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Julian Lenz 2022-11-25 17:44:08 +00:00
parent 1aa28b47ae
commit 9273f2937c
1 changed files with 138 additions and 143 deletions
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101
Grid/qcd/utils/SUn.h
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@ -194,8 +194,6 @@ public:
ta = ta * nrm; ta = ta * nrm;
} }
//////////////////////////////////////////////////////////////////////// ////////////////////////////////////////////////////////////////////////
// Map a su2 subgroup number to the pair of rows that are non zero // Map a su2 subgroup number to the pair of rows that are non zero
//////////////////////////////////////////////////////////////////////// ////////////////////////////////////////////////////////////////////////
@ -227,7 +225,6 @@ public:
autoView(source_v, source, AcceleratorRead); autoView(source_v, source, AcceleratorRead);
autoView(Determinant_v, Determinant, AcceleratorWrite); autoView(Determinant_v, Determinant, AcceleratorWrite);
accelerator_for(ss, grid->oSites(), 1, { accelerator_for(ss, grid->oSites(), 1, {
subgroup_v[ss]()()(0, 0) = source_v[ss]()()(i0, i0); subgroup_v[ss]()()(0, 0) = source_v[ss]()()(i0, i0);
subgroup_v[ss]()()(0, 1) = source_v[ss]()()(i0, i1); subgroup_v[ss]()()(0, 1) = source_v[ss]()()(i0, i1);
subgroup_v[ss]()()(1, 0) = source_v[ss]()()(i1, i0); subgroup_v[ss]()()(1, 0) = source_v[ss]()()(i1, i0);
@ -259,14 +256,12 @@ public:
dest = 1.0; // start out with identity dest = 1.0; // start out with identity
autoView(dest_v, dest, AcceleratorWrite); autoView(dest_v, dest, AcceleratorWrite);
autoView(subgroup_v, subgroup, AcceleratorRead); autoView(subgroup_v, subgroup, AcceleratorRead);
accelerator_for(ss, grid->oSites(),1, accelerator_for(ss, grid->oSites(), 1, {
{
dest_v[ss]()()(i0, i0) = subgroup_v[ss]()()(0, 0); dest_v[ss]()()(i0, i0) = subgroup_v[ss]()()(0, 0);
dest_v[ss]()()(i0, i1) = subgroup_v[ss]()()(0, 1); dest_v[ss]()()(i0, i1) = subgroup_v[ss]()()(0, 1);
dest_v[ss]()()(i1, i0) = subgroup_v[ss]()()(1, 0); dest_v[ss]()()(i1, i0) = subgroup_v[ss]()()(1, 0);
dest_v[ss]()()(i1, i1) = subgroup_v[ss]()()(1, 1); dest_v[ss]()()(i1, i1) = subgroup_v[ss]()()(1, 1);
}); });
} }
/////////////////////////////////////////////// ///////////////////////////////////////////////
@ -279,12 +274,12 @@ public:
// in action. // in action.
