def load_cgpt(*a):
result = []
r, metadata = cgpt.load(*a, gpt.default.is_verbose("io"))
if r is None:
raise gpt.LoadError()
for gr in r:
grid = gpt.grid(gr[1], eval("gpt." + gr[2]), eval("gpt." + gr[3]),
gr[0])
result_grid = []
otype = gpt.ot_matrix_su_n_fundamental_group(3)
for t_obj, s_ot, s_pr in gr[4]:
assert s_pr == gr[2]
# only allow loading su3 gauge fields from cgpt, rest done in python
# in the long run, replace *any* IO from cgpt with gpt code
assert s_ot == "ot_mcolor3"
l = gpt.lattice(grid, otype, [t_obj])
l.metadata = metadata
result_grid.append(l)
result.append(result_grid)
while len(result) == 1:
result = result[0]
return result
def separate_indices(x, st):
pos = gpt.coordinates(x)
cb = x.checkerboard()
assert st is not None
result_otype = st[-1]()
if result_otype is None:
return x
ndim = x.otype.shape[st[0]]
rank = len(st) - 1
islice = [slice(None, None, None) for i in range(len(x.otype.shape))]
ivec = [0] * rank
result = {}
for i in range(ndim ** rank):
idx = i
for j in range(rank):
c = idx % ndim
islice[st[j]] = c
ivec[j] = c
idx //= ndim
v = gpt.lattice(x.grid, result_otype)
v.checkerboard(cb)
v[pos] = x[(pos,) + tuple(islice)]
result[tuple(ivec)] = v
return result
# Show metadata of field
# g.message("Metadata", U[0].metadata)
rng = g.random("test")
U = g.qcd.gauge.random(g.grid([8, 8, 8, 16], g.double), rng)
# create a sparse sub-domain and a sparse lattice S with 1% of points
sdomain = g.domain.sparse(
U[0].grid,
rng.choice(g.coordinates(U[0]), int(0.01 * U[0].grid.gsites / U[0].grid.Nprocessors)),
)
# test sparse domain
S = sdomain.lattice(U[0].otype)
sdomain.project(S, U[0])
U0prime = g.lattice(U[0])
U0prime[:] = 0
sdomain.promote(U0prime, S)
assert np.linalg.norm(U0prime[sdomain.local_coordinates] - U[0][sdomain.local_coordinates]) < 1e-14
s_slice = sdomain.slice(S, 3)
# save in default gpt format
g.save(
f"{work_dir}/out",
{
"va\nl": [
0,
1,
3,
"tes\n\0t",
3.123456789123456789,
#!/usr/bin/env python3
#
# Authors: Christoph Lehner 2020
#
# Desc.: Illustrate core concepts and features
#
import gpt as g
import numpy as np
# load configuration
rng = g.random("test")
U = g.qcd.gauge.random(g.grid([8, 8, 8, 16], g.double), rng)
V = rng.element(g.lattice(U[0]))
U_transformed = g.qcd.gauge.transformed(U, V)
# reference plaquette
P = g.qcd.gauge.plaquette(U)
# test rectangle calculation using parallel transport and copy_plan
R_1x1, R_2x1 = g.qcd.gauge.rectangle(U, [(1, 1), (2, 1)])
eps = abs(P - R_1x1)
g.message(f"Plaquette {P} versus 1x1 rectangle {R_1x1}: {eps}")
assert eps < 1e-13
# Test gauge invariance of plaquette
P_transformed = g.qcd.gauge.plaquette(U_transformed)
eps = abs(P - P_transformed)
g.message(
f"Plaquette before {P} and after {P_transformed} gauge transformation: {eps}"
)
assert eps < 1e-13
cmath.exp(3j), cmath.exp(4j)],
}
# pf=g.params("~/gpt/tests/wilson.txt")
# print(pf)
# take slow reference implementation of wilson (kappa = 1/2/(m0 + 4) ) ;
w_ref = g.qcd.fermion.reference.wilson_clover(U, p)
# and fast Grid version
w = g.qcd.fermion.wilson_clover(U, p, kappa=0.137)
# create point source
src = rng.cnormal(g.vspincolor(grid))
dst_ref, dst = g.lattice(src), g.lattice(src)
# correctness
dst_ref @= w_ref * src
dst @= w * src
eps = g.norm2(dst - dst_ref) / g.norm2(dst)
g.message("Test wilson versus reference:", eps)
assert eps < 1e-13
