def create_source(pos, point=False):
srcD = g.mspincolor(l_exact.U_grid)
srcD[:] = 0
# create time-sparsened source
sign_of_slice = [rng.zn(n=2) for i in range(source_time_slices)]
for i in range(use_source_time_slices, source_time_slices):
sign_of_slice[i] = 0.0
pos_of_slice = [
[
pos[i] if i < 3 else (pos[i] + j * sparse_time) % full_time
for i in range(4)
]
for j in range(source_time_slices)
]
g.message(f"Signature: {pos} -> {pos_of_slice} with signs {sign_of_slice}")
for i in range(source_time_slices):
if point:
srcD += (
g.create.point(g.lattice(srcD), pos_of_slice[i]) * sign_of_slice[i]
)
else:
srcD += g.create.wall.z2(g.lattice(srcD), pos_of_slice[i][3], rng) * (
sign_of_slice[i] / vol3d ** 0.5
)
return srcD, pos_of_slice, sign_of_slice
def run_test(U):
"""
Check the exact sum rule for tr(D_5^2)
Inputs: U = gauge field
Output: imaginary parts of the eigenvalues
"""
# extract representation (for output message)
Nc = U[0].otype.Nc
if "adjoint" in U[0].otype.__name__:
rep = "adjoint"
else:
rep = "fundamental"
# compute imaginary parts of eigenvalues
ev = compute_evals(U)
summe = sum(ev * ev)
# expected sum
Volume = U[0].grid.fsites
expected = Udelta_average(U) * Volume / 2.0
# check sum rule
g.message(f"tr(-D_5^2): {summe}, expected: {expected}")
assert abs(summe - expected) / Volume < 1e-4
g.message(f"Test passed for SU({Nc}) {rep}.")
return 1
def check_unitarity(U, eps_ref):
eye = g.lattice(U)
eye[:] = np.eye(U.otype.shape[0], dtype=U.grid.precision.complex_dtype)
eps = (g.norm2(U * g.adj(U) - eye) / g.norm2(eye))**0.5
g.message(f"Test unitarity: {eps}")
assert eps < eps_ref
U.otype.is_element(U)
def perform(self, root):
global basis_size, T, current_config
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)
c = None
vcj = [
g.vcolor(current_config.l_exact.U_grid) for jr in range(basis_size)
]
for vcjj in vcj:
vcjj[:] = 0
for tprime in range(T):
basis_evec, basis_evals = g.load(self.basis_fmt %
(self.conf, tprime))
plan = g.copy_plan(vcj[0],
basis_evec[0],
embed_in_communicator=vcj[0].grid)
c = g.coordinates(basis_evec[0])
plan.destination += vcj[0].view[np.hstack(
(c, np.ones((len(c), 1), dtype=np.int32) * tprime))]
plan.source += basis_evec[0].view[c]
plan = plan()
for l in range(basis_size):
plan(vcj[l], basis_evec[l])
for l in range(basis_size):
g.message("Check norm:", l, g.norm2(vcj[l]))
g.save(f"{root}/{self.name}/basis", vcj)
def orthogonalize(w, basis, ips=None, nblock=4):
# verbosity
verbose = gpt.default.is_verbose("orthogonalize")
n = len(basis)
if n == 0:
return
grid = basis[0].grid
i = 0
t_rank_inner_product = 0.0
t_globalSum = 0.0
t_linearCombination = 0.0
for i in range(0, n, nblock):
t_rank_inner_product -= gpt.time()
lip = gpt.rank_inner_product(basis[i:i + nblock], w)
t_rank_inner_product += gpt.time()
t_globalSum -= gpt.time()
grid.globalsum(lip)
lip = [complex(x) for x in lip]
t_globalSum += gpt.time()
if ips is not None:
for j in range(len(lip)):
ips[i + j] = lip[j]
expr = w - lip[0] * basis[i + 0]
for j in range(1, len(lip)):
expr -= lip[j] * basis[i + j]
t_linearCombination -= gpt.time()
w @= expr
t_linearCombination += gpt.time()
if verbose:
gpt.message(
"Timing Ortho: %g rank_inner_product, %g globalsum, %g lc" %
(t_rank_inner_product, t_globalSum, t_linearCombination))