// //
/////////////////////////////////////////////// ///////////////////////////////////////////////
static void SubGroupHeatBath(GridSerialRNG &sRNG, GridParallelRNG &pRNG, static void SubGroupHeatBath(
GridSerialRNG &sRNG, GridParallelRNG &pRNG,
RealD beta, // coeff multiplying staple in action (with no 1/Nc) RealD beta, // coeff multiplying staple in action (with no 1/Nc)
LatticeMatrix &link, LatticeMatrix &link,
const LatticeMatrix &barestaple, // multiplied by action coeffs so th const LatticeMatrix &barestaple, // multiplied by action coeffs so th
int su2_subgroup, int nheatbath, LatticeInteger &wheremask) int su2_subgroup, int nheatbath, LatticeInteger &wheremask) {
{
GridBase *grid = link.Grid(); GridBase *grid = link.Grid();
const RealD twopi = 2.0 * M_PI; const RealD twopi = 2.0 * M_PI;
@ -297,7 +292,8 @@ public:
V = link * staple; V = link * staple;
// Subgroup manipulation in the lie algebra space // Subgroup manipulation in the lie algebra space
LatticeSU2Matrix u(grid); // Kennedy pendleton "u" real projected normalised Sigma LatticeSU2Matrix u(
grid); // Kennedy pendleton "u" real projected normalised Sigma
LatticeSU2Matrix uinv(grid); LatticeSU2Matrix uinv(grid);
LatticeSU2Matrix ua(grid); // a in pauli form LatticeSU2Matrix ua(grid); // a in pauli form
LatticeSU2Matrix b(grid); // rotated matrix after hb LatticeSU2Matrix b(grid); // rotated matrix after hb
@ -405,29 +401,24 @@ public:
r) ) r) )
= da0 r/2 sin theta dr dtheta dphi delta( (sqrt(1-a0^) - r) ) = da0 r/2 sin theta dr dtheta dphi delta( (sqrt(1-a0^) - r) )
Action factor Q(h) dh = e^-S[h] dh = e^{ xi Tr uh} dh // beta enters Action factor Q(h) dh = e^-S[h] dh = e^{ xi Tr uh} dh // beta
through xi enters through xi = e^{2 xi (h.u)} dh = e^{2 xi h0u0}.e^{2 xi h1u1}.e^{2
= e^{2 xi (h.u)} dh xi h2u2}.e^{2 xi h3u3} dh
= e^{2 xi h0u0}.e^{2 xi h1u1}.e^{2 xi
h2u2}.e^{2 xi h3u3} dh
Therefore for each site, take xi for that site Therefore for each site, take xi for that site
i) generate |a0|<1 with dist i) generate |a0|<1 with dist
(1-a0^2)^0.5 e^{2 xi a0 } da0 (1-a0^2)^0.5 e^{2 xi a0 } da0
Take alpha = 2 xi = 2 xi [ recall 2 beta/Nc unmod staple norm]; hence 2.0/Nc Take alpha = 2 xi = 2 xi [ recall 2 beta/Nc unmod staple norm];
factor in Chroma ] hence 2.0/Nc factor in Chroma ] A. Generate two uniformly distributed
A. Generate two uniformly distributed pseudo-random numbers R and R', R'', pseudo-random numbers R and R', R'', R''' in the unit interval; B. Set X =
R''' in the unit interval; -(ln R)/alpha, X' =-(ln R')/alpha; C. Set C = cos^2(2pi R"), with R"
B. Set X = -(ln R)/alpha, X' =-(ln R')/alpha; another uniform random number in [0,1] ; D. Set A = XC; E. Let d = X'+A;
C. Set C = cos^2(2pi R"), with R" another uniform random number in [0,1] ;
D. Set A = XC;
E. Let d = X'+A;
F. If R'''^2 :> 1 - 0.5 d, go back to A; F. If R'''^2 :> 1 - 0.5 d, go back to A;
G. Set a0 = 1 - d; G. Set a0 = 1 - d;
Note that in step D setting B ~ X - A and using B in place of A in step E will Note that in step D setting B ~ X - A and using B in place of A in step E
generate a second independent a 0 value. will generate a second independent a 0 value.
*/ */
///////////////////////////////////////////////////////// /////////////////////////////////////////////////////////
@ -568,8 +559,6 @@ public:
} }
} }
static void testGenerators(void) { static void testGenerators(void) {
Matrix ta; Matrix ta;
Matrix tb; Matrix tb;
@ -610,8 +599,8 @@ public:
// reunitarise?? // reunitarise??
