def chroma_sigma_star(prop_1, prop_2, prop_3, spm, polm, diquark):
#diquark = quark_contract_13(gpt.eval(prop_1 * spm), gpt.eval(spm * prop_3))
contraction = gpt.trace(gpt.eval(polm * prop_2 * gpt.spin_trace(diquark)))
diquark2 = quark_contract_24(prop_2, gpt.eval(spm * prop_3 * spm))
contraction += gpt.trace(gpt.eval(prop_1 * polm * diquark2))
diquark2 @= quark_contract_13(prop_1, gpt.eval(spm * prop_3))
contraction += gpt.trace(gpt.eval(polm * prop_2 * spm * diquark2))
return gpt.eval(contraction)
def __call__(self, link, staple, mask):
verbose = g.default.is_verbose(
"metropolis"
) # need verbosity categories [ performance, progress ]
project_method = self.params["project_method"]
step_size = self.params["step_size"]
number_accept = 0
possible_accept = 0
t = g.timer("metropolis")
t("action")
action = g.component.real(g.eval(-g.trace(link * g.adj(staple)) *
mask))
t("lattice")
V = g.lattice(link)
V_eye = g.identity(link)
t("random")
self.rng.element(V, scale=step_size, normal=True)
t("update")
V = g.where(mask, V, V_eye)
link_prime = g.eval(V * link)
action_prime = g.component.real(
g.eval(-g.trace(link_prime * g.adj(staple)) * mask))
dp = g.component.exp(g.eval(action - action_prime))
rn = g.lattice(dp)
t("random")
self.rng.uniform_real(rn)
t("random")
accept = dp > rn
accept *= mask
number_accept += g.norm2(accept)
possible_accept += g.norm2(mask)
link @= g.where(accept, link_prime, link)
t()
g.project(link, project_method)
# g.message(t)
if verbose:
g.message(
f"Metropolis acceptance rate: {number_accept / possible_accept}"
)
def baryon_decuplet_base_contraction(prop_1, prop_2, diquarks, pol_matrix):
assert isinstance(diquarks, list)
contraction = gpt.trace(
gpt.eval(pol_matrix * gpt.color_trace(prop_2 * gpt.spin_trace(diquarks[0]))) +
gpt.eval(pol_matrix * gpt.color_trace(prop_2 * diquarks[0]))
)
contraction += gpt.eval(gpt.trace(pol_matrix * gpt.color_trace(prop_2 * diquarks[1])))
contraction += gpt.eval(gpt.trace(pol_matrix * gpt.color_trace(prop_1 * diquarks[2])))
contraction *= 2
contraction += gpt.eval(gpt.trace(pol_matrix * gpt.color_trace(prop_1 * gpt.spin_trace(diquarks[2]))))
return contraction
def fundamental_to_adjoint(U_a, U_f):
grid = U_f.grid
T = U_f.otype.cartesian().generators(grid.precision.complex_dtype)
V = {}
for a in range(len(T)):
for b in range(len(T)):
V[a,
b] = gpt.eval(2.0 * gpt.trace(T[a] * U_f * T[b] * gpt.adj(U_f)))
gpt.merge_color(U_a, V)
def traceless_hermitian(src):
if isinstance(src, list):
return [traceless_hermitian(x) for x in src]
