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Domain wall fermions now invert ; have the basis set up for
Tanh/Zolo * (Cayley/PartFrac/ContFrac) * (Mobius/Shamir/Wilson) Approx Representation Kernel. All are done with space-time taking part in checkerboarding, Ls uncheckerboarded Have only so far tested the Domain Wall limit of mobius, and at that only checked that it i) Inverts ii) 5dim DW == Ls copies of 4dim D2 iii) MeeInv Mee == 1 iv) Meo+Mee+Moe+Moo == M unprec. v) MpcDagMpc is hermitan vi) Mdag is the adjoint of M between stochastic vectors. That said, the RB schur solve, RB MpcDagMpc solve, Unprec solve all converge and the true residual becomes small; so pretty good tests.
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Peter Boyle
235
lib/qcd/action/fermion/CayleyFermion5D.cc
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235
lib/qcd/action/fermion/CayleyFermion5D.cc
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#include <Grid.h>
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namespace Grid {
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namespace QCD {
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CayleyFermion5D::CayleyFermion5D(LatticeGaugeField &_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 _mass,RealD _M5) :
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WilsonFermion5D(_Umu,
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FiveDimGrid,
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FiveDimRedBlackGrid,
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FourDimGrid,
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FourDimRedBlackGrid,_M5),
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mass(_mass)
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{
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std::cout << "Constructing a CayleyFermion5D"<<std::endl;
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}
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// override multiply
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RealD CayleyFermion5D::M (const LatticeFermion &psi, LatticeFermion &chi)
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{
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LatticeFermion Din(psi._grid);
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// Assemble Din
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for(int s=0;s<Ls;s++){
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if ( s==0 ) {
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// Din = bs psi[s] + cs[s] psi[s+1}
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axpby_ssp_pminus(Din,bs[s],psi,cs[s],psi,s,s+1);
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// Din+= -mass*cs[s] psi[s+1}
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axpby_ssp_pplus (Din,1.0,Din,-mass*cs[s],psi,s,Ls-1);
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} else if ( s==(Ls-1)) {
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axpby_ssp_pminus(Din,bs[s],psi,-mass*cs[s],psi,s,0);
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axpby_ssp_pplus (Din,1.0,Din,cs[s],psi,s,s-1);
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} else {
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axpby_ssp_pminus(Din,bs[s],psi,cs[s],psi,s,s+1);
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axpby_ssp_pplus(Din,1.0,Din,cs[s],psi,s,s-1);
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}
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}
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DW(Din,chi,DaggerNo);
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// ((b D_W + D_w hop terms +1) on s-diag
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axpby(chi,1.0,1.0,chi,psi);
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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,1.0,chi,-1.0,psi,s,s+1);
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axpby_ssp_pplus (chi,1.0,chi,mass,psi,s,Ls-1);
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} else if ( s==(Ls-1)) {
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axpby_ssp_pminus(chi,1.0,chi,mass,psi,s,0);
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axpby_ssp_pplus (chi,1.0,chi,-1.0,psi,s,s-1);
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} else {
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axpby_ssp_pminus(chi,1.0,chi,-1.0,psi,s,s+1);
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axpby_ssp_pplus (chi,1.0,chi,-1.0,psi,s,s-1);
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}
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}
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return norm2(chi);
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}
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RealD CayleyFermion5D::Mdag (const LatticeFermion &psi, LatticeFermion &chi)
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{
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// Under adjoint
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//D1+ D1- P- -> D1+^dag P+ D2-^dag
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//D2- P+ D2+ P-D1-^dag D2+dag
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LatticeFermion Din(psi._grid);
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// Apply Dw
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DW(psi,Din,DaggerYes);
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for(int s=0;s<Ls;s++){
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// Collect the terms in DW
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// Chi = bs Din[s] + cs[s] Din[s+1}
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// Chi+= -mass*cs[s] psi[s+1}
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if ( s==0 ) {
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axpby_ssp_pplus (chi,bs[s],Din,cs[s+1],Din,s,s+1);
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axpby_ssp_pminus(chi,1.0,chi,-mass*cs[Ls-1],Din,s,Ls-1);