template <typename LatticeMatrixType> template <typename LatticeMatrixType>
static void LieRandomize(GridParallelRNG &pRNG, LatticeMatrixType &out, double scale = 1.0) static void LieRandomize(GridParallelRNG &pRNG, LatticeMatrixType &out,
{ double scale = 1.0) {
GridBase *grid = out.Grid(); GridBase *grid = out.Grid();
typedef typename LatticeMatrixType::vector_type vector_type; typedef typename LatticeMatrixType::vector_type vector_type;
@ -620,7 +609,8 @@ public:
typedef iSinglet<vector_type> vTComplexType; typedef iSinglet<vector_type> vTComplexType;
typedef Lattice<vTComplexType> LatticeComplexType; typedef Lattice<vTComplexType> LatticeComplexType;
typedef typename GridTypeMapper<typename LatticeMatrixType::vector_object>::scalar_object MatrixType; typedef typename GridTypeMapper<
typename LatticeMatrixType::vector_object>::scalar_object MatrixType;
LatticeComplexType ca(grid); LatticeComplexType ca(grid);
LatticeMatrixType lie(grid); LatticeMatrixType lie(grid);
@ -642,7 +632,6 @@ public:
la = ci * ca * ta; la = ci * ca * ta;
lie = lie + la; // e^{i la ta} lie = lie + la; // e^{i la ta}
} }
taExp(lie, out); taExp(lie, out);
} }
@ -700,7 +689,8 @@ public:
conformable(grid, g.Grid()); conformable(grid, g.Grid());
GaugeMat U(grid); GaugeMat U(grid);
GaugeMat ag(grid); ag = adj(g); GaugeMat ag(grid);
ag = adj(g);
for (int mu = 0; mu < Nd; mu++) { for (int mu = 0; mu < Nd; mu++) {
U = PeekIndex<LorentzIndex>(Umu, mu); U = PeekIndex<LorentzIndex>(Umu, mu);
@ -711,20 +701,23 @@ public:
template <typename GaugeMat> template <typename GaugeMat>
static void GaugeTransform(std::vector<GaugeMat> &U, GaugeMat &g) { static void GaugeTransform(std::vector<GaugeMat> &U, GaugeMat &g) {
GridBase *grid = g.Grid(); GridBase *grid = g.Grid();
GaugeMat ag(grid); ag = adj(g); GaugeMat ag(grid);
ag = adj(g);
for (int mu = 0; mu < Nd; mu++) { for (int mu = 0; mu < Nd; mu++) {
U[mu] = g * U[mu] * Cshift(ag, mu, 1); U[mu] = g * U[mu] * Cshift(ag, mu, 1);
} }
} }
template <typename GaugeField, typename GaugeMat> template <typename GaugeField, typename GaugeMat>
static void RandomGaugeTransform(GridParallelRNG &pRNG, GaugeField &Umu, GaugeMat &g){ static void RandomGaugeTransform(GridParallelRNG &pRNG, GaugeField &Umu,
GaugeMat &g) {
LieRandomize(pRNG, g, 1.0); LieRandomize(pRNG, g, 1.0);
GaugeTransform(Umu, g); GaugeTransform(Umu, g);
} }
// Projects the algebra components a lattice matrix (of dimension ncol*ncol -1 ) // Projects the algebra components a lattice matrix (of dimension ncol*ncol -1
// inverse operation: FundamentalLieAlgebraMatrix // ) inverse operation: FundamentalLieAlgebraMatrix
static void projectOnAlgebra(LatticeAlgebraVector &h_out, const LatticeMatrix &in, Real scale = 1.0) { static void projectOnAlgebra(LatticeAlgebraVector &h_out,
const LatticeMatrix &in, Real scale = 1.0) {
conformable(h_out, in); conformable(h_out, in);
h_out = Zero(); h_out = Zero();
Matrix Ta; Matrix Ta;
@ -800,8 +793,8 @@ public:
}; };
template <int N> template <int N>
LatticeComplexD Determinant(const Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > &Umu) LatticeComplexD Determinant(
{ const Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > &Umu) {
GridBase *grid = Umu.Grid(); GridBase *grid = Umu.Grid();
