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projectU3 yields a unitary matrix

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This commit is contained in:
david clarke
2024-01-23 14:43:58 -07:00
parent 00f24f8765
commit 4924b3209e
3 changed files with 23 additions and 20 deletions
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31
Grid/qcd/smearing/HISQSmearing.h
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@ -330,7 +330,7 @@ public:
// IN--u_mu
void projectU3(GF& u_proj, GF& u_mu) const {
LF V(u_mu.Grid()), Q(u_mu.Grid()), sqrtQinv(u_mu.Grid()), id_3(u_mu.Grid());
LF V(u_mu.Grid()), Q(u_mu.Grid()), sqrtQinv(u_mu.Grid()), id_3(u_mu.Grid()), diff(u_mu.Grid());
CF c0(u_mu.Grid()), c1(u_mu.Grid()), c2(u_mu.Grid()), g0(u_mu.Grid()), g1(u_mu.Grid()),
g2(u_mu.Grid()), S(u_mu.Grid()), R(u_mu.Grid()), theta(u_mu.Grid()), u(u_mu.Grid()),
v(u_mu.Grid()), w(u_mu.Grid()), den(u_mu.Grid()), f0(u_mu.Grid()), f1(u_mu.Grid()),
@ -338,18 +338,22 @@ public:
// Follow MILC 10.1103/PhysRevD.82.074501, eqs (B2-B3) and (C1-C8)
for (int mu = 0; mu < Nd; mu++) {
V = PeekIndex<LorentzIndex>(u_mu, mu);
Q = adj(V)*V;
c0 = real(trace(Q));
c1 = (1/2.)*real(trace(Q*Q));
c2 = (1/3.)*real(trace(Q*Q*Q));
S = (1/3.)*c1-(1/18.)*c0*c0;
R = (1/2.)*c2-(1/3. )*c0*c1+(1/27.)*c0*c0*c0;
theta = acos(R*pow(S,-1.5));
g0 = (1/3.)*c0+2.*sqrt(S)*cos((1/3.)*theta-2*M_PI/3.);
g1 = (1/3.)*c0+2.*sqrt(S)*cos((1/3.)*theta );
g2 = (1/3.)*c0+2.*sqrt(S)*cos((1/3.)*theta+2*M_PI/3.);
// if (fabs(Q.determinant()/(g0*g1*g2)-1.0) > 1e-5) {}
V = PeekIndex<LorentzIndex>(u_mu, mu);
Q = adj(V)*V;
c0 = real(trace(Q));
c1 = (1/2.)*real(trace(Q*Q));
c2 = (1/3.)*real(trace(Q*Q*Q));
S = (1/3.)*c1-(1/18.)*c0*c0;
if (norm2(S)<1e-28) {
g0 = (1/3.)*c0; g1 = g0; g2 = g1;
} else {
R = (1/2.)*c2-(1/3. )*c0*c1+(1/27.)*c0*c0*c0;
theta = acos(R*pow(S,-1.5));
g0 = (1/3.)*c0+2.*sqrt(S)*cos((1/3.)*theta-2*M_PI/3.);
g1 = (1/3.)*c0+2.*sqrt(S)*cos((1/3.)*theta );
g2 = (1/3.)*c0+2.*sqrt(S)*cos((1/3.)*theta+2*M_PI/3.);
}
// if (fabs(Q.determinant()/(g0*g1*g2)-1.0) > 1e-5) { SVD }
u = sqrt(g0) + sqrt(g1) + sqrt(g2);
v = sqrt(g0*g1) + sqrt(g0*g2) + sqrt(g1*g2);
w = sqrt(g0*g1*g2);
@ -360,6 +364,7 @@ public:
id_3 = 1.;
sqrtQinv = f0*id_3 + f1*Q + f2*Q*Q;
PokeIndex<LorentzIndex>(u_proj, V*sqrtQinv, mu);
}
};