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Grid/lib/qcd/action/fermion/CayleyFermion5D.cc

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#include <Grid.h>
namespace Grid {
namespace QCD {
CayleyFermion5D::CayleyFermion5D(LatticeGaugeField &_Umu,
GridCartesian &FiveDimGrid,
GridRedBlackCartesian &FiveDimRedBlackGrid,
GridCartesian &FourDimGrid,
GridRedBlackCartesian &FourDimRedBlackGrid,
RealD _mass,RealD _M5) :
WilsonFermion5D(_Umu,
FiveDimGrid,
FiveDimRedBlackGrid,
FourDimGrid,
FourDimRedBlackGrid,_M5),
mass(_mass)
{
}
// override multiply
RealD CayleyFermion5D::M (const LatticeFermion &psi, LatticeFermion &chi)
{
LatticeFermion Din(psi._grid);
// Assemble Din
for(int s=0;s<Ls;s++){
if ( s==0 ) {
// Din = bs psi[s] + cs[s] psi[s+1}
axpby_ssp_pminus(Din,bs[s],psi,cs[s],psi,s,s+1);
// Din+= -mass*cs[s] psi[s+1}
axpby_ssp_pplus (Din,1.0,Din,-mass*cs[s],psi,s,Ls-1);
} else if ( s==(Ls-1)) {
axpby_ssp_pminus(Din,bs[s],psi,-mass*cs[s],psi,s,0);
axpby_ssp_pplus (Din,1.0,Din,cs[s],psi,s,s-1);
} else {
axpby_ssp_pminus(Din,bs[s],psi,cs[s],psi,s,s+1);
axpby_ssp_pplus(Din,1.0,Din,cs[s],psi,s,s-1);
}
}
DW(Din,chi,DaggerNo);
// ((b D_W + D_w hop terms +1) on s-diag
axpby(chi,1.0,1.0,chi,psi);
for(int s=0;s<Ls;s++){
if ( s==0 ){
axpby_ssp_pminus(chi,1.0,chi,-1.0,psi,s,s+1);
axpby_ssp_pplus (chi,1.0,chi,mass,psi,s,Ls-1);
} else if ( s==(Ls-1)) {
axpby_ssp_pminus(chi,1.0,chi,mass,psi,s,0);
axpby_ssp_pplus (chi,1.0,chi,-1.0,psi,s,s-1);
} else {
axpby_ssp_pminus(chi,1.0,chi,-1.0,psi,s,s+1);
axpby_ssp_pplus (chi,1.0,chi,-1.0,psi,s,s-1);
}
}
return norm2(chi);
}
RealD CayleyFermion5D::Mdag (const LatticeFermion &psi, LatticeFermion &chi)
{
// Under adjoint
//D1+ D1- P- -> D1+^dag P+ D2-^dag
//D2- P+ D2+ P-D1-^dag D2+dag
LatticeFermion Din(psi._grid);
// Apply Dw
DW(psi,Din,DaggerYes);
for(int s=0;s<Ls;s++){
// Collect the terms in DW
// Chi = bs Din[s] + cs[s] Din[s+1}
// Chi+= -mass*cs[s] psi[s+1}
if ( s==0 ) {
axpby_ssp_pplus (chi,bs[s],Din,cs[s+1],Din,s,s+1);
axpby_ssp_pminus(chi,1.0,chi,-mass*cs[Ls-1],Din,s,Ls-1);
} else if ( s==(Ls-1)) {
axpby_ssp_pplus (chi,bs[s],Din,-mass*cs[0],Din,s,0);
axpby_ssp_pminus(chi,1.0,chi,cs[s-1],Din,s,s-1);
} else {
axpby_ssp_pplus (chi,bs[s],Din,cs[s+1],Din,s,s+1);
axpby_ssp_pminus(chi,1.0,chi,cs[s-1],Din,s,s-1);
}
// Collect the terms indept of DW
if ( s==0 ){
axpby_ssp_pplus (chi,1.0,chi,-1.0,psi,s,s+1);
axpby_ssp_pminus(chi,1.0,chi,mass,psi,s,Ls-1);
} else if ( s==(Ls-1)) {