def get_otype_from_multiplication(t_otype, t_adj, f_otype, f_adj):
if f_adj and not t_adj and f_otype.itab is not None:
# inner
tab = f_otype.itab
rtab = {}
elif not t_adj and f_adj and f_otype.otab is not None:
# outer
tab = f_otype.otab
rtab = {}
else:
tab = f_otype.mtab
rtab = t_otype.rmtab
if t_otype.__name__ in tab:
return tab[t_otype.__name__][0]()
else:
if f_otype.__name__ not in rtab:
if f_otype.data_alias is not None:
return get_otype_from_multiplication(
t_otype, t_adj, f_otype.data_alias(), f_adj
)
elif t_otype.data_alias is not None:
return get_otype_from_multiplication(
t_otype.data_alias(), t_adj, f_otype, f_adj
)
else:
gpt.message(
"Missing entry in multiplication table: %s x %s"
% (t_otype.__name__, f_otype.__name__)
)
return rtab[f_otype.__name__][0]()
def inv(dst, src):
# verbosity
verbose = g.default.is_verbose("split")
if len(src) % nparallel != 0:
raise Exception(
f"Cannot divide {len(src)} global vectors into {nparallel} groups"
)
t0 = g.time()
src_split = g.split(src, matrix_split.grid[1], cache)
dst_split = g.split(dst, matrix_split.grid[0], cache)
t1 = g.time()
operation_split(dst_split, src_split)
t2 = g.time()
g.unsplit(dst, dst_split, cache)
t3 = g.time()
if verbose:
g.message(
f"Split {len(src)} global vectors to {len(src_split)} local vectors\n"
+ f"Timing: {t1-t0} s (split), {t2-t1} s (operation), {t3-t2} s (unsplit)"
)
def get_next_name(root, jobs, max_weight, stale_seconds):
# create lut
lut = {}
for j in jobs:
lut[j.name] = j
for j in jobs:
if max_weight is None or j.weight <= max_weight:
has_started = j.has_started(root)
if has_started and stale_seconds is not None:
if not j.has_completed(root):
run_time = j.run_time(root)
if run_time > stale_seconds:
g.message(
f"Job {j.name} is stale after {run_time} seconds; purge"
)
j.purge(root)
has_started = False
if not has_started:
# check dependencies
dependencies_ok = True
for dep_j in [lut[d] for d in j.needs]:
if not dep_j.has_completed(root):
dependencies_ok = False
g.message(
f"Dependency {dep_j.name} of {j.name} is not yet satisfied."
)
break
if dependencies_ok:
# last check if in meantime somebody else has started running same job
if j.atomic_reserve_start(root):
return j.name
return ""
def __init__(self, n, precision):
self.n = n
self.fdimensions = [2**n]
self.grid = g.grid(self.fdimensions, precision)
self.verbose = g.default.is_verbose("qis_map")
self.zero_coordinate = (0, ) # |00000 ... 0> state
t = g.timer("map_init")
t("coordinates")
# TODO: need to split over multiple dimensions, single dimension can hold at most 32 bits
self.coordinates = g.coordinates(self.grid)
self.not_coordinates = [
np.bitwise_xor(self.coordinates, 2**i) for i in range(n)
]
for i in range(n):
self.not_coordinates[i].flags["WRITEABLE"] = False
t("masks")
self.one_mask = []
self.zero_mask = []
for i in range(n):
proj = np.bitwise_and(self.coordinates, 2**i)
mask = g.complex(self.grid)
g.coordinate_mask(mask, proj != 0)
self.one_mask.append(mask)
mask = g.complex(self.grid)
g.coordinate_mask(mask, proj == 0)
self.zero_mask.append(mask)
t()
if self.verbose:
g.message(t)
def converged(self, a, mat, evals, little_evec):
evals_max = np.max(np.abs(evals))
Nstop = self.params["Nstop"]
idx0 = len(evals) - Nstop
idx1 = len(evals)
n = 1
