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 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):
verbose = g.default.is_verbose("deflate")
# |dst> = sum_n 1/ev[n] |n><n|src>
t0 = g.time()
grid = src[0].grid
rip = np.zeros((len(src), len(self.evec)), dtype=np.complex128)
block = self.params["block"]
for i0 in range(0, len(self.evec), block):
rip_block = g.rank_inner_product(self.evec[i0:i0 + block], src,
True)
for i in range(rip_block.shape[0]):
for j in range(rip_block.shape[1]):
rip[j, i0 + i] = rip_block[i, j] / self.ev[i0 + i]
t1 = g.time()
grid.globalsum(rip)
t2 = g.time()
# TODO: simultaneous linear_combinations
for j in range(len(src)):
g.linear_combination(dst[j], self.evec, rip[j])
t3 = g.time()
if verbose:
g.message(
"Deflated %d vector(s) in %g s (%g s for rank_inner_product, %g s for global sum, %g s for linear combinations)"
% (len(src), t3 - t0, t1 - t0, t2 - t1, t3 - t2))
return inverter(dst, src)
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 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 __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 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 tell(self):
assert (not self.f is None)
t0 = gpt.time()
r = cgpt.ftell(self.f)
t1 = gpt.time()
#print("TELL %g" % (t1-t0))
return r
def write(self, d):
assert (not self.f is None)
t0 = gpt.time()
if type(d) != memoryview:
d = memoryview(d)
assert (cgpt.fwrite(self.f, len(d), d) == 1)
t1 = gpt.time()
def seek(self, offset, whence):
assert (not self.f is None)
t0 = gpt.time()
r = cgpt.fseek(self.f, offset, whence)
t1 = gpt.time()
#print("SEEK %g" % (t1-t0))
return r
def __init__(self, fn, md):
t0 = gpt.time()
self.f = cgpt.fopen(fn, md)
if self.f == 0:
self.f = None
raise FileNotFoundError("Can not open file %s" % fn)
t1 = gpt.time()
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 read(self, sz):
assert (not self.f is None)
t0 = gpt.time()
t = bytes(sz)
assert (cgpt.fread(self.f, sz, memoryview(t)) == 1)
t1 = gpt.time()
#print("READ %g s, %g GB" % (t1-t0,sz/1024.**3.))
return t
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 approx(dst, src):
assert src != dst
verbose = g.default.is_verbose("modes")
t0 = g.time()
dst[:] = 0
for i, x in enumerate(left):
dst += f_evals[i] * x * g.inner_product(right[i], src)
if verbose:
t1 = g.time()
g.message("Approximation by %d modes took %g s" % (len(left), t1 - t0))
def __call__(self, matrix, src, dst):
verbose = g.default.is_verbose("deflate")
# |dst> = sum_n 1/ev[n] |n><n|src>
t0 = g.time()
dst[:] = 0
for i, n in enumerate(self.evec):
dst += n * g.innerProduct(n, src) / self.ev[i]
t1 = g.time()
if verbose:
g.message("Deflated in %g s" % (t1 - t0))
return self.inverter(matrix, src, dst)
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, src_coarse, dst_coarse):
t0 = gpt.time()
gpt.block.promote(src_coarse, self.src_fine, self.basis)
t1 = gpt.time()
self.op(self.src_fine, self.dst_fine)
t2 = gpt.time()
gpt.block.project(dst_coarse, self.dst_fine, self.basis)
t3 = gpt.time()
if self.verbose:
gpt.message(
"Timing: %g s (promote), %g s (matrix), %g s (project)" %
(t1 - t0, t2 - t1, t3 - t2))
def rotate_basis_to_evec(self, little_evec):
