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feat: changed CompactWilsonExpClover exponentiation to Taylor expansion

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with Horner scheme.
This commit is contained in:
Fabian Joswig 2022-10-25 15:19:43 +01:00
parent 477ebf24f4
commit 9e4835a3e3
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2 changed files with 50 additions and 164 deletions
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203
Grid/qcd/action/fermion/CloverHelpers.h
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@ -242,6 +242,19 @@ public:
// mass term is multiplied to exp(Clover) below
}
// Can this be avoided?
static void IdentityTimesC(const CloverField& in, RealD c) {
int DimRep = Impl::Dimension;
autoView(in_v, in, AcceleratorWrite);
accelerator_for(ss, in.Grid()->oSites(), 1, {
for (int sa=0; sa<Ns; sa++)
for (int ca=0; ca<DimRep; ca++)
in_v[ss]()(sa,sa)(ca,ca) = c;
});
}
static int getNMAX(RealD prec, RealD R) {
/* compute stop condition for exponential */
int NMAX=1;
@ -254,176 +267,46 @@ public:
return NMAX;
}
static int getNMAX(Lattice<iImplCloverDiagonal<vComplexD>> &t, RealD R) {return getNMAX(1e-12,R);}
static int getNMAX(Lattice<iImplCloverDiagonal<vComplexF>> &t, RealD R) {return getNMAX(1e-6,R);}
static int getNMAX(Lattice<iImplClover<vComplexD>> &t, RealD R) {return getNMAX(1e-12,R);}
static int getNMAX(Lattice<iImplClover<vComplexF>> &t, RealD R) {return getNMAX(1e-6,R);}
static void ExponentiateHermitean6by6(const iMatrix<ComplexD,6> &arg, const RealD& alpha, const std::vector<RealD>& cN, const int Niter, iMatrix<ComplexD,6>& dest){
static void Exponentiate_Clover(CloverField& Clover, CloverField& CloverInv, RealD csw_t, RealD diag_mass) {
typedef iMatrix<ComplexD,6> mat;
GridBase* grid = Clover.Grid();
CloverField ExpClover(grid);
RealD qn[6];
RealD qnold[6];
RealD p[5];
RealD trA2, trA3, trA4;
int NMAX = getNMAX(Clover, 3.*csw_t/diag_mass);
mat A2, A3, A4, A5;
A2 = alpha * alpha * arg * arg;
A3 = alpha * arg * A2;
A4 = A2 * A2;
A5 = A2 * A3;
Clover *= (1.0/diag_mass);
trA2 = toReal( trace(A2) );
trA3 = toReal( trace(A3) );
trA4 = toReal( trace(A4));
p[0] = toReal( trace(A3 * A3)) / 6.0 - 0.125 * trA4 * trA2 - trA3 * trA3 / 18.0 + trA2 * trA2 * trA2/ 48.0;
p[1] = toReal( trace(A5)) / 5.0 - trA3 * trA2 / 6.0;
p[2] = toReal( trace(A4)) / 4.0 - 0.125 * trA2 * trA2;
p[3] = trA3 / 3.0;
p[4] = 0.5 * trA2;
qnold[0] = cN[Niter];
qnold[1] = 0.0;
qnold[2] = 0.0;
qnold[3] = 0.0;
qnold[4] = 0.0;
qnold[5] = 0.0;
for(int i = Niter-1; i >= 0; i--)
{
qn[0] = p[0] * qnold[5] + cN[i];
qn[1] = p[1] * qnold[5] + qnold[0];
qn[2] = p[2] * qnold[5] + qnold[1];
qn[3] = p[3] * qnold[5] + qnold[2];
qn[4] = p[4] * qnold[5] + qnold[3];
qn[5] = qnold[4];
qnold[0] = qn[0];
qnold[1] = qn[1];
qnold[2] = qn[2];
qnold[3] = qn[3];
qnold[4] = qn[4];
qnold[5] = qn[5];
}
mat unit(1.0);
dest = (qn[0] * unit + qn[1] * alpha * arg + qn[2] * A2 + qn[3] * A3 + qn[4] * A4 + qn[5] * A5);
}
static void Exponentiate_Clover(CloverDiagonalField& Diagonal, CloverTriangleField& Triangle, RealD csw_t, RealD diag_mass) {
GridBase* grid = Diagonal.Grid();
int NMAX = getNMAX(Diagonal, 3.*csw_t/diag_mass);
//
// Implementation completely in Daniel's layout
//
// Taylor expansion with Cayley-Hamilton recursion
// underlying Horner scheme as above
// Taylor expansion, slow but generic
// Horner scheme: a0 + a1 x + a2 x^2 + .. = a0 + x (a1 + x(...))
// qN = cN
// qn = cn + qn+1 X
std::vector<RealD> cn(NMAX+1);
cn[0] = 1.0;
for (int i=1; i<=NMAX; i++){
for (int i=1; i<=NMAX; i++)
cn[i] = cn[i-1] / RealD(i);
ExpClover = Zero();
IdentityTimesC(ExpClover, cn[NMAX]);
for (int i=NMAX-1; i>=0; i--)
ExpClover = ExpClover * Clover + cn[i];
// prepare inverse
CloverInv = (-1.0)*Clover;
Clover = ExpClover * diag_mass;
ExpClover = Zero();
IdentityTimesC(ExpClover, cn[NMAX]);
for (int i=NMAX-1; i>=0; i--)
ExpClover = ExpClover * CloverInv + cn[i];
CloverInv = ExpClover * (1.0/diag_mass);
}
// Taken over from Daniel's implementation
conformable(Diagonal, Triangle);
long lsites = grid->lSites();
{
typedef typename SiteCloverDiagonal::scalar_object scalar_object_diagonal;
typedef typename SiteCloverTriangle::scalar_object scalar_object_triangle;
typedef iMatrix<ComplexD,6> mat;
autoView(diagonal_v, Diagonal, CpuRead);
autoView(triangle_v, Triangle, CpuRead);
autoView(diagonalExp_v, Diagonal, CpuWrite);
autoView(triangleExp_v, Triangle, CpuWrite);
thread_for(site, lsites, { // NOTE: Not on GPU because of (peek/poke)LocalSite
mat srcCloverOpUL(0.0); // upper left block
mat srcCloverOpLR(0.0); // lower right block
mat ExpCloverOp;
scalar_object_diagonal diagonal_tmp = Zero();
scalar_object_diagonal diagonal_exp_tmp = Zero();
scalar_object_triangle triangle_tmp = Zero();
scalar_object_triangle triangle_exp_tmp = Zero();
Coordinate lcoor;
grid->LocalIndexToLocalCoor(site, lcoor);
peekLocalSite(diagonal_tmp, diagonal_v, lcoor);
peekLocalSite(triangle_tmp, triangle_v, lcoor);
int block;
block = 0;
for(int i = 0; i < 6; i++){
for(int j = 0; j < 6; j++){
if (i == j){
srcCloverOpUL(i,j) = static_cast<ComplexD>(TensorRemove(diagonal_tmp()(block)(i)));
}
else{
srcCloverOpUL(i,j) = static_cast<ComplexD>(TensorRemove(CompactHelpers::triangle_elem(triangle_tmp, block, i, j)));
}
}
}
block = 1;
for(int i = 0; i < 6; i++){
for(int j = 0; j < 6; j++){
if (i == j){
srcCloverOpLR(i,j) = static_cast<ComplexD>(TensorRemove(diagonal_tmp()(block)(i)));
}
else{
srcCloverOpLR(i,j) = static_cast<ComplexD>(TensorRemove(CompactHelpers::triangle_elem(triangle_tmp, block, i, j)));
}
}
}
// exp(Clover)
ExponentiateHermitean6by6(srcCloverOpUL,1.0/diag_mass,cn,NMAX,ExpCloverOp);
block = 0;
for(int i = 0; i < 6; i++){
for(int j = 0; j < 6; j++){
if (i == j){
diagonal_exp_tmp()(block)(i) = ExpCloverOp(i,j);
}
else if(i < j){
triangle_exp_tmp()(block)(CompactHelpers::triangle_index(i, j)) = ExpCloverOp(i,j);
}
}
}
ExponentiateHermitean6by6(srcCloverOpLR,1.0/diag_mass,cn,NMAX,ExpCloverOp);
block = 1;
for(int i = 0; i < 6; i++){
for(int j = 0; j < 6; j++){
if (i == j){
diagonal_exp_tmp()(block)(i) = ExpCloverOp(i,j);
}
else if(i < j){
triangle_exp_tmp()(block)(CompactHelpers::triangle_index(i, j)) = ExpCloverOp(i,j);
}
}
}
pokeLocalSite(diagonal_exp_tmp, diagonalExp_v, lcoor);
pokeLocalSite(triangle_exp_tmp, triangleExp_v, lcoor);
});
}
Diagonal *= diag_mass;
Triangle *= diag_mass;
}
static GaugeLinkField Cmunu(std::vector<GaugeLinkField> &U, GaugeLinkField &lambda, int mu, int nu) {
assert(0);
return lambda;