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} else if ( s==(Ls-1)) {
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axpby_ssp_pplus (chi,bs[s],Din,-mass*cs[0],Din,s,0);
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axpby_ssp_pminus(chi,1.0,chi,cs[s-1],Din,s,s-1);
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} else {
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axpby_ssp_pplus (chi,bs[s],Din,cs[s+1],Din,s,s+1);
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axpby_ssp_pminus(chi,1.0,chi,cs[s-1],Din,s,s-1);
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}
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// Collect the terms indept of DW
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if ( s==0 ){
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axpby_ssp_pplus (chi,1.0,chi,-1.0,psi,s,s+1);
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axpby_ssp_pminus(chi,1.0,chi,mass,psi,s,Ls-1);
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} else if ( s==(Ls-1)) {
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axpby_ssp_pplus (chi,1.0,chi,mass,psi,s,0);
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axpby_ssp_pminus(chi,1.0,chi,-1.0,psi,s,s-1);
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} else {
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axpby_ssp_pplus(chi,1.0,chi,-1.0,psi,s,s+1);
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axpby_ssp_pminus(chi,1.0,chi,-1.0,psi,s,s-1);
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}
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}
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// ((b D_W + D_w hop terms +1) on s-diag
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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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// half checkerboard operations
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void CayleyFermion5D::Meooe (const LatticeFermion &psi, LatticeFermion &chi)
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{
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LatticeFermion tmp(psi._grid);
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// Assemble the 5d matrix
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for(int s=0;s<Ls;s++){
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if ( s==0 ) {
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// tmp = bs psi[s] + cs[s] psi[s+1}
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// tmp+= -mass*cs[s] psi[s+1}
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axpby_ssp_pminus(tmp,beo[s],psi,-ceo[s],psi ,s, s+1);
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axpby_ssp_pplus(tmp,1.0,tmp,mass*ceo[s],psi,s,Ls-1);
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} else if ( s==(Ls-1)) {
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axpby_ssp_pminus(tmp,beo[s],psi,mass*ceo[s],psi,s,0);
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axpby_ssp_pplus(tmp,1.0,tmp,-ceo[s],psi,s,s-1);
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} else {
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axpby_ssp_pminus(tmp,beo[s],psi,-ceo[s],psi,s,s+1);
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axpby_ssp_pplus (tmp,1.0,tmp,-ceo[s],psi,s,s-1);
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}
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}
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// Apply 4d dslash
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if ( psi.checkerboard == Odd ) {
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DhopEO(tmp,chi,DaggerNo);
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} else {
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DhopOE(tmp,chi,DaggerNo);
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}
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}
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void CayleyFermion5D::MeooeDag (const LatticeFermion &psi, LatticeFermion &chi)
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{
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LatticeFermion tmp(psi._grid);
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// Apply 4d dslash
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if ( psi.checkerboard == Odd ) {
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DhopEO(psi,tmp,DaggerYes);
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} else {
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DhopOE(psi,tmp,DaggerYes);
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}
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// Assemble the 5d matrix
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for(int s=0;s<Ls;s++){
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if ( s==0 ) {
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axpby_ssp_pplus(chi,beo[s],tmp, -ceo[s+1] ,tmp,s,s+1);
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axpby_ssp_pminus(chi, 1.0,chi,mass*ceo[Ls-1],tmp,s,Ls-1);
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} else if ( s==(Ls-1)) {
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axpby_ssp_pplus(chi,beo[s],tmp,mass*ceo[0],tmp,s,0);
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axpby_ssp_pminus(chi,1.0,chi,-ceo[s-1],tmp,s,s-1);
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} else {
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axpby_ssp_pplus(chi,beo[s],tmp,-ceo[s+1],tmp,s,s+1);
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axpby_ssp_pminus(chi,1.0 ,chi,-ceo[s-1],tmp,s,s-1);
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}
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}
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}
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void CayleyFermion5D::Mooee (const LatticeFermion &psi, LatticeFermion &chi)
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{
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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,bee[s],psi ,-cee[s],psi,s,s+1);