src = g.eval(src)
N = src.otype.shape[0]
ret = g(0.5 * src + 0.5 * g.adj(src))
ret -= g.identity(src) * g.trace(ret) / N
return ret
def energy_density(U, field=False):
Nd = len(U)
accumulator = accumulator_field if field else accumulator_average
res = accumulator(U[0])
for mu in range(Nd):
for nu in range(mu):
Fmunu = field_strength(U, mu, nu)
res += g.trace(Fmunu * Fmunu)
return res.scaled_real(-1.0)
def coordinates(self, l, c=None):
assert l.otype.__name__ == self.__name__
gen = self.generators(l.grid.precision.complex_dtype)
if c is None:
nhalf = len(gen) // 2
l_real = gpt.component.real(l)
l_imag = gpt.component.imag(l)
return [
gpt.eval(gpt.trace(gpt.adj(l_real) * Ta))
for Ta in gen[0:nhalf]
] + [
gpt.eval(gpt.trace(gpt.adj(l_imag) * Ta))
for Ta in gen[0:nhalf]
]
else:
l[:] = 0
for ca, Ta in zip(c, gen):
l += ca * Ta
def coordinates(self, l, c=None):
assert l.otype.__name__ == self.__name__
gen = self.generators(l.grid.precision.complex_dtype)
if c is None:
return [gpt.eval(gpt.trace(gpt.adj(l) * Ta)) for Ta in gen]
else:
l[:] = 0
for ca, Ta in zip(c, gen):
l += ca * Ta
def plaquette(U):
# U[mu](x)*U[nu](x+mu)*adj(U[mu](x+nu))*adj(U[nu](x))
tr = 0.0
vol = float(U[0].grid.gsites)
for mu in range(4):
for nu in range(mu):
tr += g.sum(
g.trace(U[mu] * g.cshift(U[nu], mu, 1) *
g.adj(g.cshift(U[mu], nu, 1)) * g.adj(U[nu])))
return 2. * tr.real / vol / 4. / 3. / 3.
def polyakov_loop(U, mu):
# tr[ prod_j U_{\mu}(m, j) ]
vol = float(U[0].grid.fsites)
Nc = U[0].otype.Nc
tmp_polyakov_loop = g.copy(U[mu])
for n in range(1, U[0].grid.fdimensions[mu]):
tmp = g.cshift(tmp_polyakov_loop, mu, 1)
tmp_polyakov_loop = g.eval(U[mu] * tmp)
return g.sum(g.trace(tmp_polyakov_loop)) / Nc / vol
def project_onto_suN(dest, u_unprojected, params):
t_total = -gpt.time()
t_trace, t_projectstep = 0.0, 0.0
vol = dest.grid.fsites
t_trace -= gpt.time()
old_trace = gpt.sum(gpt.trace(dest * u_unprojected)).real / (vol * 3)
t_trace += gpt.time()
for _ in range(params["max_iteration"]):
# perform a single projection step
t_projectstep -= gpt.time()
project_to_suN_step(dest, u_unprojected)
t_projectstep += gpt.time()
# calculate new trace
t_trace -= gpt.time()
new_trace = gpt.sum(gpt.trace(dest * u_unprojected)).real / (vol * 3)
t_trace += gpt.time()
epsilon = np.abs((new_trace - old_trace) / old_trace)
gpt.message(f"APE iter {_}, epsilon: {epsilon}")
if epsilon < params["accuracy"]:
break
old_trace = new_trace
else:
raise RuntimeError("Projection to SU(3) did not converge.")
