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Namespace, clean up
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paboyle
@@ -28,475 +28,474 @@ with this program; if not, write to the Free Software Foundation, Inc.,
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See the full license in the file "LICENSE" in the top level distribution directory
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*************************************************************************************/
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/* END LEGAL */
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/* END LEGAL */
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#include <Grid/Grid_Eigen_Dense.h>
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#include <Grid/qcd/action/fermion/FermionCore.h>
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#include <Grid/qcd/action/fermion/MobiusEOFAFermion.h>
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namespace Grid {
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namespace QCD {
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NAMESPACE_BEGIN(Grid);
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template<class Impl>
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MobiusEOFAFermion<Impl>::MobiusEOFAFermion(
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GaugeField &_Umu,
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GridCartesian &FiveDimGrid,
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GridRedBlackCartesian &FiveDimRedBlackGrid,
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GridCartesian &FourDimGrid,
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GridRedBlackCartesian &FourDimRedBlackGrid,
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RealD _mq1, RealD _mq2, RealD _mq3,
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RealD _shift, int _pm, RealD _M5,
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RealD _b, RealD _c, const ImplParams &p) :
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AbstractEOFAFermion<Impl>(_Umu, FiveDimGrid, FiveDimRedBlackGrid,
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FourDimGrid, FourDimRedBlackGrid, _mq1, _mq2, _mq3,
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_shift, _pm, _M5, _b, _c, p)
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{
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int Ls = this->Ls;
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template<class Impl>
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MobiusEOFAFermion<Impl>::MobiusEOFAFermion(
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GaugeField &_Umu,
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GridCartesian &FiveDimGrid,
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GridRedBlackCartesian &FiveDimRedBlackGrid,
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GridCartesian &FourDimGrid,
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GridRedBlackCartesian &FourDimRedBlackGrid,
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RealD _mq1, RealD _mq2, RealD _mq3,
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RealD _shift, int _pm, RealD _M5,
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RealD _b, RealD _c, const ImplParams &p) :
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AbstractEOFAFermion<Impl>(_Umu, FiveDimGrid, FiveDimRedBlackGrid,
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FourDimGrid, FourDimRedBlackGrid, _mq1, _mq2, _mq3,
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_shift, _pm, _M5, _b, _c, p)
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{
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int Ls = this->Ls;
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RealD eps = 1.0;
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Approx::zolotarev_data *zdata = Approx::higham(eps, this->Ls);
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assert(zdata->n == this->Ls);
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RealD eps = 1.0;
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Approx::zolotarev_data *zdata = Approx::higham(eps, this->Ls);
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assert(zdata->n == this->Ls);
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std::cout << GridLogMessage << "MobiusEOFAFermion (b=" << _b <<
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",c=" << _c << ") with Ls=" << Ls << std::endl;
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this->SetCoefficientsTanh(zdata, _b, _c);
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std::cout << GridLogMessage << "EOFA parameters: (mq1=" << _mq1 <<
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",mq2=" << _mq2 << ",mq3=" << _mq3 << ",shift=" << _shift <<
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",pm=" << _pm << ")" << std::endl;
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std::cout << GridLogMessage << "MobiusEOFAFermion (b=" << _b <<
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",c=" << _c << ") with Ls=" << Ls << std::endl;
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this->SetCoefficientsTanh(zdata, _b, _c);
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std::cout << GridLogMessage << "EOFA parameters: (mq1=" << _mq1 <<
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",mq2=" << _mq2 << ",mq3=" << _mq3 << ",shift=" << _shift <<
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",pm=" << _pm << ")" << std::endl;
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Approx::zolotarev_free(zdata);
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Approx::zolotarev_free(zdata);
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if(_shift != 0.0){
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SetCoefficientsPrecondShiftOps();
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if(_shift != 0.0){
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SetCoefficientsPrecondShiftOps();
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} else {
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Mooee_shift.resize(Ls, 0.0);
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MooeeInv_shift_lc.resize(Ls, 0.0);
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MooeeInv_shift_norm.resize(Ls, 0.0);
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MooeeInvDag_shift_lc.resize(Ls, 0.0);
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MooeeInvDag_shift_norm.resize(Ls, 0.0);
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}
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}
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/****************************************************************
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* Additional EOFA operators only called outside the inverter.
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* Since speed is not essential, simple axpby-style
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* implementations should be fine.
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***************************************************************/
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template<class Impl>
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void MobiusEOFAFermion<Impl>::Omega(const FermionField& psi, FermionField& Din, int sign, int dag)
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{
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int Ls = this->Ls;
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RealD alpha = this->alpha;
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Din = zero;
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if((sign == 1) && (dag == 0)) { // \Omega_{+}
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for(int s=0; s<Ls; ++s){
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axpby_ssp(Din, 0.0, psi, 2.0*std::pow(1.0-alpha,Ls-s-1)/std::pow(1.0+alpha,Ls-s), psi, s, 0);
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}
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} else if((sign == -1) && (dag == 0)) { // \Omega_{-}
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for(int s=0; s<Ls; ++s){
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axpby_ssp(Din, 0.0, psi, 2.0*std::pow(1.0-alpha,s)/std::pow(1.0+alpha,s+1), psi, s, 0);
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}
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} else if((sign == 1 ) && (dag == 1)) { // \Omega_{+}^{\dagger}
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for(int sp=0; sp<Ls; ++sp){
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axpby_ssp(Din, 1.0, Din, 2.0*std::pow(1.0-alpha,Ls-sp-1)/std::pow(1.0+alpha,Ls-sp), psi, 0, sp);
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}
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} else if((sign == -1) && (dag == 1)) { // \Omega_{-}^{\dagger}
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for(int sp=0; sp<Ls; ++sp){
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axpby_ssp(Din, 1.0, Din, 2.0*std::pow(1.0-alpha,sp)/std::pow(1.0+alpha,sp+1), psi, 0, sp);
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}
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}
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}
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// This is the operator relating the usual Ddwf to TWQCD's EOFA Dirac operator (arXiv:1706.05843, Eqn. 6).
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// It also relates the preconditioned and unpreconditioned systems described in Appendix B.2.