axpby_ssp_pplus (chi,1.0,chi,mass,psi,s,0);
axpby_ssp_pminus(chi,1.0,chi,-1.0,psi,s,s-1);
} else {
axpby_ssp_pplus(chi,1.0,chi,-1.0,psi,s,s+1);
axpby_ssp_pminus(chi,1.0,chi,-1.0,psi,s,s-1);
}
}
// ((b D_W + D_w hop terms +1) on s-diag
axpby (chi,1.0,1.0,chi,psi);
return norm2(chi);
}
// half checkerboard operations
void CayleyFermion5D::Meooe (const LatticeFermion &psi, LatticeFermion &chi)
{
LatticeFermion tmp(psi._grid);
// Assemble the 5d matrix
for(int s=0;s<Ls;s++){
if ( s==0 ) {
// tmp = bs psi[s] + cs[s] psi[s+1}
// tmp+= -mass*cs[s] psi[s+1}
axpby_ssp_pminus(tmp,beo[s],psi,-ceo[s],psi ,s, s+1);
axpby_ssp_pplus(tmp,1.0,tmp,mass*ceo[s],psi,s,Ls-1);
} else if ( s==(Ls-1)) {
axpby_ssp_pminus(tmp,beo[s],psi,mass*ceo[s],psi,s,0);
axpby_ssp_pplus(tmp,1.0,tmp,-ceo[s],psi,s,s-1);
} else {
axpby_ssp_pminus(tmp,beo[s],psi,-ceo[s],psi,s,s+1);
axpby_ssp_pplus (tmp,1.0,tmp,-ceo[s],psi,s,s-1);
}
}
// Apply 4d dslash
if ( psi.checkerboard == Odd ) {
DhopEO(tmp,chi,DaggerNo);
} else {
DhopOE(tmp,chi,DaggerNo);
}
}
void CayleyFermion5D::MeooeDag (const LatticeFermion &psi, LatticeFermion &chi)
{
LatticeFermion tmp(psi._grid);
// Apply 4d dslash
if ( psi.checkerboard == Odd ) {
DhopEO(psi,tmp,DaggerYes);
} else {
DhopOE(psi,tmp,DaggerYes);
}
// Assemble the 5d matrix
for(int s=0;s<Ls;s++){
if ( s==0 ) {
axpby_ssp_pplus(chi,beo[s],tmp, -ceo[s+1] ,tmp,s,s+1);
axpby_ssp_pminus(chi, 1.0,chi,mass*ceo[Ls-1],tmp,s,Ls-1);
} else if ( s==(Ls-1)) {
axpby_ssp_pplus(chi,beo[s],tmp,mass*ceo[0],tmp,s,0);
axpby_ssp_pminus(chi,1.0,chi,-ceo[s-1],tmp,s,s-1);
} else {
axpby_ssp_pplus(chi,beo[s],tmp,-ceo[s+1],tmp,s,s+1);
axpby_ssp_pminus(chi,1.0 ,chi,-ceo[s-1],tmp,s,s-1);
}
}
}
void CayleyFermion5D::Mooee (const LatticeFermion &psi, LatticeFermion &chi)
{
for (int s=0;s<Ls;s++){
if ( s==0 ) {
axpby_ssp_pminus(chi,bee[s],psi ,-cee[s],psi,s,s+1);
axpby_ssp_pplus (chi,1.0,chi,mass*cee[s],psi,s,Ls-1);
} else if ( s==(Ls-1)) {
axpby_ssp_pminus(chi,bee[s],psi,mass*cee[s],psi,s,0);
axpby_ssp_pplus (chi,1.0,chi,-cee[s],psi,s,s-1);
} else {
axpby_ssp_pminus(chi,bee[s],psi,-cee[s],psi,s,s+1);
axpby_ssp_pplus (chi,1.0,chi,-cee[s],psi,s,s-1);
}
}
}
void CayleyFermion5D::Mdir (const LatticeFermion &psi, LatticeFermion &chi,int dir,int disp){
LatticeFermion tmp(psi._grid);
// Assemble the 5d matrix
for(int s=0;s<Ls;s++){
if ( s==0 ) {
// tmp = bs psi[s] + cs[s] psi[s+1}
// tmp+= -mass*cs[s] psi[s+1}
axpby_ssp_pminus(tmp,beo[s],psi,-ceo[s],psi ,s, s+1);