Nconv = 0
while True:
idx = idx0 + n - 1
if idx >= idx1:
idx = idx1 - 1
n *= 2
ev, eps2 = g.algorithms.eigen.evals(
mat, [a.single_evec(little_evec, idx)])
eps2 = eps2[0] / evals_max**2.0
if self.verbose:
g.message(f"eval[{idx1 - idx - 1}] = {ev[0]} ; eps^2 = {eps2}")
if eps2 < self.params["resid"]:
Nconv = max([Nconv, idx1 - idx])
if idx == idx1 - 1:
break
if self.verbose:
g.message(f"Arnoldi: {Nconv} eigenmodes converged")
return Nconv >= Nstop
def next(root, jobs, max_weight=None, stale_seconds=None):
if g.rank() == 0:
j = get_next_name(root, jobs, max_weight,
stale_seconds).encode("utf-8")
else:
j = bytes()
j_name = g.broadcast(0, j).decode("utf-8")
for j in jobs:
if j.name == j_name:
g.message(f"""
--------------------------------------------------------------------------------
Start job {j.name}
--------------------------------------------------------------------------------
""")
t0 = g.time()
j(root)
t1 = g.time()
g.message(f"""
--------------------------------------------------------------------------------
Completed {j.name} in {t1-t0} seconds
--------------------------------------------------------------------------------
""")
return j
return None
def implicit_restart(self, H, evals, p):
n = len(self.H)
k = n - p
Q = np.identity(n, np.complex128)
eye = np.identity(n, np.complex128)
t0 = g.time()
for i in range(p):
Qi, Ri = np.linalg.qr(H - evals[i] * eye)
H = Ri @ Qi + evals[i] * eye
Q = Q @ Qi
t1 = g.time()
if self.verbose:
g.message(f"Arnoldi: QR in {t1-t0} s")
r = g.eval(self.basis[k] * H[k, k - 1] +
self.basis[-1] * self.H[-1][-1] * Q[n - 1, k - 1])
rn = g.norm2(r)**0.5
t0 = g.time()
g.rotate(self.basis, np.ascontiguousarray(Q.T), 0, k, 0, n)
t1 = g.time()
if self.verbose:
g.message(f"Arnoldi: rotate in {t1-t0} s")
self.basis = self.basis[0:k]
self.basis.append(g.eval(r / rn))
self.H = [[H[j, i] for j in range(i + 2)] for i in range(k)]
self.H[-1][-1] = rn
def inv(dst, src):
dst[:] = 0
eta = gpt.copy(src)
ws = [gpt.copy(src) for _ in range(2)]
for eo in range(2):
ws[0][:] = 0
src_blk = F_domains[eo].lattice(op.otype)
dst_blk = F_domains[eo].lattice(op.otype)
F_domains[eo].project(src_blk, eta)
dst_blk[:] = 0 # for now
solver[eo](dst_blk, src_blk)
F_domains[eo].promote(ws[0], dst_blk)
if eo == 0:
op(ws[1], ws[0])
eta -= ws[1]
dst += ws[0]
gpt.message(
f"SAP cycle; |rho|^2 = {gpt.norm2(eta):g}; |dst|^2 = {gpt.norm2(dst):g}"
)
def open_view(self, xk, iview, write, mpi, fdimensions, g_cb, l_cb):
cv = gpt.cartesian_view(iview if iview is not None else -1, mpi,
fdimensions, g_cb, l_cb)
dn, fn = get_local_name(self.root, cv)
loc_desc = cv.describe() + "/" + ("Write" if write else "Read")
tag = "%d-%s" % (xk, str(iview))
tag_pos = "%s-%s-%s-%s" % (tag, str(fdimensions), str(g_cb), str(l_cb))
if loc_desc != self.loc_desc:
self.close_views()
self.loc_desc = loc_desc
if self.verbose:
gpt.message("Switching view to %s" % self.loc_desc)
if tag not in self.loc:
if write and dn is not None:
os.makedirs(dn, exist_ok=True)
self.loc[tag] = gpt.FILE(
fn, "a+b" if write else "rb") if fn is not None else None
if tag_pos not in self.pos:
self.pos[tag_pos] = gpt.coordinates(cv)
return self.loc[tag], self.pos[tag_pos]
def inv(dst, src):
dst[:] = 0
eta = gpt.copy(src)
ws = [gpt.copy(src) for _ in range(2)]