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template<class Impl>
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void MobiusEOFAFermion<Impl>::Dtilde(const FermionField& psi, FermionField& chi)
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{
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int Ls = this->Ls;
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RealD b = 0.5 * ( 1.0 + this->alpha );
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RealD c = 0.5 * ( 1.0 - this->alpha );
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RealD mq1 = this->mq1;
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for(int s=0; s<Ls; ++s){
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if(s == 0) {
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axpby_ssp_pminus(chi, b, psi, -c, psi, s, s+1);
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axpby_ssp_pplus (chi, 1.0, chi, mq1*c, psi, s, Ls-1);
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} else if(s == (Ls-1)) {
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axpby_ssp_pminus(chi, b, psi, mq1*c, psi, s, 0);
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axpby_ssp_pplus (chi, 1.0, chi, -c, psi, s, s-1);
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} else {
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axpby_ssp_pminus(chi, b, psi, -c, psi, s, s+1);
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axpby_ssp_pplus (chi, 1.0, chi, -c, psi, s, s-1);
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}
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}
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}
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template<class Impl>
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void MobiusEOFAFermion<Impl>::DtildeInv(const FermionField& psi, FermionField& chi)
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{
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int Ls = this->Ls;
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RealD m = this->mq1;
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RealD c = 0.5 * this->alpha;
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RealD d = 0.5;
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RealD DtInv_p(0.0), DtInv_m(0.0);
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RealD N = std::pow(c+d,Ls) + m*std::pow(c-d,Ls);
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FermionField tmp(this->FermionGrid());
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for(int s=0; s<Ls; ++s){
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for(int sp=0; sp<Ls; ++sp){
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DtInv_p = m * std::pow(-1.0,s-sp+1) * std::pow(c-d,Ls+s-sp) / std::pow(c+d,s-sp+1) / N;
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DtInv_p += (s < sp) ? 0.0 : std::pow(-1.0,s-sp) * std::pow(c-d,s-sp) / std::pow(c+d,s-sp+1);
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DtInv_m = m * std::pow(-1.0,sp-s+1) * std::pow(c-d,Ls+sp-s) / std::pow(c+d,sp-s+1) / N;
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DtInv_m += (s > sp) ? 0.0 : std::pow(-1.0,sp-s) * std::pow(c-d,sp-s) / std::pow(c+d,sp-s+1);
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if(sp == 0){
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axpby_ssp_pplus (tmp, 0.0, tmp, DtInv_p, psi, s, sp);
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axpby_ssp_pminus(tmp, 0.0, tmp, DtInv_m, psi, s, sp);
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} else {
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Mooee_shift.resize(Ls, 0.0);
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MooeeInv_shift_lc.resize(Ls, 0.0);
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MooeeInv_shift_norm.resize(Ls, 0.0);
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MooeeInvDag_shift_lc.resize(Ls, 0.0);
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MooeeInvDag_shift_norm.resize(Ls, 0.0);
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axpby_ssp_pplus (tmp, 1.0, tmp, DtInv_p, psi, s, sp);
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axpby_ssp_pminus(tmp, 1.0, tmp, DtInv_m, psi, s, sp);
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}
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}}
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}
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/*****************************************************************************************************/
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template<class Impl>
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RealD MobiusEOFAFermion<Impl>::M(const FermionField& psi, FermionField& chi)
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{
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int Ls = this->Ls;
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FermionField Din(psi._grid);
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this->Meooe5D(psi, Din);
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this->DW(Din, chi, DaggerNo);
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axpby(chi, 1.0, 1.0, chi, psi);
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this->M5D(psi, chi);
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return(norm2(chi));
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}
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template<class Impl>
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RealD MobiusEOFAFermion<Impl>::Mdag(const FermionField& psi, FermionField& chi)
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{
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int Ls = this->Ls;
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FermionField Din(psi._grid);
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this->DW(psi, Din, DaggerYes);
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this->MeooeDag5D(Din, chi);
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this->M5Ddag(psi, chi);
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axpby(chi, 1.0, 1.0, chi, psi);
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return(norm2(chi));
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}
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/********************************************************************
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* Performance critical fermion operators called inside the inverter
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********************************************************************/
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template<class Impl>
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void MobiusEOFAFermion<Impl>::M5D(const FermionField& psi, FermionField& chi)
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{
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int Ls = this->Ls;
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std::vector<Coeff_t> diag(Ls,1.0);
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std::vector<Coeff_t> upper(Ls,-1.0); upper[Ls-1] = this->mq1;
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std::vector<Coeff_t> lower(Ls,-1.0); lower[0] = this->mq1;
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// no shift term
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if(this->shift == 0.0){ this->M5D(psi, chi, chi, lower, diag, upper); }
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// fused M + shift operation
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else{ this->M5D_shift(psi, chi, chi, lower, diag, upper, Mooee_shift); }
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}
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template<class Impl>
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void MobiusEOFAFermion<Impl>::M5Ddag(const FermionField& psi, FermionField& chi)
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{
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int Ls = this->Ls;
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std::vector<Coeff_t> diag(Ls,1.0);
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std::vector<Coeff_t> upper(Ls,-1.0); upper[Ls-1] = this->mq1;
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std::vector<Coeff_t> lower(Ls,-1.0); lower[0] = this->mq1;
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// no shift term
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if(this->shift == 0.0){ this->M5Ddag(psi, chi, chi, lower, diag, upper); }
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// fused M + shift operation
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else{ this->M5Ddag_shift(psi, chi, chi, lower, diag, upper, Mooee_shift); }
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}
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// half checkerboard operations
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template<class Impl>
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void MobiusEOFAFermion<Impl>::Mooee(const FermionField& psi, FermionField& chi)
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{
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int Ls = this->Ls;
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// coefficients of Mooee
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std::vector<Coeff_t> diag = this->bee;
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std::vector<Coeff_t> upper(Ls);
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std::vector<Coeff_t> lower(Ls);
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for(int s=0; s<Ls; s++){
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upper[s] = -this->cee[s];
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lower[s] = -this->cee[s];
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}
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upper[Ls-1] *= -this->mq1;
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lower[0] *= -this->mq1;
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// no shift term
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if(this->shift == 0.0){ this->M5D(psi, psi, chi, lower, diag, upper); }
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// fused M + shift operation
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else { this->M5D_shift(psi, psi, chi, lower, diag, upper, Mooee_shift); }
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}
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template<class Impl>
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void MobiusEOFAFermion<Impl>::MooeeDag(const FermionField& psi, FermionField& chi)
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{
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int Ls = this->Ls;
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// coefficients of MooeeDag
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std::vector<Coeff_t> diag = this->bee;
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std::vector<Coeff_t> upper(Ls);
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std::vector<Coeff_t> lower(Ls);
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for(int s=0; s<Ls; s++){
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if(s==0) {
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upper[s] = -this->cee[s+1];
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lower[s] = this->mq1*this->cee[Ls-1];
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} else if(s==(Ls-1)) {
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upper[s] = this->mq1*this->cee[0];
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lower[s] = -this->cee[s-1];
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} else {
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upper[s] = -this->cee[s+1];
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lower[s] = -this->cee[s-1];
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}
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/****************************************************************
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* Additional EOFA operators only called outside the inverter.
