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 inner_product_norm2(a, b):
if type(a) == gpt.tensor and type(b) == gpt.tensor:
return gpt.adj(a) * b, a.norm2()
a = gpt.eval(a)
b = gpt.eval(b)
assert len(a.otype.v_idx) == len(b.otype.v_idx)
r = [
cgpt.lattice_inner_product_norm2(a.v_obj[i], b.v_obj[i]) for i in a.otype.v_idx
]
return (
sum([x[0] for x in r]),
sum([x[1] for x in r]),
) # todo, make local version of this too
def inv(A):
A = gpt.eval(A)
assert type(A) == gpt.lattice
A_inv = gpt.lattice(A)
to_list = gpt.util.to_list
cgpt.invert_matrix(to_list(A_inv), to_list(A))
return A_inv
def __init__(self, Nc):
super().__init__(Nc, Nc, f"ot_matrix_su_n_fundamental_algebra({Nc})")
self.ctab = {
f"ot_matrix_su_n_fundamental_group({Nc})":
lambda dst, src: gpt.eval(dst, gpt.matrix.exp(src * 1j))
}
self.CA = Nc
def rank_inner_product(a, b, use_accelerator=True):
return_list = (type(a) == list) or (type(b) == list)
a = gpt.util.to_list(a)
b = gpt.util.to_list(b)
if type(a[0]) == gpt.tensor and type(b[0]) == gpt.tensor:
res = numpy.array([[gpt.adj(x) * y for y in b] for x in a],
dtype=numpy.complex128)
else:
a = [gpt.eval(x) for x in a]
b = [gpt.eval(x) for x in b]
otype = a[0].otype
assert len(otype.v_idx) == len(b[0].otype.v_idx)
res = cgpt.lattice_rank_inner_product(a, b, use_accelerator)
if return_list:
return res
return gpt.util.to_num(res[0, 0])
def __init__(self, U, boundary_phases):
self.nd = len(U)
self.U = [gpt.copy(u) for u in U]
self.L = U[0].grid.fdimensions
if boundary_phases is not None:
for mu in range(self.nd):
last_slice = tuple([
self.L[mu] - 1 if mu == nu else slice(None, None, None)
for nu in range(self.nd)
])
self.U[mu][
last_slice] = self.U[mu][last_slice] * boundary_phases[mu]
# now take boundary_phase from params and apply here
self.Udag = [gpt.eval(gpt.adj(u)) for u in self.U]
def _forward(mu):
def wrap(dst, src):
dst @= self.U[mu] * gpt.cshift(src, mu, +1)
return wrap
def _backward(mu):
def wrap(dst, src):
dst @= gpt.cshift(self.Udag[mu] * src, mu, -1)
return wrap
self.forward = [
gpt.matrix_operator(mat=_forward(mu), inv_mat=_backward(mu))
for mu in range(self.nd)
]
self.backward = [o.inv() for o in self.forward]
def __init__(self):
super().__init__("ot_u_1_group()")
self.ctab = {
"ot_u_1_algebra()":
lambda dst, src: gpt.eval(dst,
gpt.component.log(src) / 1j)
}
def det(A):
A = gpt.eval(A)
assert type(A) == gpt.lattice
r = gpt.complex(A.grid)
to_list = gpt.util.to_list
cgpt.determinant(r.v_obj[0], to_list(A))
return r
def __call__(self, links, site_fields=[]):
assert len(site_fields) == self.n_site_fields
assert len(links) == self.dim
buffers = self.cshifts(links + site_fields)
for p in self.paths:
d = [0 for mu in range(self.dim)]
r = None
# pr = prof.Profile(timer=lambda: g.time()*100000.0)
# pr.enable()
for mu, distance in p.path:
for step in range(abs(distance)):
factor = None
if distance > 0:
factor = buffers[self.link_indices[mu][tuple(d)]]
d[mu] += distance // abs(distance)
if distance < 0:
factor = g.adj(
buffers[self.link_indices[mu][tuple(d)]])
assert factor is not None
if r is None:
r = factor
else:
r = r * factor
# pr.disable()
# pr.print_stats(sort="cumulative")
assert r is not None
yield g.eval(r)
for i in range(self.n_site_fields):
site_fields_indices_i = self.site_fields_indices[i]
for sfi in site_fields_indices_i:
yield (sfi, buffers[site_fields_indices_i[sfi]])
def __call__(self, mat):
inverter_mat = [
self.inverter(
g.matrix_operator(
mat=lambda dst, src, s_val=s: g.eval(dst, mat * src + s_val * src),
accept_list=True,
)
)
for s in self.shifts
]
@self.timed_function
def inv(dst, src, t):
for j, i in enumerate(inverter_mat):
i(dst[j * len(src) : (j + 1) * len(src)], src)
vector_space = None
if isinstance(mat, g.matrix_operator):
vector_space = mat.vector_space
return g.matrix_operator(
mat=inv,
vector_space=vector_space,