dt_solv = dt_distr = dt_hop = 0.0
for eo in range(2):
ws[0][:] = 0
dt_distr -= gpt.time()
src_blk[sap.pos] = eta[sap.coor[
eo]] # reminder view interface eta[[pos]], ... eta[...,idx]
dt_distr += gpt.time()
dt_solv -= gpt.time()
solver[eo](dst_blk, src_blk)
dt_solv += gpt.time()
dt_distr -= gpt.time()
ws[0][sap.coor[eo]] = dst_blk[sap.pos]
dt_distr += gpt.time()
dt_hop -= gpt.time()
if eo == 0:
sap.op(ws[1], ws[0])
eta -= ws[1]
dst += ws[0]
dt_hop += gpt.time()
gpt.message(
f"SAP cycle; |rho|^2 = {gpt.norm2(eta):g}; |dst|^2 = {gpt.norm2(dst):g}"
)
gpt.message(
f"SAP Timings: distr {dt_distr:g} secs, blk_solver {dt_solv:g} secs, hop+update {dt_hop:g} secs"
)
def __call__(self, mat, src, psi):
assert (src != psi)
self.history = []
verbose = g.default.is_verbose("cg")
t0 = g.time()
p, mmp, r = g.copy(src), g.copy(src), g.copy(src)
guess = g.norm2(psi)
mat(psi, mmp) # in, out
d = g.innerProduct(psi, mmp).real
b = g.norm2(mmp)
r @= src - mmp
p @= r
a = g.norm2(p)
cp = a
ssq = g.norm2(src)
rsq = self.eps**2. * ssq
for k in range(1, self.maxiter + 1):
c = cp
mat(p, mmp)
dc = g.innerProduct(p, mmp)
d = dc.real
a = c / d
cp = g.axpy_norm2(r, -a, mmp, r)
b = cp / c
psi += a * p
p @= b * p + r
self.history.append(cp)
if verbose:
g.message("res^2[ %d ] = %g" % (k, cp))
if cp <= rsq:
if verbose:
t1 = g.time()
g.message("Converged in %g s" % (t1 - t0))
break
def sample(self, t, p):
if type(t) == list:
for x in t:
self.sample(x, p)
elif t is None:
return cgpt.random_sample(self.obj, t, p)
elif type(t) == gpt.lattice:
if "pos" in p:
pos = p["pos"]
else:
pos = gpt.coordinates(t)
t0 = gpt.time()
mv = cgpt.random_sample(
self.obj,
pos,
{
**p,
**{
"shape": list(t.otype.shape),
"grid": t.grid.obj,
"precision": t.grid.precision,
},
},
)
t1 = gpt.time()
t[pos] = mv
if self.verbose:
szGB = mv.size * mv.itemsize / 1024.0**3.0
gpt.message("Generated %g GB of random data at %g GB/s" %
(szGB, szGB / (t1 - t0)))
return t
else:
assert 0
def orthogonalize(w, basis, ips=None, nblock=4):
# verbosity
t = gpt.timer("orthogonalize", verbose_performance)
n = len(basis)
if n == 0:
return
grid = basis[0].grid
i = 0
if verbose_performance:
cgpt.timer_begin()
for i in range(0, n, nblock):
t("rank_inner_product")
lip = gpt.rank_inner_product(basis[i : i + nblock], w)
t("global_sum")
grid.globalsum(lip)
t("create expression")
lip = [complex(x) for x in lip]
if ips is not None:
for j in range(len(lip)):
ips[i + j] = lip[j]
expr = w - lip[0] * basis[i + 0]
for j in range(1, len(lip)):
expr -= lip[j] * basis[i + j]
t("linear combination")
w @= expr
t()
if verbose_performance:
t_cgpt = gpt.timer("cgpt_orthogonalize", True)
t_cgpt += cgpt.timer_end()
gpt.message(f"\nPerformance of orthogonalize:\n{t}\n{t_cgpt}")
def expr_eval(first, second=None, ac=False):
if not second is None:
t_obj = first.v_obj
e = gpt.expr(second)
else:
if type(first) == gpt.lattice:
return first
e = gpt.expr(first)
lat = get_lattice(e)
grid = lat.grid
otype = lat.otype
n = len(otype.v_idx)
t_obj = None
if gpt.default.is_verbose("eval"):
gpt.message("GPT::verbose::eval: " + str(e))
if not t_obj is None:
for i, t in enumerate(t_obj):
assert (0 == cgpt.eval(t, e.val, e.unary, ac, i))
return first
else:
assert (ac == False)
t_obj, s_ot, s_pr = [0] * n, [0] * n, [0] * n