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* Since speed is not essential, simple axpby-style
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* implementations should be fine.
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***************************************************************/
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template<class Impl>
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void MobiusEOFAFermion<Impl>::Omega(const FermionField& psi, FermionField& Din, int sign, int dag)
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{
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int Ls = this->Ls;
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RealD alpha = this->alpha;
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Din = zero;
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if((sign == 1) && (dag == 0)) { // \Omega_{+}
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for(int s=0; s<Ls; ++s){
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axpby_ssp(Din, 0.0, psi, 2.0*std::pow(1.0-alpha,Ls-s-1)/std::pow(1.0+alpha,Ls-s), psi, s, 0);
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}
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} else if((sign == -1) && (dag == 0)) { // \Omega_{-}
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for(int s=0; s<Ls; ++s){
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axpby_ssp(Din, 0.0, psi, 2.0*std::pow(1.0-alpha,s)/std::pow(1.0+alpha,s+1), psi, s, 0);
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}
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} else if((sign == 1 ) && (dag == 1)) { // \Omega_{+}^{\dagger}
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for(int sp=0; sp<Ls; ++sp){
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axpby_ssp(Din, 1.0, Din, 2.0*std::pow(1.0-alpha,Ls-sp-1)/std::pow(1.0+alpha,Ls-sp), psi, 0, sp);
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}
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} else if((sign == -1) && (dag == 1)) { // \Omega_{-}^{\dagger}
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for(int sp=0; sp<Ls; ++sp){
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axpby_ssp(Din, 1.0, Din, 2.0*std::pow(1.0-alpha,sp)/std::pow(1.0+alpha,sp+1), psi, 0, sp);
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}
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}
|
||||
}
|
||||
|
||||
// This is the operator relating the usual Ddwf to TWQCD's EOFA Dirac operator (arXiv:1706.05843, Eqn. 6).
|
||||
// It also relates the preconditioned and unpreconditioned systems described in Appendix B.2.
|
||||
template<class Impl>
|
||||
void MobiusEOFAFermion<Impl>::Dtilde(const FermionField& psi, FermionField& chi)
|
||||
{
|
||||
int Ls = this->Ls;
|
||||
RealD b = 0.5 * ( 1.0 + this->alpha );
|
||||
RealD c = 0.5 * ( 1.0 - this->alpha );
|
||||
RealD mq1 = this->mq1;
|
||||
|
||||
for(int s=0; s<Ls; ++s){
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||||
if(s == 0) {
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axpby_ssp_pminus(chi, b, psi, -c, psi, s, s+1);
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axpby_ssp_pplus (chi, 1.0, chi, mq1*c, psi, s, Ls-1);
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} else if(s == (Ls-1)) {
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axpby_ssp_pminus(chi, b, psi, mq1*c, psi, s, 0);
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axpby_ssp_pplus (chi, 1.0, chi, -c, psi, s, s-1);
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} else {
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axpby_ssp_pminus(chi, b, psi, -c, psi, s, s+1);
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axpby_ssp_pplus (chi, 1.0, chi, -c, psi, s, s-1);
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}
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}
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}
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||||
template<class Impl>
|
||||
void MobiusEOFAFermion<Impl>::DtildeInv(const FermionField& psi, FermionField& chi)
|
||||
{
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||||