accept_guess=(True, False),
accept_list=lambda src: len(src) * len(self.shifts),
)
def log(i, convergence_threshold=0.5):
i = gpt.eval(i)
# i = n*(1 + x), log(i) = log(n) + log(1+x)
# x = i/n - 1, |x|^2 = <i/n - 1, i/n - 1> = |i|^2/n^2 + |1|^2 - (<i,1> + <1,i>)/n
# d/dn |x|^2 = -2 |i|^2/n^3 + (<i,1> + <1,i>)/n^2 = 0 -> 2|i|^2 == n (<i,1> + <1,i>)
if i.grid.precision != gpt.double:
x = gpt.convert(i, gpt.double)
else:
x = gpt.copy(i)
lI = gpt.identity(gpt.lattice(x))
n = gpt.norm2(x) / gpt.inner_product(x, lI).real
x /= n
x -= lI
n2 = gpt.norm2(x)**0.5 / x.grid.gsites
order = 8 * int(16 / (-numpy.log10(n2)))
assert n2 < convergence_threshold
o = gpt.copy(x)
xn = gpt.copy(x)
for j in range(2, order + 1):
xn @= xn * x
o -= xn * ((-1.0)**j / j)
o += lI * numpy.log(n)
if i.grid.precision != gpt.double:
r = gpt.lattice(i)
gpt.convert(r, o)
o = r
return o
def norm2(l):
if type(l) == gpt.tensor:
return l.norm2()
l = gpt.eval(l)
if type(l) == gpt.lattice:
return sum([cgpt.lattice_norm2(o) for o in l.v_obj])
else:
assert (0)
def _Meooe(self, dst, src):
assert dst != src
cb = src.checkerboard()
scb = self.checkerboard[cb]
scbi = self.checkerboard[cb.inv()]
dst.checkerboard(cb.inv())
dst[:] = 0
for mu in range(self.nd):
src_plus = g.eval(scbi.forward[mu] * src)
src_minus = g.eval(scb.backward[mu] * src)
if mu == self.nd - 1:
cc = 1.0
else:
cc = self.nu / self.xi_0
dst += (cc / 2.0 * (g.gamma[mu] - g.gamma["I"]) * src_plus -
cc / 2.0 * (g.gamma[mu] + g.gamma["I"]) * src_minus)
self.apply_boundaries(dst)
def cshift(first, second, third, fourth=None):
if (type(first) == gpt.lattice and type(second) == gpt.lattice
and fourth is not None):
t = first
l = gpt.eval(second)
d = third
o = fourth
else:
l = gpt.eval(first)
d = second
o = third
t = gpt.lattice(l)
for i in t.otype.v_idx:
cgpt.cshift(t.v_obj[i], l.v_obj[i], d, o)
return t
def __init__(self, Nc):
super().__init__(Nc, Nc * Nc - 1,
f"ot_matrix_su_n_adjoint_group({Nc})")
self.ctab = {
f"ot_matrix_su_n_adjoint_algebra({Nc})":
lambda dst, src: gpt.eval(dst,
gpt.matrix.log(src) / 1j)
}
def trace(l, t=None):
if isinstance(l, gpt.expr):
l = gpt.eval(l)
if t is None:
t = gpt.expr_unary.BIT_SPINTRACE | gpt.expr_unary.BIT_COLORTRACE
if type(l) == gpt.tensor:
return l.trace(t)
return gpt.expr(l, t)
def p2p_dbard(src, Pol_i, Spin_M, t_sink):
tmp_seq_src = g.lattice(src)
q1_tmp = g.eval(Pol_i * src * Spin_M) # e.g. Pol_i * D * Cg5
q2_tmp = g.eval(Spin_M * src) # e.g. Cg5 * D
tmp_seq_src = -qC.quarkContract14(q1_tmp, q2_tmp)
q1_tmp = g.eval(q2_tmp * Spin_M) # e.g. Cg5 * D * Cg5
q2_tmp = g.eval(src * Pol_i) # e.g. D * Pol_i
tmp_seq_src -= g.spin_transpose(qC.quarkContract12(q2_tmp, q1_tmp))
tmp_seq_src = g.eval(g.gamma[5] * g.adj(tmp_seq_src) * g.gamma[5])
seq_src = g.lattice(src)
seq_src[:] = 0
seq_src[:, :, :, t_sink] = tmp_seq_src[:, :, :, t_sink]
return seq_src
def split_chiral(basis, factor=None):
nb = len(basis)
factor = 0.5 if factor is None else factor
g5 = gamma5(basis[0])
tmp = gpt.lattice(basis[0])
for n in range(nb):
tmp @= g5 * basis[n]
basis.append(gpt.eval((basis[n] - tmp) * factor))
basis[n] @= (basis[n] + tmp) * factor
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 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 __init__(self, Nc):
super().__init__(Nc, Nc, f"ot_matrix_su_n_fundamental_group({Nc})")
self.ctab = {
f"ot_matrix_su_n_adjoint_group({Nc})":
fundamental_to_adjoint,
f"ot_matrix_su_n_fundamental_algebra({Nc})":
lambda dst, src: gpt.eval(dst,
gpt.matrix.log(src) / 1j),
}
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 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 contract_lambda_to_sigma_zero(prop_up, prop_down, prop_strange, spin_matrix, pol_matrix, diquarks=None):
if diquarks is None:
diquarks = []
prop_dict = {"up": prop_up, "down": prop_down, "strange": prop_strange}
for diquark_flavors in [