t_total += gpt.time()
if gpt.default.is_verbose("project_onto_suN"):
t_profiled = t_trace + t_projectstep
t_unprofiled = t_total - t_profiled
gpt.message("project_onto_suN: total", t_total, "s")
gpt.message("project_onto_suN: t_trace", t_trace, "s",
round(100 * t_trace / t_total, 1), "%")
gpt.message("project_onto_suN: t_projectstep", t_projectstep, "s",
round(100 * t_projectstep / t_total, 1), "%")
gpt.message("project_onto_suN: unprofiled", t_unprofiled, "s",
round(100 * t_unprofiled / t_total, 1), "%")
def Udelta_average(U):
"""
compute < tr Udelta * Udelta^\dagger >
"""
Volume = float(U[0].grid.fsites)
Udelta = g.lattice(U[0].grid, U[0].otype)
Udelta[:] = 0.0
for [i, j, k] in permutations([0, 1, 2]):
Udelta += U[i] * g.cshift(U[j], i, 1) * g.cshift(
g.cshift(U[k], i, 1), j, 1)
return g.sum(g.trace(Udelta * g.adj(Udelta))).real / Volume / 36.0
def coordinates(self, l, c=None):
assert l.otype.__name__ == self.__name__
gen = self.generators(l.grid.precision.complex_dtype)
if c is None:
norm = [numpy.trace(Ta.array @ Ta.array) for Ta in gen]
return [
gpt.eval(gpt.trace(l * Ta) / n) for n, Ta in zip(norm, gen)
]
else:
l[:] = 0
for ca, Ta in zip(c, gen):
l += ca * Ta
def plaquette(U):
# U[mu](x)*U[nu](x+mu)*adj(U[mu](x+nu))*adj(U[nu](x))
tr = 0.0
vol = float(U[0].grid.fsites)
Nd = len(U)
ndim = U[0].otype.shape[0]
for mu in range(Nd):
for nu in range(mu):
tr += g.sum(
g.trace(U[mu] * g.cshift(U[nu], mu, 1) *
g.adj(g.cshift(U[mu], nu, 1)) * g.adj(U[nu])))
return 2.0 * tr.real / vol / Nd / (Nd - 1) / ndim
def check_representation(U, eps_ref):
generators = U.otype.generators(U.grid.precision.complex_dtype)
# first test generators normalization
for a in range(len(generators)):
for b in range(len(generators)):
eye_ab = 2.0 * g.trace(generators[a] * generators[b])
if a == b:
assert abs(eye_ab - 1) < eps_ref
else:
assert abs(eye_ab) < eps_ref
# now project to algebra and make sure it is a linear combination of
# the provided generators
algebra = g.matrix.log(U)
algebra /= 1j
n0 = g.norm2(algebra)
for Ta in generators:
algebra -= Ta * g.trace(algebra * Ta) * 2.0
eps = (g.norm2(algebra) / n0)**0.5
g.message(f"Test representation: {eps}")
assert eps < eps_ref
def fundamental_to_adjoint(U_a, U_f):
"""
Convert fundamental to adjoint representation. For now only SU(2) is supported.
Input: fundamental gauge field
Output: adjoint gauge field
"""
grid = U_f.grid
T = U_f.otype.generators(grid.precision.complex_dtype)
V = {}
for a in range(len(T)):
for b in range(len(T)):
V[a, b] = g.eval(2.0 * g.trace(T[a] * U_f * T[b] * g.adj(U_f)))
g.merge_color(U_a, V)
def contract(pos, prop, tag, may_save_prop=True):
t0 = pos[3]
prop_tag = "%s/%s" % (tag, str(pos))
# save propagators
if params["save_propagators"] and may_save_prop:
output.write({prop_tag: prop})
output.flush()
# create and save correlators
for op_snk, op_src in correlators:
G_snk = operators[op_snk]
G_src = operators[op_src]
corr = g.slice(g.trace(G_src * g.gamma[5] * g.adj(prop) * g.gamma[5] * G_snk * prop), 3)
corr = corr[t0:] + corr[:t0]
corr_tag = "%s/snk%s-src%s" % (prop_tag, op_snk, op_src)