int Ls = this->Ls;
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||||
RealD m = this->mq1;
|
||||
RealD c = 0.5 * this->alpha;
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||||
RealD d = 0.5;
|
||||
|
||||
RealD DtInv_p(0.0), DtInv_m(0.0);
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||||
RealD N = std::pow(c+d,Ls) + m*std::pow(c-d,Ls);
|
||||
FermionField tmp(this->FermionGrid());
|
||||
|
||||
for(int s=0; s<Ls; ++s){
|
||||
for(int sp=0; sp<Ls; ++sp){
|
||||
|
||||
DtInv_p = m * std::pow(-1.0,s-sp+1) * std::pow(c-d,Ls+s-sp) / std::pow(c+d,s-sp+1) / N;
|
||||
DtInv_p += (s < sp) ? 0.0 : std::pow(-1.0,s-sp) * std::pow(c-d,s-sp) / std::pow(c+d,s-sp+1);
|
||||
DtInv_m = m * std::pow(-1.0,sp-s+1) * std::pow(c-d,Ls+sp-s) / std::pow(c+d,sp-s+1) / N;
|
||||
DtInv_m += (s > sp) ? 0.0 : std::pow(-1.0,sp-s) * std::pow(c-d,sp-s) / std::pow(c+d,sp-s+1);
|
||||
|
||||
if(sp == 0){
|
||||
axpby_ssp_pplus (tmp, 0.0, tmp, DtInv_p, psi, s, sp);
|
||||
axpby_ssp_pminus(tmp, 0.0, tmp, DtInv_m, psi, s, sp);
|
||||
} else {
|
||||
axpby_ssp_pplus (tmp, 1.0, tmp, DtInv_p, psi, s, sp);
|
||||
axpby_ssp_pminus(tmp, 1.0, tmp, DtInv_m, psi, s, sp);
|
||||
}
|
||||
|
||||
}}
|
||||
}
|
||||
|
||||
/*****************************************************************************************************/
|
||||
|
||||
template<class Impl>
|
||||
RealD MobiusEOFAFermion<Impl>::M(const FermionField& psi, FermionField& chi)
|
||||
{
|
||||
int Ls = this->Ls;
|
||||
|
||||
FermionField Din(psi._grid);
|
||||
|
||||
this->Meooe5D(psi, Din);
|
||||
this->DW(Din, chi, DaggerNo);
|
||||
axpby(chi, 1.0, 1.0, chi, psi);
|
||||
this->M5D(psi, chi);
|
||||
return(norm2(chi));
|
||||
}
|
||||
|
||||
template<class Impl>
|
||||
RealD MobiusEOFAFermion<Impl>::Mdag(const FermionField& psi, FermionField& chi)
|
||||
{
|
||||
int Ls = this->Ls;
|
||||
|
||||
FermionField Din(psi._grid);
|
||||
|
||||
this->DW(psi, Din, DaggerYes);
|
||||
this->MeooeDag5D(Din, chi);
|
||||
this->M5Ddag(psi, chi);
|
||||
axpby(chi, 1.0, 1.0, chi, psi);
|
||||
return(norm2(chi));
|
||||
}
|
||||
|
||||
/********************************************************************
|
||||
* Performance critical fermion operators called inside the inverter
|
||||
********************************************************************/
|
||||
|
||||
template<class Impl>
|
||||
void MobiusEOFAFermion<Impl>::M5D(const FermionField& psi, FermionField& chi)
|
||||
{
|
||||
int Ls = this->Ls;
|
||||
|
||||
std::vector<Coeff_t> diag(Ls,1.0);
|
||||
std::vector<Coeff_t> upper(Ls,-1.0); upper[Ls-1] = this->mq1;
|
||||
std::vector<Coeff_t> lower(Ls,-1.0); lower[0] = this->mq1;
|
||||
|
||||
// no shift term
|
||||
if(this->shift == 0.0){ this->M5D(psi, chi, chi, lower, diag, upper); }
|
||||
|
||||
// fused M + shift operation
|
||||
else{ this->M5D_shift(psi, chi, chi, lower, diag, upper, Mooee_shift); }
|
||||
}
|
||||
|
||||
template<class Impl>
|
||||
void MobiusEOFAFermion<Impl>::M5Ddag(const FermionField& psi, FermionField& chi)
|
||||
{
|
||||
int Ls = this->Ls;
|
||||
|
||||
std::vector<Coeff_t> diag(Ls,1.0);
|
||||
std::vector<Coeff_t> upper(Ls,-1.0); upper[Ls-1] = this->mq1;
|
||||
std::vector<Coeff_t> lower(Ls,-1.0); lower[0] = this->mq1;
|
||||
|
||||
// no shift term
|
||||
if(this->shift == 0.0){ this->M5Ddag(psi, chi, chi, lower, diag, upper); }
|
||||
|
||||
// fused M + shift operation
|
||||
else{ this->M5Ddag_shift(psi, chi, chi, lower, diag, upper, Mooee_shift); }
|
||||
}
|
||||
|
||||
// half checkerboard operations
|
||||
template<class Impl>
|
||||
void MobiusEOFAFermion<Impl>::Mooee(const FermionField& psi, FermionField& chi)
|
||||
{
|
||||
int Ls = this->Ls;
|
||||
|
||||
// coefficients of Mooee
|
||||
std::vector<Coeff_t> diag = this->bee;
|
||||
std::vector<Coeff_t> upper(Ls);
|
||||
std::vector<Coeff_t> lower(Ls);
|
||||
for(int s=0; s<Ls; s++){
|
||||
upper[s] = -this->cee[s];
|
||||
lower[s] = -this->cee[s];
|
||||
}
|
||||
upper[Ls-1] *= -this->mq1;
|
||||
lower[0] *= -this->mq1;
|
||||
|
||||
// no shift term
|
||||
if(this->shift == 0.0){ this->M5D(psi, psi, chi, lower, diag, upper); }
|
||||
|
||||
// fused M + shift operation
|
||||