11
Grid/qcd/action/fermion/implementation/CompactWilsonCloverFermionImplementation.h
View File

@ -305,6 +305,7 @@ void CompactWilsonCloverFermion<Impl, CloverHelpers>::ImportGauge(const GaugeFie
GridBase* grid = _Umu.Grid();
typename Impl::GaugeLinkField Bx(grid), By(grid), Bz(grid), Ex(grid), Ey(grid), Ez(grid);
CloverField TmpOriginal(grid);
CloverField TmpInverse(grid);
// Compute the field strength terms mu>nu
double t2 = usecond();
@ -326,14 +327,14 @@ void CompactWilsonCloverFermion<Impl, CloverHelpers>::ImportGauge(const GaugeFie
TmpOriginal += Helpers::fillCloverZT(Ez) * csw_t;
// Handle mass term based on clover policy
CloverHelpers::MassTerm(TmpOriginal, this->diag_mass);
// Convert the data layout of the clover term
double t4 = usecond();
CompactHelpers::ConvertLayout(TmpOriginal, Diagonal, Triangle);
CloverHelpers::Exponentiate_Clover(TmpOriginal, TmpInverse, csw_t, this->diag_mass);
// Exponentiate the clover (nothing happens in case of the standard clover)
double t5 = usecond();
CloverHelpers::Exponentiate_Clover(Diagonal, Triangle, csw_t, this->diag_mass);
CompactHelpers::ConvertLayout(TmpOriginal, Diagonal, Triangle);
// Possible modify the boundary values
double t6 = usecond();
@ -341,7 +342,9 @@ void CompactWilsonCloverFermion<Impl, CloverHelpers>::ImportGauge(const GaugeFie
// Invert the Clover term (explicit inversion needed for the improvement in case of open boundary conditions)
double t7 = usecond();
CompactHelpers::Invert(Diagonal, Triangle, DiagonalInv, TriangleInv);
//CompactHelpers::Invert(Diagonal, Triangle, DiagonalInv, TriangleInv);
CompactHelpers::ConvertLayout(TmpInverse, DiagonalInv, TriangleInv);
//if(open_boundaries) handle differently!
// Fill the remaining clover fields
double t8 = usecond();