output_correlator.write(corr_tag, corr)
g.message("Correlator %s\n" % corr_tag, corr)
def __call__(self, link, staple, mask):
verbose = g.default.is_verbose(
"su2_heat_bath"
) # need verbosity categories [ performance, progress ]
project_method = self.params["project_method"]
# params
niter = self.params["niter"]
# temporaries
grid = link.grid
u2 = g.lattice(grid, g.ot_matrix_su_n_fundamental_group(2))
u2_eye = g.identity(u2)
one = g.identity(g.complex(grid))
zero = g.complex(grid)
zero[:] = 0
eps = g.complex(grid)
eps[:] = grid.precision.eps * 10.0
xr = [g.complex(grid) for i in range(4)]
a = [g.complex(grid) for i in range(4)]
two_pi = g.complex(grid)
two_pi[:] = 2.0 * np.pi
accepted = g.complex(grid)
d = g.complex(grid)
V_eye = g.identity(link)
# pauli
pauli1, pauli2, pauli3 = tuple([g.lattice(u2) for i in range(3)])
ident = g.identity(u2)
pauli1[:] = 1j * np.array([[0, 1], [1, 0]], dtype=grid.precision.complex_dtype)
pauli2[:] = 1j * np.array([[0, 1j], [-1j, 0]], dtype=grid.precision.complex_dtype)
pauli3[:] = 1j * np.array([[1, 0], [0, -1]], dtype=grid.precision.complex_dtype)
# counter
num_sites = round(g.norm2(g.where(mask, one, zero)))
# shortcuts
inv = g.component.pow(-1.0)
# go through subgroups
for subgroup in link.otype.su2_subgroups():
V = g.eval(link * g.adj(staple))
# extract u2 subgroup following Kennedy/Pendleton
link.otype.block_extract(u2, V, subgroup)
u2 @= u2 - g.adj(u2) + g.identity(u2) * g.trace(g.adj(u2))
udet = g.matrix.det(u2)
adet = g.component.abs(udet)
nzmask = adet > eps
u2 @= g.where(nzmask, u2, u2_eye)
udet = g.where(nzmask, udet, one)
xi = g.eval(0.5 * g.component.sqrt(udet))
u2 @= 0.5 * u2 * inv(xi)
# make sure that su2 subgroup projection worked
assert g.group.defect(u2) < u2.grid.precision.eps * 10.0
xi @= 2.0 * xi
alpha = g.component.real(xi)
# main loop
it = 0
num_accepted = 0
accepted[:] = 0
d[:] = 0
while (num_accepted < num_sites) and (it < niter):
self.rng.uniform_real(xr, min=0.0, max=1.0)
xr[1] @= -g.component.log(xr[1]) * inv(alpha)
xr[2] @= -g.component.log(xr[2]) * inv(alpha)
xr[3] @= g.component.cos(g.eval(xr[3] * two_pi))
xr[3] @= xr[3] * xr[3]
xrsq = g.eval(xr[2] + xr[1] * xr[3])
d = g.where(accepted, d, xrsq)
thresh = g.eval(one - d * 0.5)
xrsq @= xr[0] * xr[0]
newly_accepted = g.where(xrsq < thresh, one, zero)
accepted = g.where(mask, g.where(newly_accepted, newly_accepted, accepted), zero)
num_accepted = round(g.norm2(g.where(accepted, one, zero)))
it += 1
if verbose:
g.message(f"SU(2)-heatbath update needed {it} / {niter} iterations")
# update link
a[0] @= g.where(mask, one - d, zero)
a123mag = g.component.sqrt(g.component.abs(one - a[0] * a[0]))
phi, cos_theta = g.complex(grid), g.complex(grid)
self.rng.uniform_real([phi, cos_theta])
phi @= phi * two_pi
cos_theta @= (cos_theta * 2.0) - one
sin_theta = g.component.sqrt(g.component.abs(one - cos_theta * cos_theta))
a[1] @= a123mag * sin_theta * g.component.cos(phi)
a[2] @= a123mag * sin_theta * g.component.sin(phi)
a[3] @= a123mag * cos_theta
ua = g.eval(a[0] * ident + a[1] * pauli1 + a[2] * pauli2 + a[3] * pauli3)
