fopr_CloverTerm_eo.cpp

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#include "Fopr/fopr_CloverTerm_eo.h"
#include "Measurements/Gauge/staple_eo.h"

#include "ResourceManager/threadManager_OpenMP.h"
#include "Solver/solver_CG.h"

namespace Imp {
#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

//====================================================================

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

    unique_ptr<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.

    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;
    std::vector<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, "Error at %s: input parameter not found.\n", class_name.c_str());
      exit(EXIT_FAILURE);
    }

    set_parameters(kappa, cSW, bc);
  }


//====================================================================
  void Fopr_CloverTerm_eo::set_parameters(const double kappa, const double cSW,
                                          const std::vector<int> bc)
  {
    //- print input parameters
    vout.general(m_vl, "%s:\n", class_name.c_str());
    vout.general(m_vl, "  kappa = %12.8f\n", kappa);
    vout.general(m_vl, "  cSW   = %12.8f\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();

#if 1
    Parameters params_solver;

    params_solver.set_string("solver_type", "CG");
    params_solver.set_int("maximum_number_of_iteration", 100);
    params_solver.set_int("maximum_number_of_restart", 40);
    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");
#else
    //
#endif

    int    Nconv;
    double diff;

    unique_ptr<Solver_CG> solver(new Solver_CG(this));

#if 1
    solver->set_parameters(params_solver);
#else
    const int    Niter              = 100;
    const int    Nrestart           = 40;
    const double Stopping_condition = 1.0e-30;

    solver->set_parameters(Niter, Nrestart, Stopping_condition);
    solver->set_parameter_verboselevel(Bridge::CRUCIAL);
#endif

    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.set(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);
        }
      }
    }

    // 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);
          }
        }
      }
    }
  }


//====================================================================
  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;

    const double *v1 = f.ptr(0);
    double       *v2 = v.ptr(0);

    double *csw_inv = 0;

    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, "Error at %s: wrong parameter, ieo = %d.\n",
                                            class_name.c_str(), ieo);
      exit(EXIT_FAILURE);
      */
    }

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

    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;

    const double *v1 = f.ptr(0);
    double       *v2 = v.ptr(0);

    double *csw_inv = 0;

    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, "Error at %s: wrong parameter, ieo = %d.\n",
                                            class_name.c_str(), ieo);
      exit(EXIT_FAILURE);
      */
    }

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

    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);

    const double *fp = f.ptr(0);
    double       *vp = v.ptr(0);
    double       *tp = m_T.ptr(0, m_Nvol2 * ieo, 0);

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

    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)
  {
    const double *fp = f.ptr(0);
    double       *vp = v.ptr(0);
    double       *tp = m_T.ptr(0, m_Nvol2 * ieo, 0);

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

    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, "Error at %s: unsupported gamma matrix repr. %s.\n",
                   class_name.c_str(), m_repr.c_str());
      exit(EXIT_FAILURE);
    }
  }


//====================================================================
  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)
  {
    // Staple_eo staple;
    unique_ptr<Staple> staple(Staple::New("EvenOdd"));

    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);

    staple->upper(Cup, *m_Ueo, mu, nu);
    staple->lower(Cdn, *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));
    }

    axpy(w, -1.0, 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));
    }

    axpy(v, -1.0, v2);

    m_shift_eo.forward(v2, v, mu);

    axpy(w, 1.0, v2);

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

    scal(Fst, 0.25);
  }


//====================================================================
  void Fopr_CloverTerm_eo::trSigmaInv(Field_G& tr_sigma_inv, 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);

    assert(tr_sigma_inv.nvol() == m_Nvol);
    assert(tr_sigma_inv.nex() == 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));
          }
        }
      }
    }
  }


//====================================================================
  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=====