else { this->M5D_shift(psi, psi, chi, lower, diag, upper, Mooee_shift); }
|
||||
}
|
||||
|
||||
template<class Impl>
|
||||
void MobiusEOFAFermion<Impl>::MooeeDag(const FermionField& psi, FermionField& chi)
|
||||
{
|
||||
int Ls = this->Ls;
|
||||
|
||||
// coefficients of MooeeDag
|
||||
std::vector<Coeff_t> diag = this->bee;
|
||||
std::vector<Coeff_t> upper(Ls);
|
||||
std::vector<Coeff_t> lower(Ls);
|
||||
for(int s=0; s<Ls; s++){
|
||||
if(s==0) {
|
||||
upper[s] = -this->cee[s+1];
|
||||
lower[s] = this->mq1*this->cee[Ls-1];
|
||||
} else if(s==(Ls-1)) {
|
||||
upper[s] = this->mq1*this->cee[0];
|
||||
lower[s] = -this->cee[s-1];
|
||||
} else {
|
||||
upper[s] = -this->cee[s+1];
|
||||
lower[s] = -this->cee[s-1];
|
||||
}
|
||||
}
|
||||
|
||||
// no shift term
|
||||
if(this->shift == 0.0){ this->M5Ddag(psi, psi, chi, lower, diag, upper); }
|
||||
|
||||
// fused M + shift operation
|
||||
else{ this->M5Ddag_shift(psi, psi, chi, lower, diag, upper, Mooee_shift); }
|
||||
}
|
||||
|
||||
/****************************************************************************************/
|
||||
|
||||
// Computes coefficients for applying Cayley preconditioned shift operators
|
||||
// (Mooee + \Delta) --> Mooee_shift
|
||||
// (Mooee + \Delta)^{-1} --> MooeeInv_shift_lc, MooeeInv_shift_norm
|
||||
// (Mooee + \Delta)^{-dag} --> MooeeInvDag_shift_lc, MooeeInvDag_shift_norm
|
||||
// For the latter two cases, the operation takes the form
|
||||
// [ (Mooee + \Delta)^{-1} \psi ]_{i} = Mooee_{ij} \psi_{j} +
|
||||
// ( MooeeInv_shift_norm )_{i} ( \sum_{j} [ MooeeInv_shift_lc ]_{j} P_{pm} \psi_{j} )
|
||||
template<class Impl>
|
||||
void MobiusEOFAFermion<Impl>::SetCoefficientsPrecondShiftOps()
|
||||
{
|
||||
int Ls = this->Ls;
|
||||
int pm = this->pm;
|
||||
RealD alpha = this->alpha;
|
||||
RealD k = this->k;
|
||||
RealD mq1 = this->mq1;
|
||||
RealD shift = this->shift;
|
||||
|
||||
// Initialize
|
||||
Mooee_shift.resize(Ls);
|
||||
MooeeInv_shift_lc.resize(Ls);
|
||||
MooeeInv_shift_norm.resize(Ls);
|
||||
MooeeInvDag_shift_lc.resize(Ls);
|
||||
MooeeInvDag_shift_norm.resize(Ls);
|
||||
|
||||
// Construct Mooee_shift
|
||||
int idx(0);
|
||||
Coeff_t N = ( (pm == 1) ? 1.0 : -1.0 ) * (2.0*shift*k) *
|
||||
( std::pow(alpha+1.0,Ls) + mq1*std::pow(alpha-1.0,Ls) );
|
||||
for(int s=0; s<Ls; ++s){
|
||||
idx = (pm == 1) ? (s) : (Ls-1-s);
|
||||
Mooee_shift[idx] = N * std::pow(-1.0,s) * std::pow(alpha-1.0,s) / std::pow(alpha+1.0,Ls+s+1);
|
||||
}
|
||||
|
||||
// Tridiagonal solve for MooeeInvDag_shift_lc
|
||||
{
|
||||
Coeff_t m(0.0);
|
||||
std::vector<Coeff_t> d = Mooee_shift;
|
||||
std::vector<Coeff_t> u(Ls,0.0);
|
||||
std::vector<Coeff_t> y(Ls,0.0);
|
||||
std::vector<Coeff_t> q(Ls,0.0);
|
||||
if(pm == 1){ u[0] = 1.0; }
|
||||
else{ u[Ls-1] = 1.0; }
|
||||
|
||||
// Tridiagonal matrix algorithm + Sherman-Morrison formula
|
||||
//
|
||||
// We solve
|
||||
// ( Mooee' + u \otimes v ) MooeeInvDag_shift_lc = Mooee_shift
|
||||
// where Mooee' is the tridiagonal part of Mooee_{+}, and
|
||||
// u = (1,0,...,0) and v = (0,...,0,mq1*cee[0]) are chosen
|
||||
// so that the outer-product u \otimes v gives the (0,Ls-1)
|
||||
// entry of Mooee_{+}.
|
||||
//
|
||||
// We do this as two solves: Mooee'*y = d and Mooee'*q = u,
|
||||
// and then construct the solution to the original system
|
||||
// MooeeInvDag_shift_lc = y - <v,y> / ( 1 + <v,q> ) q
|
||||
if(pm == 1){
|
||||
for(int s=1; s<Ls; ++s){
|
||||
m = -this->cee[s] / this->bee[s-1];
|
||||
d[s] -= m*d[s-1];
|
||||
u[s] -= m*u[s-1];
|
||||
}
|
||||
}
|
||||
y[Ls-1] = d[Ls-1] / this->bee[Ls-1];
|
||||
q[Ls-1] = u[Ls-1] / this->bee[Ls-1];
|
||||
for(int s=Ls-2; s>=0; --s){
|
||||
if(pm == 1){
|
||||
y[s] = d[s] / this->bee[s];
|
||||
q[s] = u[s] / this->bee[s];
|
||||
} else {
|
||||
y[s] = ( d[s] + this->cee[s]*y[s+1] ) / this->bee[s];
|
||||
q[s] = ( u[s] + this->cee[s]*q[s+1] ) / this->bee[s];
|
||||
}
|
||||
}
|
||||
|
||||
// Construct MooeeInvDag_shift_lc
|
||||
for(int s=0; s<Ls; ++s){
|
||||
if(pm == 1){
|
||||
MooeeInvDag_shift_lc[s] = y[s] - mq1*this->cee[0]*y[Ls-1] /
|
||||
(1.0+mq1*this->cee[0]*q[Ls-1]) * q[s];
|
||||
} else {
|
||||