n = len(self.H)
t0 = g.time()
g.rotate(self.basis[0:n], np.ascontiguousarray(little_evec.T), 0, n, 0,
n)
t1 = g.time()
if self.verbose:
g.message(f"Arnoldi: rotate in {t1-t0} s")
return self.basis[0:n]
def test(a, name):
t0 = g.time()
evec, evals = a(w, start)
t1 = g.time()
evals_test, evals_eps2 = g.algorithms.eigen.evals(w, evec)
largest_eval = 7.437
g.message(f"{name} finished in {t1-t0} s")
for i in range(len(evals_eps2)):
assert evals_eps2[i] / largest_eval**2.0 < 1e-5
assert abs(evals_test[i] - evals[i]) < 1e-6
def mat(dst_coarse, src_coarse):
t0 = gpt.time()
self.promote(src_fine, src_coarse)
t1 = gpt.time()
op(dst_fine, src_fine)
t2 = gpt.time()
self.project(dst_coarse, dst_fine)
t3 = gpt.time()
if verbose:
gpt.message(
"Timing: %g s (promote), %g s (matrix), %g s (project)"
% (t1 - t0, t2 - t1, t3 - t2)
)
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 little_eig(self):
t0 = g.time()
H = self.hessenberg()
t1 = g.time()
evals, little_evec = np.linalg.eig(H)
t2 = g.time()
idx = evals.argsort()
if self.verbose:
g.message(
f"Arnoldi: hessenberg() in {t1-t0} s and eig(H) in {t2-t1} s")
return evals[idx], little_evec[:, idx]
def mat(dst_coarse, src_coarse):
src_fine = [gpt.lattice(self.basis[0]) for x in src_coarse]
dst_fine = [gpt.lattice(self.basis[0]) for x in src_coarse]
t0 = gpt.time()
self.promote(src_fine, src_coarse)
t1 = gpt.time()
fine_operator(dst_fine, src_fine)
t2 = gpt.time()
self.project(dst_coarse, dst_fine)
t3 = gpt.time()
if verbose:
gpt.message(
"coarse_operator acting on %d vector(s) in %g s (promote %g s, fine_operator %g s, project %g s)"
% (len(src_coarse), t3 - t0, t1 - t0, t2 - t1, t3 - t2))
def mat(dst, src):
csrc = [gpt.lattice(self.coarse_grid, coarse_otype) for x in src]
cdst = [gpt.lattice(self.coarse_grid, coarse_otype) for x in src]
t0 = gpt.time()
self.project(csrc, src)
t1 = gpt.time()
coarse_operator(cdst, csrc)
t2 = gpt.time()
self.promote(dst, cdst)
t3 = gpt.time()
if verbose:
gpt.message(
"fine_operator acting on %d vector(s) in %g s (project %g s, coarse_operator %g s, promote %g s)"
% (len(src), t3 - t0, t1 - t0, t2 - t1, t3 - t2))
def message(*a):
# conversion to string can be an mpi process (i.e. for lattice),
# so need to do it on all ranks
s = [str(x) for x in a]
if gpt.rank() == 0:
print("GPT : %14.6f s :" % gpt.time(), *s)
sys.stdout.flush()
def __call__(self, dst, src):
dst = gpt.util.to_list(dst)
src = gpt.util.to_list(src)
if verbose_performance:
t0 = gpt.time()
cgpt.copy_execute_plan(self.obj, dst, src, self.lattice_view_location)
if verbose_performance:
t1 = gpt.time()
info = [a for v in self.info().values() for a in v.values()]
blocks = sum([a["blocks"] for a in info])
size = sum([a["size"] for a in info])
block_size = size // blocks
GB = 2 * size / 1e9 # read + write = factor of 2
gpt.message(
f"copy_plan: execute: {GB:g} GB at {GB/(t1-t0):g} GB/s/rank with block_size {block_size}"
)
def save(filename, objs, params):
t0 = gpt.time()
# create io
x = gpt_io(filename, True, params)
# create index
x.write(objs)
# close
x.close()
# goodbye
if x.verbose:
t1 = gpt.time()
gpt.message("Completed writing %s in %g s" % (filename, t1 - t0))