b = g.where(mask, g.adj(u2) * ua, ident)
link.otype.block_insert(V, b, subgroup)
link @= g.where(accepted, V * link, link)
# check
check = g.where(accepted, ua * g.adj(ua) - ident, 0.0 * ident)
delta = (g.norm2(check) / g.norm2(ident)) ** 0.5
assert delta < grid.precision.eps * 10.0
check = g.where(accepted, b * g.adj(b) - ident, 0.0 * ident)
delta = (g.norm2(check) / g.norm2(ident)) ** 0.5
assert delta < grid.precision.eps * 10.0
check = g.where(accepted, V * g.adj(V) - V_eye, 0.0 * V_eye)
delta = (g.norm2(check) / g.norm2(V_eye)) ** 0.5
assert delta < grid.precision.eps * 10.0
# project
g.project(link, project_method)
)
U = representation(grid)
rng.element(U)
check_unitarity(U, eps_ref)
check_representation(U, eps_ref)
################################################################################
# Test su2 subalgebras
################################################################################
for eps_ref, grid in [(1e-12, grid_dp)]:
U = g.lattice(grid, g.ot_matrix_su_n_fundamental_group(3))
u2 = g.lattice(grid, g.ot_matrix_su_n_fundamental_group(2))
u2p = g.lattice(grid, g.ot_matrix_su_n_fundamental_group(2))
for sg in U.otype.su2_subgroups():
rng.element(u2)
u2p = g.eval(u2 - g.adj(u2) + g.identity(u2) * g.trace(g.adj(u2)))
eps = (g.norm2(u2 - u2p) / g.norm2(u2))**0.5
g.message(eps, g.norm2(u2), g.norm2(u2p))
U.otype.block_insert(U, u2, sg)
u2p[:] = 0
U.otype.block_extract(u2p, U, sg)
eps = (g.norm2(u2 - u2p) / g.norm2(u2))**0.5
g.message(eps, g.norm2(u2), g.norm2(u2p))
assert eps < eps_ref
check_unitarity(U, eps_ref)
check_representation(U, eps_ref)
src[:, :, :, 0] = val
for x in range(grid.fdimensions[0]):
for t in range(grid.fdimensions[3]):
compare = val if t == 0 else zero
eps = g.norm2(src[x, 0, 0, t] - compare)
assert eps < 1e-13
# spin and color traces
mc = g.eval(g.spin_trace(msc))
assert g.norm2(mc[0, 0, 0, 0] - g.spin_trace(msc[0, 0, 0, 0])) < 1e-13
ms = g.eval(g.color_trace(msc))
assert g.norm2(ms[0, 0, 0, 0] - g.color_trace(msc[0, 0, 0, 0])) < 1e-13
eps0 = g.norm2(g.trace(msc) - g.spin_trace(ms))
eps1 = g.norm2(g.trace(msc) - g.color_trace(mc))
assert eps0 < 1e-9 and eps1 < 1e-9
# create singlet by number
assert g.complex(0.5).array[0] == 0.5
# test expression -> string conversion;
# at this point only make sure that it
# produces a string without failing
g.message(
f"Test string conversion of expression:\n{g.trace(0.5 * msc * msc - msc)}")
# left and right multiplication of different data types with scalar
mc = g.mcomplex(grid, ntest)
for dti in [cv, cm, vsc, msc, vc, mc]:
eps2 = g.norm2(w * dst_eo1 - src) / g.norm2(src)
g.message("Result of M M^-1 = 1 test: eps2=", eps2)
assert eps2 < 1e-10
# and a reference
if True:
dst = g.mspincolor(grid)
dst @= slv * src
eps2 = g.norm2(dst_eo1 - dst) / g.norm2(dst_eo1)
g.message("Result of test EO1 versus G5M: eps2=", eps2)
assert eps2 < 1e-10
dst = dst_eo2
# two-point
correlator = g.slice(g.trace(dst * g.adj(dst)), 3)
# test value of correlator
correlator_ref = [
1.0710210800170898,
0.08988216519355774,
0.015699388459324837,
