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Grid/lib/qcd/action/fermion/MobiusEOFAFermion.cc
paboyle bf58557fb1 Block compressed Lanczos
2017-10-10 14:15:11 +01:00

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/*************************************************************************************
Grid physics library, www.github.com/paboyle/Grid
Source file: ./lib/qcd/action/fermion/MobiusEOFAFermion.cc
Copyright (C) 2017
Author: Peter Boyle <pabobyle@ph.ed.ac.uk>
Author: Peter Boyle <paboyle@ph.ed.ac.uk>
Author: Peter Boyle <peterboyle@Peters-MacBook-Pro-2.local>
Author: paboyle <paboyle@ph.ed.ac.uk>
Author: David Murphy <dmurphy@phys.columbia.edu>
This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License along
with this program; if not, write to the Free Software Foundation, Inc.,
51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
See the full license in the file "LICENSE" in the top level distribution directory
*************************************************************************************/
/* END LEGAL */
#include <Grid/Grid_Eigen_Dense.h>
#include <Grid/qcd/action/fermion/FermionCore.h>
#include <Grid/qcd/action/fermion/MobiusEOFAFermion.h>
namespace Grid {
namespace QCD {
template<class Impl>
MobiusEOFAFermion<Impl>::MobiusEOFAFermion(
GaugeField &_Umu,
GridCartesian &FiveDimGrid,
GridRedBlackCartesian &FiveDimRedBlackGrid,
GridCartesian &FourDimGrid,
GridRedBlackCartesian &FourDimRedBlackGrid,
RealD _mq1, RealD _mq2, RealD _mq3,
RealD _shift, int _pm, RealD _M5,
RealD _b, RealD _c, const ImplParams &p) :
AbstractEOFAFermion<Impl>(_Umu, FiveDimGrid, FiveDimRedBlackGrid,
FourDimGrid, FourDimRedBlackGrid, _mq1, _mq2, _mq3,
_shift, _pm, _M5, _b, _c, p)
{
int Ls = this->Ls;
RealD eps = 1.0;
Approx::zolotarev_data *zdata = Approx::higham(eps, this->Ls);
assert(zdata->n == this->Ls);
std::cout << GridLogMessage << "MobiusEOFAFermion (b=" << _b <<
",c=" << _c << ") with Ls=" << Ls << std::endl;
this->SetCoefficientsTanh(zdata, _b, _c);
std::cout << GridLogMessage << "EOFA parameters: (mq1=" << _mq1 <<
",mq2=" << _mq2 << ",mq3=" << _mq3 << ",shift=" << _shift <<
",pm=" << _pm << ")" << std::endl;
Approx::zolotarev_free(zdata);
if(_shift != 0.0){
SetCoefficientsPrecondShiftOps();
} else {
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);
}
}
/****************************************************************
* Additional EOFA operators only called outside the inverter.
* Since speed is not essential, simple axpby-style
* implementations should be fine.
***************************************************************/
template<class Impl>
void MobiusEOFAFermion<Impl>::Omega(const FermionField& psi, FermionField& Din, int sign, int dag)
{
int Ls = this->Ls;
RealD alpha = this->alpha;
Din = zero;
if((sign == 1) && (dag == 0)) { // \Omega_{+}
for(int s=0; s<Ls; ++s){
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);
}
} else if((sign == -1) && (dag == 0)) { // \Omega_{-}
for(int s=0; s<Ls; ++s){
axpby_ssp(Din, 0.0, psi, 2.0*std::pow(1.0-alpha,s)/std::pow(1.0+alpha,s+1), psi, s, 0);
}
} else if((sign == 1 ) && (dag == 1)) { // \Omega_{+}^{\dagger}
for(int sp=0; sp<Ls; ++sp){
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);
}
} else if((sign == -1) && (dag == 1)) { // \Omega_{-}^{\dagger}
for(int sp=0; sp<Ls; ++sp){
axpby_ssp(Din, 1.0, Din, 2.0*std::pow(1.0-alpha,sp)/std::pow(1.0+alpha,sp+1), psi, 0, sp);
}
}
}
// 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){
if(s == 0) {
axpby_ssp_pminus(chi, b, psi, -c, psi, s, s+1);
axpby_ssp_pplus (chi, 1.0, chi, mq1*c, psi, s, Ls-1);
} else if(s == (Ls-1)) {
axpby_ssp_pminus(chi, b, psi, mq1*c, psi, s, 0);
axpby_ssp_pplus (chi, 1.0, chi, -c, psi, s, s-1);
} else {
axpby_ssp_pminus(chi, b, psi, -c, psi, s, s+1);
axpby_ssp_pplus (chi, 1.0, chi, -c, psi, s, s-1);
}
}
}
template<class Impl>
void MobiusEOFAFermion<Impl>::DtildeInv(const FermionField& psi, FermionField& chi)
{
int Ls = this->Ls;
RealD m = this->mq1;
RealD c = 0.5 * this->alpha;
RealD d = 0.5;
RealD DtInv_p(0.0), DtInv_m(0.0);
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);
}}
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