axpby_ssp_pplus(tmp,1.0,tmp,mass*ceo[s],psi,s,Ls-1);
} else if ( s==(Ls-1)) {
axpby_ssp_pminus(tmp,beo[s],psi,mass*ceo[s],psi,s,0);
axpby_ssp_pplus(tmp,1.0,tmp,-ceo[s],psi,s,s-1);
} else {
axpby_ssp_pminus(tmp,beo[s],psi,-ceo[s],psi,s,s+1);
axpby_ssp_pplus (tmp,1.0,tmp,-ceo[s],psi,s,s-1);
}
}
// Apply 4d dslash fragment
DhopDir(tmp,chi,dir,disp);
}
void CayleyFermion5D::MooeeDag (const LatticeFermion &psi, LatticeFermion &chi)
{
for (int s=0;s<Ls;s++){
// Assemble the 5d matrix
if ( s==0 ) {
axpby_ssp_pplus(chi,bee[s],psi,-cee[s+1] ,psi,s,s+1);
axpby_ssp_pminus(chi,1.0,chi,mass*cee[Ls-1],psi,s,Ls-1);
} else if ( s==(Ls-1)) {
axpby_ssp_pplus(chi,bee[s],psi,mass*cee[0],psi,s,0);
axpby_ssp_pminus(chi,1.0,chi,-cee[s-1],psi,s,s-1);
} else {
axpby_ssp_pplus(chi,bee[s],psi,-cee[s+1],psi,s,s+1);
axpby_ssp_pminus(chi,1.0 ,chi,-cee[s-1],psi,s,s-1);
}
}
}
void CayleyFermion5D::MooeeInv (const LatticeFermion &psi, LatticeFermion &chi)
{
// Apply (L^{\prime})^{-1}
axpby_ssp (chi,1.0,psi, 0.0,psi,0,0); // chi[0]=psi[0]
for (int s=1;s<Ls;s++){
axpby_ssp_pplus(chi,1.0,psi,-lee[s-1],chi,s,s-1);// recursion Psi[s] -lee P_+ chi[s-1]
}
// L_m^{-1}
for (int s=0;s<Ls-1;s++){ // Chi[ee] = 1 - sum[s<Ls-1] -leem[s]P_- chi
axpby_ssp_pminus(chi,1.0,chi,-leem[s],chi,Ls-1,s);
}
// U_m^{-1} D^{-1}
for (int s=0;s<Ls-1;s++){
// Chi[s] + 1/d chi[s]
axpby_ssp_pplus(chi,1.0/dee[s],chi,-ueem[s]/dee[Ls-1],chi,s,Ls-1);
}
axpby_ssp(chi,1.0/dee[Ls-1],chi,0.0,chi,Ls-1,Ls-1); // Modest avoidable
// Apply U^{-1}
for (int s=Ls-2;s>=0;s--){
axpby_ssp_pminus (chi,1.0,chi,-uee[s],chi,s,s+1); // chi[Ls]
}
}
void CayleyFermion5D::MooeeInvDag (const LatticeFermion &psi, LatticeFermion &chi)
{
// Apply (U^{\prime})^{-dagger}
axpby_ssp (chi,1.0,psi, 0.0,psi,0,0); // chi[0]=psi[0]
for (int s=1;s<Ls;s++){
axpby_ssp_pminus(chi,1.0,psi,-uee[s-1],chi,s,s-1);
}
// U_m^{-\dagger}
for (int s=0;s<Ls-1;s++){
axpby_ssp_pplus(chi,1.0,chi,-ueem[s],chi,Ls-1,s);
}
// L_m^{-\dagger} D^{-dagger}
for (int s=0;s<Ls-1;s++){
axpby_ssp_pminus(chi,1.0/dee[s],chi,-leem[s]/dee[Ls-1],chi,s,Ls-1);
}
axpby_ssp(chi,1.0/dee[Ls-1],chi,0.0,chi,Ls-1,Ls-1); // Modest avoidable
// Apply L^{-dagger}
for (int s=Ls-2;s>=0;s--){
axpby_ssp_pplus (chi,1.0,chi,-lee[s],chi,s,s+1); // chi[Ls]
}
}
// Tanh
void CayleyFermion5D::SetCoefficientsTanh(Approx::zolotarev_data *zdata,RealD b,RealD c)
{
SetCoefficientsZolotarev(1.0,zdata,b,c);
}
//Zolo