0.003721018321812153,
0.0010877142194658518,
0.0003579717595130205,
0.00012700144725386053,
5.180457083042711e-05,
3.406393443583511e-05,
5.2738148951902986e-05,
0.0001297977869398892,
0.0003634534077718854,
print(gre) sys.exit(0) # Calculate U^\dag U u = U[0][0, 1, 2, 3] v = g.vcolor([0, 1, 0]) g.message(g.adj(v)) g.message(g.adj(u) * u * v) gr = g.grid([2, 2, 2, 2], g.single) g.message(g.mspincolor(gr)[0, 0, 0, 0] * g.vspincolor(gr)[0, 0, 0, 0]) g.message(g.trace(g.mspincolor(gr)[0, 0, 0, 0])) # Expression including numpy array r = g.eval(u * U[0] + U[1] * u) g.message(g.norm2(r)) # test inner and outer products v = g.vspincolor([[0, 0, 0], [0, 0, 2], [0, 0, 0], [0, 0, 0]]) w = g.vspincolor([[0, 0, 0], [0, 0, 0], [0, 0, 0], [1, 0, 0]]) xx = v * g.adj(w) g.message(xx[1][3][2][0]) g.message(xx) g.message(g.adj(v) * v) g.message(g.transpose(v) * v)
dst @= P * l
ref @= g.gamma[0] * g.gamma[1] * l - g.gamma[2] * g.gamma[3] * l
eps = g.norm2(dst - ref) / g.norm2(l)
g.message("Test Regular Expression: ", eps)
assert eps == 0.0
# test algebra versus matrix
for mu in [0, 1, 2, 3, 5, "I"]:
for op in [
lambda a, b: a * b,
lambda a, b: b * a,
lambda a, b: g.spin_trace(a * b),
lambda a, b: g.spin_trace(b * a),
lambda a, b: g.color_trace(a * b),
lambda a, b: g.color_trace(b * a),
lambda a, b: g.trace(a * b),
lambda a, b: g.trace(b * a),
]:
dst_alg = g(op(g.gamma[mu], l))
dst_mat = g(op(g.gamma[mu].tensor(), l))
eps2 = g.norm2(dst_alg - dst_mat) / g.norm2(dst_mat)
g.message(f"Algebra<>Matrix {mu}: {eps2}")
assert eps2 < 1e-14
# reconstruct and test the gamma matrix elements
for mu in g.gamma:
gamma = g.gamma[mu]
g.message("Test numpy matrix representation of", mu)
gamma_mu_mat = np.identity(4, dtype=np.complex128)
for j in range(4):
c = g.vspin([1 if i == j else 0 for i in range(4)])
if "WORK_DIR" in os.environ:
work_dir = os.environ["WORK_DIR"]
else:
work_dir = "."
# request test files
files = ["psrc-prop-0.field", "pion-corr.txt"]
for f in files:
gpt.repository.load(f"{work_dir}/{f}", f"gpt://tests/io/qlat/{f}")
# load field
prop = gpt.load(f"{work_dir}/psrc-prop-0.field")
gpt.message("Grid from qlat propagator =", prop.grid)
# calculate correlator
corr_pion = gpt.slice(gpt.trace(gpt.adj(prop) * prop), 3)
# load reference
with open(f"{work_dir}/pion-corr.txt", "r") as f:
txt = f.readlines()
# read lines corresponding to real part of time slices and
# check difference w.r.t. what we have loaded above
for i in range(8):
ref = float(txt[1 + i * 2].split(" ")[-1][:-1])
diff = abs(ref - corr_pion[i].real)
assert diff < 1e-7 # propagator was computed in single precision
gpt.message("Time slice %d difference %g" % (i, diff))
gpt.message("Test successful")
dst_qm = g.mspincolor(grid)
dst_qz = g.mspincolor(grid)
dst_qm @= slv_qm * src
dst_qz @= slv_qz * src
# test madwf
src_sc = rng.cnormal(g.vspincolor(grid))
dst_madwf_sc = g(slv_madwf * src_sc)
dst_dwf_sc = g(slv_qm * src_sc)
eps2 = g.norm2(dst_madwf_sc - dst_dwf_sc) / g.norm2(dst_dwf_sc)
g.message(f"MADWF test: {eps2}")
assert eps2 < 5e-4
# two-point
correlator_qm = g.slice(g.trace(dst_qm * g.adj(dst_qm)), 3)