auto lvol = grid->lSites(); auto lvol = grid->lSites();
LatticeComplexD ret(grid); LatticeComplexD ret(grid);
@ -817,15 +810,16 @@ LatticeComplexD Determinant(const Lattice<iScalar<iScalar<iMatrix<vComplexD, N>
for (int i = 0; i < N; i++) { for (int i = 0; i < N; i++) {
for (int j = 0; j < N; j++) { for (int j = 0; j < N; j++) {
EigenU(i, j) = Us()()(i, j); EigenU(i, j) = Us()()(i, j);
}} }
}
ComplexD det = EigenU.determinant(); ComplexD det = EigenU.determinant();
pokeLocalSite(det, ret_v, lcoor); pokeLocalSite(det, ret_v, lcoor);
}); });
return ret; return ret;
} }
template <int N> template <int N>
static void ProjectSUn(Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > &Umu) static void ProjectSUn(
{ Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > &Umu) {
Umu = ProjectOnGroup(Umu); Umu = ProjectOnGroup(Umu);
auto det = Determinant(Umu); auto det = Determinant(Umu);
@ -838,8 +832,8 @@ static void ProjectSUn(Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > &Umu)
} }
} }
template <int N> template <int N>
static void ProjectSUn(Lattice<iVector<iScalar<iMatrix<vComplexD, N> >,Nd> > &U) static void ProjectSUn(
{ Lattice<iVector<iScalar<iMatrix<vComplexD, N> >, Nd> > &U) {
GridBase *grid = U.Grid(); GridBase *grid = U.Grid();
// Reunitarise // Reunitarise
for (int mu = 0; mu < Nd; mu++) { for (int mu = 0; mu < Nd; mu++) {
@ -851,9 +845,8 @@ static void ProjectSUn(Lattice<iVector<iScalar<iMatrix<vComplexD, N> >,Nd> > &U)
} }
// Explicit specialisation for SU(3). // Explicit specialisation for SU(3).
// Explicit specialisation for SU(3). // Explicit specialisation for SU(3).
static void static void ProjectSU3(
ProjectSU3 (Lattice<iScalar<iScalar<iMatrix<vComplexD, 3> > > > &Umu) Lattice<iScalar<iScalar<iMatrix<vComplexD, 3> > > > &Umu) {
{
GridBase *grid = Umu.Grid(); GridBase *grid = Umu.Grid();
const int x = 0; const int x = 0;
const int y = 1; const int y = 1;
@ -863,14 +856,17 @@ ProjectSU3 (Lattice<iScalar<iScalar<iMatrix<vComplexD, 3> > > > &Umu)
autoView(Umu_v, Umu, CpuWrite); autoView(Umu_v, Umu, CpuWrite);
thread_for(ss, grid->oSites(), { thread_for(ss, grid->oSites(), {
auto cm = Umu_v[ss]; auto cm = Umu_v[ss];
cm()()(2,x) = adj(cm()()(0,y)*cm()()(1,z)-cm()()(0,z)*cm()()(1,y)); //x= yz-zy cm()()(2, x) = adj(cm()()(0, y) * cm()()(1, z) -
cm()()(2,y) = adj(cm()()(0,z)*cm()()(1,x)-cm()()(0,x)*cm()()(1,z)); //y= zx-xz cm()()(0, z) * cm()()(1, y)); // x= yz-zy
cm()()(2,z) = adj(cm()()(0,x)*cm()()(1,y)-cm()()(0,y)*cm()()(1,x)); //z= xy-yx cm()()(2, y) = adj(cm()()(0, z) * cm()()(1, x) -
cm()()(0, x) * cm()()(1, z)); // y= zx-xz
cm()()(2, z) = adj(cm()()(0, x) * cm()()(1, y) -
cm()()(0, y) * cm()()(1, x)); // z= xy-yx
Umu_v[ss] = cm; Umu_v[ss] = cm;
}); });
} }
static void ProjectSU3(Lattice<iVector<iScalar<iMatrix<vComplexD, 3> >,Nd> > &U) static void ProjectSU3(
{ Lattice<iVector<iScalar<iMatrix<vComplexD, 3> >, Nd> > &U) {
GridBase *grid = U.Grid(); GridBase *grid = U.Grid();
// Reunitarise // Reunitarise
for (int mu = 0; mu < Nd; mu++) { for (int mu = 0; mu < Nd; mu++) {
@ -886,7 +882,6 @@ typedef SU<3> SU3;
typedef SU<4> SU4; typedef SU<4> SU4;
typedef SU<5> SU5; typedef SU<5> SU5;
typedef SU<Nc> FundamentalMatrices; typedef SU<Nc> FundamentalMatrices;
NAMESPACE_END(Grid); NAMESPACE_END(Grid);