = static_cast<double>(4 * m_Nc * m_Nc * m_Nd * m_Nd);
  }

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

  return flop;
}


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