correlator_qz = g.slice(g.trace(dst_qz * g.adj(dst_qz)), 3)
correlator_ref = [
0.4873415231704712,
0.14763720333576202,
0.021136583760380745,
0.007964665070176125,
0.005833963863551617,
0.00796868372708559,
0.021054629236459732,
0.14703410863876343,
]
# output
eps_qm = 0.0
eps_qz = 0.0
# Test gauge invariance of R_2x1
R_2x1_transformed = g.qcd.gauge.rectangle(U_transformed, 2, 1)
eps = abs(R_2x1 - R_2x1_transformed)
g.message(
f"R_2x1 before {R_2x1} and after {R_2x1_transformed} gauge transformation: {eps}"
)
assert eps < 1e-13
# Without trace and real projection
R_2x1_notp = g.qcd.gauge.rectangle(U_transformed,
2,
1,
trace=False,
real=False)
eps = abs(g.trace(R_2x1_notp).real - R_2x1)
g.message(f"R_2x1 no real and trace check: {eps}")
assert eps < 1e-13
# Test field version
R_2x1_field = g(
g.sum(g.qcd.gauge.rectangle(U, 2, 1, field=True)) / U[0].grid.gsites)
eps = abs(R_2x1 - R_2x1_field)
g.message(f"R_2x1 field check: {eps}")
assert eps < 1e-13
# Without trace and real projection and field
R_2x1_notp = g.qcd.gauge.rectangle(U_transformed,
2,
1,
trace=False,
# Test gauge invariance of R_2x1
R_2x1_transformed = g.qcd.gauge.rectangle(U_transformed, 2, 1)
eps = abs(R_2x1 - R_2x1_transformed)
g.message(
f"R_2x1 before {R_2x1} and after {R_2x1_transformed} gauge transformation: {eps}"
)
assert eps < 1e-13
# Test gauge covariance of staple
rho = np.array([[0.0 if i == j else 0.1 for i in range(4)] for j in range(4)],
dtype=np.float64)
C = g.qcd.gauge.staple_sum(U, rho=rho)
C_transformed = g.qcd.gauge.staple_sum(U_transformed, rho=rho)
for mu in range(len(C)):
q = g.sum(g.trace(C[mu] * g.adj(U[mu]))) / U[0].grid.gsites
q_transformed = (
g.sum(g.trace(C_transformed[mu] * g.adj(U_transformed[mu]))) /
U[0].grid.gsites)
eps = abs(q - q_transformed)
g.message(
f"Staple q[{mu}] before {q} and after {q_transformed} gauge transformation: {eps}"
)
assert eps < 1e-14
# Test stout smearing
U_stout = U
P_stout = []
for i in range(3):
U_stout = g.qcd.gauge.smear.stout(U_stout, rho=0.1)
# test madwf with defect_correcting
dst_madwf_dc_sc = g(slv_madwf_dc * src_sc)
eps2 = g.norm2(dst_madwf_dc_sc - dst_dwf_sc) / g.norm2(dst_dwf_sc)
g.message(f"MADWF defect_correcting test: {eps2}")
assert eps2 < 1e-10
# propagator
dst_qm = g.mspincolor(grid)
dst_qz = g.mspincolor(grid)
dst_qm @= slv_qm * src
dst_qz @= slv_qz * src
# two-point
correlator_qm = g.slice(
g.trace(g.gamma[0] * g.gamma[0] * dst_qm * g.gamma[0] * g.gamma[0] *
g.adj(dst_qm)),
3,
)
correlator_qz = g.slice(g.trace(dst_qz * g.adj(dst_qz)), 3)
correlator_ref = [
0.4873415231704712,
0.14763720333576202,
0.021136583760380745,
0.007964665070176125,
0.005833963863551617,
0.00796868372708559,
0.021054629236459732,
0.14703410863876343,
]
# output
def project_to_traceless_anti_hermitian(src):
src = g.eval(src)
N = src.otype.shape[0]
ret = g(0.5 * src - 0.5 * g.adj(src))
ret -= g.identity(src) * g.trace(ret) / N
return ret
def __call__(self, V):
V = g.util.from_list(V)
return sum(
[g.sum(g.trace(u))
for u in g.qcd.gauge.transformed(self.U, V)]).real * (-2.0)