"up_down", "down_up",
"strange_up", "strange_down"
]:
flav1, flav2 = diquark_flavors.split("_")
diquarks.append(quark_contract_13(
gpt.eval(prop_dict[flav1] * spin_matrix), gpt.eval(spin_matrix * prop_dict[flav2])
))
return (
2 * baryon_octet_base_contraction(prop_strange, diquarks[0], pol_matrix) -
2 * baryon_octet_base_contraction(prop_strange, diquarks[1], pol_matrix) +
baryon_octet_base_contraction(prop_down, diquarks[2], pol_matrix) -
baryon_octet_base_contraction(prop_up, diquarks[3], pol_matrix)
) / sqrt(12)
def test(slv, name):
t0 = g.time()
dst = g.eval(slv * src)
t1 = g.time()
eps2 = g.norm2(dst_cg - dst) / g.norm2(dst_cg)
g.message("%s finished: eps^2(CG) = %g" % (name, eps2))
timings[name] = t1 - t0
resid[name] = eps2**0.5
assert eps2 < 5e-7
def __init__(self, U, params):
if "mass" in params:
assert (not "kappa" in params)
self.kappa = 1. / (params["mass"] + 4.) / 2.
else:
self.kappa = params["kappa"]
self.U = U
self.Udag = [g.eval(g.adj(u)) for u in U]
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 inv(psi, src):
# verbosity
verbose = g.default.is_verbose("dci")
t_start = g.time()
# leading order
n = len(src)
_s = [g.copy(x) for x in src]
for j in range(n):
psi[j][:] = 0
self.history = []
for i in range(self.maxiter):
# correction step
t0 = g.time()
_d = g.eval(inner_inv_mat * _s)
t1 = g.time()
for j in range(n):
_s[j] -= outer_mat * _d[j]
t2 = g.time()
for j in range(n):
psi[j] += _d[j]
# true resid
eps = max([
g.norm2(outer_mat * psi[j] - src[j])**0.5 for j in range(n)
])
self.history.append(eps)
if verbose:
g.message(
"Defect-correcting inverter: eps[",
i,
"] =",
eps,
". Timing:",
t1 - t0,
"s (innver_inv), ",
t2 - t1,
"s (outer_mat)",
)
if eps < self.eps:
if verbose:
g.message(
"Defect-correcting inverter: converged at iteration",
i,
"after",
g.time() - t_start,
"s",
)
break
def __call__(self, link, staple, mask):
verbose = g.default.is_verbose(
"local_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("local_metropolis")
t("action")
action = g.component.real(-g.trace(link * g.adj(staple)) * mask)
t("lattice")
V = g.lattice(link)
V_eye = g.identity(link)
t("random")
self.rng.normal_element(V, scale=step_size)
t("update")
V = g.where(mask, V, V_eye)
link_prime = g.eval(V * link)
action_prime = g.component.real(-g.trace(link_prime * g.adj(staple)) *
mask)
dp = g.component.exp(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"Local metropolis acceptance rate: {number_accept / possible_accept}"
)
def perform(self, root):
global current_config, current_light_quark
if current_config is not None and current_config.conf_file != self.conf_file:
current_config = None
if current_config is None:
current_config = config(self.conf_file)
if (current_light_quark is not None
and current_light_quark.evec_dir != self.evec_dir):
current_light_quark = None
if current_light_quark is None:
current_light_quark = light_quark(current_config, self.evec_dir)
prop_l = {
"sloppy": current_light_quark.prop_l_sloppy,
"exact": current_light_quark.prop_l_exact,
}[self.solver]
vcj = g.load(f"{root}/{self.conf}/pm_basis/basis")
c = g.coordinates(vcj[0])
c = c[c[:, 3] == self.t]
g.message(
f"t = {self.t}, ilist = {self.ilist}, basis size = {len(vcj)}, solver = {self.solver}"
)
root_job = f"{root}/{self.name}"
output = g.gpt_io.writer(f"{root_job}/propagators")
# create sources
srcD = [
g.vspincolor(current_config.l_exact.U_grid) for spin in range(4)
]
for i in self.ilist:
for spin in range(4):
srcD[spin][:] = 0
srcD[spin][c, spin, :] = vcj[i][c]
g.message("Norm of source:", g.norm2(srcD[spin]))
if i == 0:
g.message("Source at origin:", srcD[spin][0, 0, 0, 0])
g.message("Source at time-origin:", srcD[spin][0, 0, 0,
self.t])
prop = g.eval(prop_l * srcD)
g.mem_report(details=False)
for spin in range(4):
output.write(
{f"t{self.t}s{spin}c{i}_{self.solver}": prop[spin]})
output.flush()