MooeeInvDag_shift_lc[s] = y[s] - mq1*this->cee[Ls-1]*y[0] /
|
||||
(1.0+mq1*this->cee[Ls-1]*q[0]) * q[s];
|
||||
}
|
||||
}
|
||||
|
||||
// Compute remaining coefficients
|
||||
N = (pm == 1) ? (1.0 + MooeeInvDag_shift_lc[Ls-1]) : (1.0 + MooeeInvDag_shift_lc[0]);
|
||||
for(int s=0; s<Ls; ++s){
|
||||
|
||||
// MooeeInv_shift_lc
|
||||
if(pm == 1){ MooeeInv_shift_lc[s] = std::pow(this->bee[s],s) * std::pow(this->cee[s],Ls-1-s); }
|
||||
else{ MooeeInv_shift_lc[s] = std::pow(this->bee[s],Ls-1-s) * std::pow(this->cee[s],s); }
|
||||
|
||||
// MooeeInv_shift_norm
|
||||
MooeeInv_shift_norm[s] = -MooeeInvDag_shift_lc[s] /
|
||||
( std::pow(this->bee[s],Ls) + mq1*std::pow(this->cee[s],Ls) ) / N;
|
||||
|
||||
// MooeeInvDag_shift_norm
|
||||
if(pm == 1){ MooeeInvDag_shift_norm[s] = -std::pow(this->bee[s],s) * std::pow(this->cee[s],Ls-1-s) /
|
||||
( std::pow(this->bee[s],Ls) + mq1*std::pow(this->cee[s],Ls) ) / N; }
|
||||
else{ MooeeInvDag_shift_norm[s] = -std::pow(this->bee[s],Ls-1-s) * std::pow(this->cee[s],s) /
|
||||
( std::pow(this->bee[s],Ls) + mq1*std::pow(this->cee[s],Ls) ) / N; }
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// Recompute coefficients for a different value of shift constant
|
||||
template<class Impl>
|
||||
void MobiusEOFAFermion<Impl>::RefreshShiftCoefficients(RealD new_shift)
|
||||
{
|
||||
this->shift = new_shift;
|
||||
if(new_shift != 0.0){
|
||||
SetCoefficientsPrecondShiftOps();
|
||||
} else {
|
||||
int Ls = this->Ls;
|
||||
Mooee_shift.resize(Ls,0.0);
|
||||
MooeeInv_shift_lc.resize(Ls,0.0);
|
||||
MooeeInv_shift_norm.resize(Ls,0.0);
|
||||
MooeeInvDag_shift_lc.resize(Ls,0.0);
|
||||
MooeeInvDag_shift_norm.resize(Ls,0.0);
|
||||
}
|
||||
}
|
||||
|
||||
template<class Impl>
|
||||
void MobiusEOFAFermion<Impl>::MooeeInternalCompute(int dag, int inv,
|
||||
Vector<iSinglet<Simd> >& Matp, Vector<iSinglet<Simd> >& Matm)
|
||||
{
|
||||
int Ls = this->Ls;
|
||||
|
||||
GridBase* grid = this->FermionRedBlackGrid();
|
||||
int LLs = grid->_rdimensions[0];
|
||||
|
||||
if(LLs == Ls){ return; } // Not vectorised in 5th direction
|
||||
|
||||
Eigen::MatrixXcd Pplus = Eigen::MatrixXcd::Zero(Ls,Ls);
|
||||
Eigen::MatrixXcd Pminus = Eigen::MatrixXcd::Zero(Ls,Ls);
|
||||
|
||||
for(int s=0; s<Ls; s++){
|
||||
Pplus(s,s) = this->bee[s];
|
||||
Pminus(s,s) = this->bee[s];
|
||||
}
|
||||
|
||||
for(int s=0; s<Ls-1; s++){
|
||||
Pminus(s,s+1) = -this->cee[s];
|
||||
Pplus(s+1,s) = -this->cee[s+1];
|
||||
}
|
||||
|
||||
Pplus (0,Ls-1) = this->mq1*this->cee[0];
|
||||
Pminus(Ls-1,0) = this->mq1*this->cee[Ls-1];
|
||||
|
||||
if(this->shift != 0.0){
|
||||
RealD c = 0.5 * this->alpha;
|
||||
RealD d = 0.5;
|
||||
RealD N = this->shift * this->k * ( std::pow(c+d,Ls) + this->mq1*std::pow(c-d,Ls) );
|
||||
if(this->pm == 1) {
|
||||
for(int s=0; s<Ls; ++s){
|
||||
Pplus(s,Ls-1) += N * std::pow(-1.0,s) * std::pow(c-d,s) / std::pow(c+d,Ls+s+1);
|
||||
}
|
||||
} else {
|
||||
for(int s=0; s<Ls; ++s){
|
||||
Pminus(s,0) += N * std::pow(-1.0,s+1) * std::pow(c-d,Ls-1-s) / std::pow(c+d,2*Ls-s);
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
Eigen::MatrixXcd PplusMat ;
|
||||
Eigen::MatrixXcd PminusMat;
|
||||
|
||||
if(inv) {
|
||||
PplusMat = Pplus.inverse();
|
||||
PminusMat = Pminus.inverse();
|
||||
} else {
|
||||
PplusMat = Pplus;
|
||||
PminusMat = Pminus;
|
||||
}
|
||||
|
||||
if(dag){
|
||||
PplusMat.adjointInPlace();
|
||||
PminusMat.adjointInPlace();
|
||||
}
|
||||
|
||||
typedef typename SiteHalfSpinor::scalar_type scalar_type;
|
||||
const int Nsimd = Simd::Nsimd();
|
||||
Matp.resize(Ls*LLs);
|
||||
Matm.resize(Ls*LLs);
|
||||
|
||||
for(int s2=0; s2<Ls; s2++){
|
||||
for(int s1=0; s1<LLs; s1++){
|
||||
int istride = LLs;
|
||||
int ostride = 1;
|
||||
Simd Vp;
|
||||
Simd Vm;
|
||||
scalar_type *sp = (scalar_type*) &Vp;
|
||||
scalar_type *sm = (scalar_type*) &Vm;
|
||||
for(int l=0; l<Nsimd; l++){
|
||||
if(switcheroo<Coeff_t>::iscomplex()) {
|
||||
sp[l] = PplusMat (l*istride+s1*ostride,s2);
|
||||
sm[l] = PminusMat(l*istride+s1*ostride,s2);
|
||||
} else {
|
||||
// if real
|
||||
scalar_type tmp;
|
||||
tmp = PplusMat (l*istride+s1*ostride,s2);
|
||||
sp[l] = scalar_type(tmp.real(),tmp.real());