for i in otype.v_idx:
t_obj[i], s_ot[i], s_pr[i] = cgpt.eval(t_obj[i], e.val, e.unary,
False, i)
if len(s_ot) == 1:
otype = eval("gpt.otype." + s_ot[0])
else:
otype = gpt.otype.from_v_otype(s_ot)
return gpt.lattice(grid, otype, t_obj)
def converged(self, a, mat, evals, little_evec):
n = 1
Nconv = 0
while True:
idx = len(evals) - n
n *= 2
if idx < 0:
idx = 0
try:
g.algorithms.eigen.evals(
mat,
[a.single_evec(little_evec, idx)],
check_eps2=evals[-1]**2.0 * self.params["resid"],
verbose=self.verbose,
)
except g.algorithms.eigen.EvalsNotConverged:
break
Nconv = len(evals) - idx
if idx == 0:
break
if self.verbose:
g.message(f"Arnoldi: {Nconv} eigenmodes converged")
return Nconv >= self.params["Nstop"]
def sample(self, t, p):
if type(t) == list:
for x in t:
self.sample(x, p)
return t
elif t is None:
return cgpt.random_sample(self.obj, p)
elif type(t) == gpt.lattice:
t0 = gpt.time()
cgpt.random_sample(
self.obj,
{
**p,
**{
"lattices": [t]
},
},
)
t1 = gpt.time()
assert "pos" not in p # to ensure that deprecated code is not used
# optimize memory mapping
t.swap(gpt.copy(t))
if self.verbose_performance:
szGB = t.global_bytes() / 1024.0**3.0
gpt.message("Generated %g GB of random data at %g GB/s" %
(szGB, szGB / (t1 - t0)))
return t
else:
assert 0
def _ac(*arguments):
r = f(*arguments)
if iterative.converged is None:
gpt.message("Warning: could not determine converged state")
else:
assert iterative.converged
return r
def assert_gradient_error(self, rng, fields, dfields, epsilon_approx,
epsilon_assert):
fields = g.util.to_list(fields)
dfields = g.util.to_list(dfields)
weights = rng.normal_element(g.group.cartesian(dfields))
# the functional needs to be real
eps = complex(self(fields)).imag
g.message(f"Test that functional is real: {eps}")
assert eps == 0.0
# the gradient needs to be correct
gradient = self.gradient(fields, dfields)
a = sum(
[g.group.inner_product(w, gr) for gr, w in zip(gradient, weights)])
b = self.approximate_gradient(fields,
dfields,
weights,
epsilon=epsilon_approx)
eps = abs(a - b) / abs(b)
g.message(f"Assert gradient error: {eps} < {epsilon_assert}")
if eps > epsilon_assert:
g.message(f"Error: gradient = {a} <> approximate_gradient = {b}")
assert False
# the gradient needs to live in cartesian
for gr in gradient:
if gr.otype.__name__ != weights[0].otype.__name__:
g.message(
f"Gradient has incorrect object type: {gr.otype.__name__} != {weights[0].otype.__name__}"
)
eps = g.group.defect(gr)
if eps > epsilon_assert:
g.message(f"Error: cartesian defect: {eps} > {epsilon_assert}")
assert False
def timed_end(self, t):
if self.verbose_performance:
t()
self.timer += t
gpt.message(
f"\nPerformance of {self.name}:\n\nThis call:\n{t}\n\nAll calls:\n{self.timer}\n"
)
def save(self, obj):
if type(obj) == list:
for o in obj:
self.save(o)
elif type(obj) == gpt.lattice:
self.save(obj.mview())
elif type(obj) == float:
self.save(memoryview(struct.pack("d", obj)))
elif type(obj) == complex:
self.save(memoryview(struct.pack("dd", obj.real, obj.imag)))
elif type(obj) == memoryview:
self.f.seek(0, 1)
sz = len(obj)
szGB = sz / 1024.0**3
self.f.write(sz.to_bytes(8, "little"))
t0 = gpt.time()
self.f.write(gpt.crc32(obj).to_bytes(4, "little"))
t1 = gpt.time()
self.f.write(obj)
self.f.flush()
t2 = gpt.time()