void CayleyFermion5D::SetCoefficientsZolotarev(RealD zolo_hi,Approx::zolotarev_data *zdata,RealD b,RealD c)
{
///////////////////////////////////////////////////////////
// The Cayley coeffs (unprec)
///////////////////////////////////////////////////////////
omega.resize(Ls);
bs.resize(Ls);
cs.resize(Ls);
as.resize(Ls);
//
// Ts = ( [bs+cs]Dw )^-1 ( (bs+cs) Dw )
// -(g5 ------- -1 ) ( g5 --------- + 1 )
// ( {2+(bs-cs)Dw} ) ( 2+(bs-cs) Dw )
//
// bs = 1/2( (1/omega_s + 1)*b + (1/omega - 1)*c ) = 1/2( 1/omega(b+c) + (b-c) )
// cs = 1/2( (1/omega_s - 1)*b + (1/omega + 1)*c ) = 1/2( 1/omega(b+c) - (b-c) )
//
// bs+cs = 0.5*( 1/omega(b+c) + (b-c) + 1/omega(b+c) - (b-c) ) = 1/omega(b+c)
// bs-cs = 0.5*( 1/omega(b+c) + (b-c) - 1/omega(b+c) + (b-c) ) = b-c
//
// So
//
// Ts = ( [b+c]Dw/omega_s )^-1 ( (b+c) Dw /omega_s )
// -(g5 ------- -1 ) ( g5 --------- + 1 )
// ( {2+(b-c)Dw} ) ( 2+(b-c) Dw )
//
// Ts = ( [b+c]Dw )^-1 ( (b+c) Dw )
// -(g5 ------- -omega_s) ( g5 --------- + omega_s )
// ( {2+(b-c)Dw} ) ( 2+(b-c) Dw )
//
double bpc = b+c;
double bmc = b-c;
for(int i=0; i < Ls; i++){
as[i] = 1.0;
omega[i] = ((double)zdata->gamma[i])*zolo_hi; //NB reciprocal relative to Chroma NEF code
bs[i] = 0.5*(bpc/omega[i] + bmc);
cs[i] = 0.5*(bpc/omega[i] - bmc);
}
////////////////////////////////////////////////////////
// Constants for the preconditioned matrix Cayley form
////////////////////////////////////////////////////////
bee.resize(Ls);
cee.resize(Ls);
beo.resize(Ls);
ceo.resize(Ls);
for(int i=0;i<Ls;i++){
bee[i]=as[i]*(bs[i]*(4.0-M5) +1.0);
cee[i]=as[i]*(1.0-cs[i]*(4.0-M5));
beo[i]=as[i]*bs[i];
ceo[i]=-as[i]*cs[i];
}
aee.resize(Ls);
aeo.resize(Ls);
for(int i=0;i<Ls;i++){
aee[i]=cee[i];
aeo[i]=ceo[i];
}
//////////////////////////////////////////
// LDU decomposition of eeoo
//////////////////////////////////////////
dee.resize(Ls);
lee.resize(Ls);
leem.resize(Ls);
uee.resize(Ls);
ueem.resize(Ls);
for(int i=0;i<Ls;i++){
dee[i] = bee[i];
if ( i < Ls-1 ) {
lee[i] =-cee[i+1]/bee[i]; // sub-diag entry on the ith column
leem[i]=mass*cee[Ls-1]/bee[0];
for(int j=0;j<i;j++) leem[i]*= aee[j]/bee[j+1];
uee[i] =-aee[i]/bee[i]; // up-diag entry on the ith row
ueem[i]=mass;
for(int j=1;j<=i;j++) ueem[i]*= cee[j]/bee[j];
ueem[i]*= aee[0]/bee[0];
} else {
lee[i] =0.0;
leem[i]=0.0;
uee[i] =0.0;
ueem[i]=0.0;
}
}
{
double delta_d=mass*cee[Ls-1];
for(int j=0;j<Ls-1;j++) delta_d *= cee[j]/bee[j];
dee[Ls-1] += delta_d;
}
}
}}
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