|
||||
tmp = PminusMat(l*istride+s1*ostride,s2);
|
||||
sm[l] = scalar_type(tmp.real(),tmp.real());
|
||||
}
|
||||
}
|
||||
Matp[LLs*s2+s1] = Vp;
|
||||
Matm[LLs*s2+s1] = Vm;
|
||||
}}
|
||||
}
|
||||
|
||||
FermOpTemplateInstantiate(MobiusEOFAFermion);
|
||||
GparityFermOpTemplateInstantiate(MobiusEOFAFermion);
|
||||
// no shift term
|
||||
if(this->shift == 0.0){ this->M5Ddag(psi, psi, chi, lower, diag, upper); }
|
||||
|
||||
}}
|
||||
// fused M + shift operation
|
||||
else{ this->M5Ddag_shift(psi, psi, chi, lower, diag, upper, Mooee_shift); }
|
||||
}
|
||||
|
||||
/****************************************************************************************/
|
||||
|
||||
// Computes coefficients for applying Cayley preconditioned shift operators
|
||||
// (Mooee + \Delta) --> Mooee_shift
|
||||
// (Mooee + \Delta)^{-1} --> MooeeInv_shift_lc, MooeeInv_shift_norm
|
||||
// (Mooee + \Delta)^{-dag} --> MooeeInvDag_shift_lc, MooeeInvDag_shift_norm
|
||||
// For the latter two cases, the operation takes the form
|
||||
// [ (Mooee + \Delta)^{-1} \psi ]_{i} = Mooee_{ij} \psi_{j} +
|
||||
// ( MooeeInv_shift_norm )_{i} ( \sum_{j} [ MooeeInv_shift_lc ]_{j} P_{pm} \psi_{j} )
|
||||
template<class Impl>
|
||||
void MobiusEOFAFermion<Impl>::SetCoefficientsPrecondShiftOps()
|
||||
{
|
||||
int Ls = this->Ls;
|
||||
int pm = this->pm;
|
||||
RealD alpha = this->alpha;
|
||||
RealD k = this->k;
|
||||
RealD mq1 = this->mq1;
|
||||
RealD shift = this->shift;
|
||||
|
||||
// Initialize
|
||||
Mooee_shift.resize(Ls);
|
||||
MooeeInv_shift_lc.resize(Ls);
|
||||
MooeeInv_shift_norm.resize(Ls);
|
||||
MooeeInvDag_shift_lc.resize(Ls);
|
||||
MooeeInvDag_shift_norm.resize(Ls);
|
||||
|
||||
// Construct Mooee_shift
|
||||
int idx(0);
|
||||
Coeff_t N = ( (pm == 1) ? 1.0 : -1.0 ) * (2.0*shift*k) *
|
||||
( std::pow(alpha+1.0,Ls) + mq1*std::pow(alpha-1.0,Ls) );
|
||||
for(int s=0; s<Ls; ++s){
|
||||
idx = (pm == 1) ? (s) : (Ls-1-s);
|
||||
Mooee_shift[idx] = N * std::pow(-1.0,s) * std::pow(alpha-1.0,s) / std::pow(alpha+1.0,Ls+s+1);
|
||||
}
|
||||
|
||||
// Tridiagonal solve for MooeeInvDag_shift_lc
|
||||
{
|
||||
Coeff_t m(0.0);
|
||||
std::vector<Coeff_t> d = Mooee_shift;
|
||||
std::vector<Coeff_t> u(Ls,0.0);
|
||||
std::vector<Coeff_t> y(Ls,0.0);
|
||||
std::vector<Coeff_t> q(Ls,0.0);
|
||||
if(pm == 1){ u[0] = 1.0; }
|
||||
else{ u[Ls-1] = 1.0; }
|
||||
|
||||
// Tridiagonal matrix algorithm + Sherman-Morrison formula
|
||||
//
|
||||
// We solve
|
||||
// ( Mooee' + u \otimes v ) MooeeInvDag_shift_lc = Mooee_shift
|
||||
// where Mooee' is the tridiagonal part of Mooee_{+}, and
|
||||
// u = (1,0,...,0) and v = (0,...,0,mq1*cee[0]) are chosen
|
||||
// so that the outer-product u \otimes v gives the (0,Ls-1)
|
||||
// entry of Mooee_{+}.
|
||||
//
|
||||
// We do this as two solves: Mooee'*y = d and Mooee'*q = u,
|
||||
// and then construct the solution to the original system
|
||||
// MooeeInvDag_shift_lc = y - <v,y> / ( 1 + <v,q> ) q
|
||||
if(pm == 1){
|
||||
for(int s=1; s<Ls; ++s){
|
||||
m = -this->cee[s] / this->bee[s-1];
|
||||
d[s] -= m*d[s-1];
|
||||
u[s] -= m*u[s-1];
|
||||
}
|
||||
}
|
||||
y[Ls-1] = d[Ls-1] / this->bee[Ls-1];
|
||||
q[Ls-1] = u[Ls-1] / this->bee[Ls-1];
|
||||
for(int s=Ls-2; s>=0; --s){
|
||||
if(pm == 1){
|
||||
y[s] = d[s] / this->bee[s];
|
||||
q[s] = u[s] / this->bee[s];
|
||||
} else {
|
||||
y[s] = ( d[s] + this->cee[s]*y[s+1] ) / this->bee[s];
|
||||
q[s] = ( u[s] + this->cee[s]*q[s+1] ) / this->bee[s];
|
||||
}
|
||||
}
|
||||
|
||||
// Construct MooeeInvDag_shift_lc
|
||||
for(int s=0; s<Ls; ++s){
|
||||
if(pm == 1){
|
||||
MooeeInvDag_shift_lc[s] = y[s] - mq1*this->cee[0]*y[Ls-1] /
|
||||
(1.0+mq1*this->cee[0]*q[Ls-1]) * q[s];
|
||||
} else {
|
||||
MooeeInvDag_shift_lc[s] = y[s] - mq1*this->cee[Ls-1]*y[0] /
|
||||
(1.0+mq1*this->cee[Ls-1]*q[0]) * q[s];
|
||||
}
|
||||
}
|
||||
|
||||
// Compute remaining coefficients
|
||||
N = (pm == 1) ? (1.0 + MooeeInvDag_shift_lc[Ls-1]) : (1.0 + MooeeInvDag_shift_lc[0]);
|
||||
for(int s=0; s<Ls; ++s){
|
||||
|
||||
// MooeeInv_shift_lc
|
||||
if(pm == 1){ MooeeInv_shift_lc[s] = std::pow(this->bee[s],s) * std::pow(this->cee[s],Ls-1-s); }