if self.verbose:
if self.grid is None:
gpt.message(
"Checkpoint %g GB on head node at %g GB/s for crc32 and %g GB/s for write in %g s total"
% (szGB, szGB / (t1 - t0), szGB / (t2 - t1), t2 - t0))
else:
szGB = self.grid.globalsum(szGB)
gpt.message(
"Checkpoint %g GB at %g GB/s for crc32 and %g GB/s for write in %g s total"
% (szGB, szGB / (t1 - t0), szGB / (t2 - t1), t2 - t0))
else:
assert 0
def __call__(self, mat, src, psi):
verbose = g.default.is_verbose("mr")
t0 = time()
r, mmr = g.copy(src), g.copy(src)
mat(psi, mmr)
r @= src - mmr
ssq = g.norm2(src)
rsq = self.eps**2. * ssq
for k in range(self.maxiter):
mat(r, mmr)
ip, mmr2 = g.innerProductNorm2(mmr, r)
if mmr2 == 0.:
continue
alpha = ip.real / mmr2 * self.relax
psi += alpha * r
r2 = g.axpy_norm2(r, -alpha, mmr, r)
if verbose:
g.message("res^2[ %d ] = %g" % (k, r2))
if r2 <= rsq:
if verbose:
t1 = time()
g.message("Converged in %g s" % (t1 - t0))
break
def hamiltonian(draw):
if draw:
rng.normal_element(U_mom)
project_open_bc(U_mom)
s = action_gauge(U)
if not pure_gauge:
#sp = sd(fields)
for i in range(len(hasenbusch_ratios)):
if hasenbusch_ratios[i][3] is not two_flavor_ratio:
si = action_fermions_e[i].draw(fields[i], rng,
hasenbusch_ratios[i][2])
#si = sp[i]
si_check = action_fermions_e[i](fields[i])
g.message("action", i, si_check)
r = f"{hasenbusch_ratios[i][0]}/{hasenbusch_ratios[i][1]}"
e = abs(si / si_check - 1)
g.message(
f"Error of rational approximation for Hasenbusch ratio {r}: {e}"
)
else:
si = action_fermions_e[i].draw(fields[i], rng)
s += si
h = s + action_gauge_mom(U_mom)
else:
s = action_gauge(U)
if not pure_gauge:
for i in range(len(hasenbusch_ratios)):
s += action_fermions_e[i](fields[i])
h = s + action_gauge_mom(U_mom)
return h, s
def __init__(self, op, bs):
self.op = op
self.op_blk = []
dt = -gpt.time()
# thanks to double copy inside operator, U only temporary
Ublk = [sap_blk(op.U_grid, bs, eo) for eo in range(2)]
U = [gpt.mcolor(Ublk[0].grid) for _ in range(4)]
for eo in range(2):
Ucoor = Ublk[eo].coor(op.U_grid)
for mu in range(4):
U[mu][Ublk[eo].pos] = op.U[mu][Ucoor]
Ublk[eo].set_BC_Ufld(U)
self.op_blk.append(op.updated(U))
if self.op.F_grid.nd == len(bs) + 1:
_bs = [self.op.F_grid.fdimensions[0]] + bs
else:
_bs = bs
blk = [sap_blk(self.op.F_grid, _bs, eo) for eo in range(2)]
self.pos = blk[0].pos
self.pos.flags["WRITEABLE"] = False
self.coor = [blk[eo].coor(op.F_grid) for eo in range(2)]
for eo in range(2):
self.coor[eo].flags["WRITEABLE"] = False
dt += gpt.time()
gpt.message(f"SAP Initialized in {dt:g} secs")
def save(filename, objs, params):
t0 = gpt.time()
# create io
x = gpt_io(filename, params, True)
# create index
f = io.StringIO("")
x.create_index(f, "", objs)
mvidx = memoryview(f.getvalue().encode("utf-8"))
# write index to fs
index_crc = gpt.crc32(mvidx)
if gpt.rank() == 0:
open(filename + "/index", "wb").write(mvidx)
open(filename + "/index.crc32", "wt").write("%X\n" % index_crc)
# close
x.close()
# goodbye
if x.verbose:
t1 = gpt.time()
gpt.message("Completed writing %s in %g s" % (filename, t1 - t0))
def inv(dst, src):
for i in range(len(dst)):
eps = g.norm2(mat * dst[i] - src[i]) ** 0.5
nrm = g.norm2(src[i]) ** 0.5
g.message(
f"{self.tag}| mat * dst[{i}] - src[{i}] | / | src | = {eps/nrm}, | src[{i}] | = {nrm}"
)