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axpby_ssp_pplus (chi,1.0,chi,mass*cee[s],psi,s,Ls-1);
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} else if ( s==(Ls-1)) {
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axpby_ssp_pminus(chi,bee[s],psi,mass*cee[s],psi,s,0);
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axpby_ssp_pplus (chi,1.0,chi,-cee[s],psi,s,s-1);
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} else {
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axpby_ssp_pminus(chi,bee[s],psi,-cee[s],psi,s,s+1);
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axpby_ssp_pplus (chi,1.0,chi,-cee[s],psi,s,s-1);
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}
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}
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}
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void CayleyFermion5D::MooeeDag (const LatticeFermion &psi, LatticeFermion &chi)
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{
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for (int s=0;s<Ls;s++){
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// Assemble the 5d matrix
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if ( s==0 ) {
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axpby_ssp_pplus(chi,bee[s],psi,-cee[s+1] ,psi,s,s+1);
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axpby_ssp_pminus(chi,1.0,chi,mass*cee[Ls-1],psi,s,Ls-1);
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} else if ( s==(Ls-1)) {
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axpby_ssp_pplus(chi,bee[s],psi,mass*cee[0],psi,s,0);
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axpby_ssp_pminus(chi,1.0,chi,-cee[s-1],psi,s,s-1);
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} else {
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axpby_ssp_pplus(chi,bee[s],psi,-cee[s+1],psi,s,s+1);
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axpby_ssp_pminus(chi,1.0 ,chi,-cee[s-1],psi,s,s-1);
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}
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}
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}
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void CayleyFermion5D::MooeeInv (const LatticeFermion &psi, LatticeFermion &chi)
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{
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// Apply (L^{\prime})^{-1}
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axpby_ssp (chi,1.0,psi, 0.0,psi,0,0); // chi[0]=psi[0]
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for (int s=1;s<Ls;s++){
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axpby_ssp_pplus(chi,1.0,psi,-lee[s-1],chi,s,s-1);// recursion Psi[s] -lee P_+ chi[s-1]
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}
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// L_m^{-1}
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for (int s=0;s<Ls-1;s++){ // Chi[ee] = 1 - sum[s<Ls-1] -leem[s]P_- chi
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axpby_ssp_pminus(chi,1.0,chi,-leem[s],chi,Ls-1,s);
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}
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// U_m^{-1} D^{-1}
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for (int s=0;s<Ls-1;s++){
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// Chi[s] + 1/d chi[s]
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axpby_ssp_pplus(chi,1.0/dee[s],chi,-ueem[s]/dee[Ls-1],chi,s,Ls-1);
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}
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axpby_ssp(chi,1.0/dee[Ls-1],chi,0.0,chi,Ls-1,Ls-1); // Modest avoidable
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// Apply U^{-1}
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for (int s=Ls-2;s>=0;s--){
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axpby_ssp_pminus (chi,1.0,chi,-uee[s],chi,s,s+1); // chi[Ls]
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}
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}
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void CayleyFermion5D::MooeeInvDag (const LatticeFermion &psi, LatticeFermion &chi)
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{
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// Apply (U^{\prime})^{-dagger}
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axpby_ssp (chi,1.0,psi, 0.0,psi,0,0); // chi[0]=psi[0]
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for (int s=1;s<Ls;s++){
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axpby_ssp_pminus(chi,1.0,psi,-uee[s-1],chi,s,s-1);
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}
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// U_m^{-\dagger}
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for (int s=0;s<Ls-1;s++){
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axpby_ssp_pplus(chi,1.0,chi,-ueem[s],chi,Ls-1,s);
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}
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// L_m^{-\dagger} D^{-dagger}
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for (int s=0;s<Ls-1;s++){
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axpby_ssp_pminus(chi,1.0/dee[s],chi,-leem[s]/dee[Ls-1],chi,s,Ls-1);
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}
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axpby_ssp(chi,1.0/dee[Ls-1],chi,0.0,chi,Ls-1,Ls-1); // Modest avoidable
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// Apply L^{-dagger}
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for (int s=Ls-2;s>=0;s--){
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axpby_ssp_pplus (chi,1.0,chi,-lee[s],chi,s,s+1); // chi[Ls]
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}
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}
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}
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}
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