|
||||
else{ MooeeInv_shift_lc[s] = std::pow(this->bee[s],Ls-1-s) * std::pow(this->cee[s],s); }
|
||||
|
||||
// MooeeInv_shift_norm
|
||||
MooeeInv_shift_norm[s] = -MooeeInvDag_shift_lc[s] /
|
||||
( std::pow(this->bee[s],Ls) + mq1*std::pow(this->cee[s],Ls) ) / N;
|
||||
|
||||
// MooeeInvDag_shift_norm
|
||||
if(pm == 1){ MooeeInvDag_shift_norm[s] = -std::pow(this->bee[s],s) * std::pow(this->cee[s],Ls-1-s) /
|
||||
( std::pow(this->bee[s],Ls) + mq1*std::pow(this->cee[s],Ls) ) / N; }
|
||||
else{ MooeeInvDag_shift_norm[s] = -std::pow(this->bee[s],Ls-1-s) * std::pow(this->cee[s],s) /
|
||||
( std::pow(this->bee[s],Ls) + mq1*std::pow(this->cee[s],Ls) ) / N; }
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// Recompute coefficients for a different value of shift constant
|
||||
template<class Impl>
|
||||
void MobiusEOFAFermion<Impl>::RefreshShiftCoefficients(RealD new_shift)
|
||||
{
|
||||
this->shift = new_shift;
|
||||
if(new_shift != 0.0){
|
||||
SetCoefficientsPrecondShiftOps();
|
||||
} else {
|
||||
int Ls = this->Ls;
|
||||
Mooee_shift.resize(Ls,0.0);
|
||||
MooeeInv_shift_lc.resize(Ls,0.0);
|
||||
MooeeInv_shift_norm.resize(Ls,0.0);
|
||||
MooeeInvDag_shift_lc.resize(Ls,0.0);
|
||||
MooeeInvDag_shift_norm.resize(Ls,0.0);
|
||||
}
|
||||
}
|
||||
|
||||
template<class Impl>
|
||||
void MobiusEOFAFermion<Impl>::MooeeInternalCompute(int dag, int inv,
|
||||
Vector<iSinglet<Simd> >& Matp, Vector<iSinglet<Simd> >& Matm)
|
||||
{
|
||||
int Ls = this->Ls;
|
||||
|
||||
GridBase* grid = this->FermionRedBlackGrid();
|
||||
int LLs = grid->_rdimensions[0];
|
||||
|
||||
if(LLs == Ls){ return; } // Not vectorised in 5th direction
|
||||
|
||||
Eigen::MatrixXcd Pplus = Eigen::MatrixXcd::Zero(Ls,Ls);
|
||||
Eigen::MatrixXcd Pminus = Eigen::MatrixXcd::Zero(Ls,Ls);
|
||||
|
||||
for(int s=0; s<Ls; s++){
|
||||
Pplus(s,s) = this->bee[s];
|
||||
Pminus(s,s) = this->bee[s];
|
||||
}
|
||||
|
||||
for(int s=0; s<Ls-1; s++){
|
||||
Pminus(s,s+1) = -this->cee[s];
|
||||
Pplus(s+1,s) = -this->cee[s+1];
|
||||
}
|
||||
|
||||
Pplus (0,Ls-1) = this->mq1*this->cee[0];
|
||||
Pminus(Ls-1,0) = this->mq1*this->cee[Ls-1];
|
||||
|
||||
if(this->shift != 0.0){
|
||||
RealD c = 0.5 * this->alpha;
|
||||
RealD d = 0.5;
|
||||
RealD N = this->shift * this->k * ( std::pow(c+d,Ls) + this->mq1*std::pow(c-d,Ls) );
|
||||
if(this->pm == 1) {
|
||||
for(int s=0; s<Ls; ++s){
|
||||
Pplus(s,Ls-1) += N * std::pow(-1.0,s) * std::pow(c-d,s) / std::pow(c+d,Ls+s+1);
|
||||
}
|
||||
} else {
|
||||
for(int s=0; s<Ls; ++s){
|
||||
Pminus(s,0) += N * std::pow(-1.0,s+1) * std::pow(c-d,Ls-1-s) / std::pow(c+d,2*Ls-s);
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
Eigen::MatrixXcd PplusMat ;
|
||||
Eigen::MatrixXcd PminusMat;
|
||||
|
||||
if(inv) {
|
||||
PplusMat = Pplus.inverse();
|
||||
PminusMat = Pminus.inverse();
|
||||
} else {
|
||||
PplusMat = Pplus;
|
||||
PminusMat = Pminus;
|
||||
}
|
||||
|
||||
if(dag){
|
||||
PplusMat.adjointInPlace();
|
||||
PminusMat.adjointInPlace();
|
||||
}
|
||||
|
||||
typedef typename SiteHalfSpinor::scalar_type scalar_type;
|
||||
const int Nsimd = Simd::Nsimd();
|
||||
Matp.resize(Ls*LLs);
|
||||
Matm.resize(Ls*LLs);
|
||||
|
||||
for(int s2=0; s2<Ls; s2++){
|
||||
for(int s1=0; s1<LLs; s1++){
|
||||
int istride = LLs;
|
||||
int ostride = 1;
|
||||
Simd Vp;
|
||||
Simd Vm;
|
||||
scalar_type *sp = (scalar_type*) &Vp;
|
||||
scalar_type *sm = (scalar_type*) &Vm;
|
||||
for(int l=0; l<Nsimd; l++){
|
||||
if(switcheroo<Coeff_t>::iscomplex()) {
|
||||
sp[l] = PplusMat (l*istride+s1*ostride,s2);
|
||||
sm[l] = PminusMat(l*istride+s1*ostride,s2);
|
||||
} else {
|
||||
// if real
|
||||
scalar_type tmp;
|
||||
tmp = PplusMat (l*istride+s1*ostride,s2);
|
||||
sp[l] = scalar_type(tmp.real(),tmp.real());
|
||||
tmp = PminusMat(l*istride+s1*ostride,s2);
|
||||
sm[l] = scalar_type(tmp.real(),tmp.real());
|
||||
}
|
||||
}
|
||||
Matp[LLs*s2+s1] = Vp;
|
||||
Matm[LLs*s2+s1] = Vm;
|
||||
}}
|
||||
}
|
||||
|
||||
FermOpTemplateInstantiate(MobiusEOFAFermion);
|
||||
GparityFermOpTemplateInstantiate(MobiusEOFAFermion);
|
||||
|
||||
NAMESPACE_END(Grid);
|
||||
|
||||
Reference in New Issue
Block a user