# now timing
t0 = g.time()
for i in range(100):
w_ref(dst_ref, src)
t1 = g.time()
for i in range(100):
V = [g.matrix_su2_adjoint(grid) for x in U]
for i in range(3):
g.convert(
V[i], U[i]
) # this used to be a separate function: fundamental_to_adjoint
check_unitarity(V[i], eps_ref)
check_representation(V[i], eps_ref)
# check if fundamental_to_adjoint is a homomorphism
eps = (g.norm2(V[2] - V[0] * V[1]) / g.norm2(V[2]))**0.5
g.message(f"Test fundamental_to_adjoint is homomorphism: {eps}")
assert eps < eps_ref
a = [
g.lattice(V[0].grid, g.ot_matrix_su_n_fundamental_algebra(2))
for i in range(3)
]
g.convert(a, U)
V_c = []
for i in range(3):
# convert through canonical coordinates
coor = a[i].otype.coordinates(a[i])
a_adj = g.lattice(a[i].grid, g.ot_matrix_su_n_adjoint_algebra(2))
a_adj.otype.coordinates(a_adj, coor)
v = g.convert(a_adj, g.ot_matrix_su_n_adjoint_group(2))
check_unitarity(v, eps_ref)
check_representation(v, eps_ref)
V_c.append(v)
def create_links(A, fmat, basis, params):
# NOTE: we expect the blocks in the basis vectors
# to already be orthogonalized!
# parameters
make_hermitian = params["make_hermitian"]
save_links = params["save_links"]
assert not (make_hermitian and not save_links)
# verbosity
verbose = gpt.default.is_verbose("coarsen")
# setup timings
t = gpt.timer("coarsen")
t("setup")
# get grids
f_grid = basis[0].grid
c_grid = A[0].grid
# directions/displacements we coarsen for
dirs = [1, 2, 3, 4] if f_grid.nd == 5 else [0, 1, 2, 3]
disp = +1
dirdisps_full = list(zip(dirs * 2, [+1] * 4 + [-1] * 4))
dirdisps_forward = list(zip(dirs, [disp] * 4))
nhops = len(dirdisps_full)
selflink = nhops
# setup fields
Mvr = [gpt.lattice(basis[0]) for i in range(nhops)]
tmp = gpt.lattice(basis[0])
oproj = gpt.vcomplex(c_grid, len(basis))
selfproj = gpt.vcomplex(c_grid, len(basis))
# setup masks
onemask, blockevenmask, blockoddmask = (
gpt.complex(f_grid),
gpt.complex(f_grid),
gpt.complex(f_grid),
)
dirmasks = [gpt.complex(f_grid) for p in range(nhops)]
# auxilliary stuff needed for masks
t("masks")
onemask[:] = 1.0
coor = gpt.coordinates(blockevenmask)
block = numpy.array(f_grid.ldimensions) / numpy.array(c_grid.ldimensions)
block_cb = coor[:, :] // block[:]
# fill masks for sites within even/odd blocks
gpt.coordinate_mask(blockevenmask, numpy.sum(block_cb, axis=1) % 2 == 0)
blockoddmask @= onemask - blockevenmask
# fill masks for sites on borders of blocks
dirmasks_forward_np = coor[:, :] % block[:] == block[:] - 1
dirmasks_backward_np = coor[:, :] % block[:] == 0
for mu in dirs:
gpt.coordinate_mask(dirmasks[mu], dirmasks_forward_np[:, mu])
gpt.coordinate_mask(dirmasks[mu + 4], dirmasks_backward_np[:, mu])
# save applications of matrix and coarsening if possible
dirdisps = dirdisps_forward if save_links else dirdisps_full
# create block maps
t("blockmap")
dirbms = [
gpt.block.map(c_grid, basis, dirmasks[p])
for p, (mu, fb) in enumerate(dirdisps)
]
fullbm = gpt.block.map(c_grid, basis)
for i, vr in enumerate(basis):
# apply directional hopping terms
# this triggers len(dirdisps) comms -> TODO expose DhopdirAll from Grid
# BUT problem with vector<Lattice<...>> in rhs
t("apply_hop")
[fmat.Mdir(*dirdisp)(Mvr[p], vr) for p, dirdisp in enumerate(dirdisps)]
# coarsen directional terms + write to link
for p, (mu, fb) in enumerate(dirdisps):
t("coarsen_hop")
dirbms[p].project(oproj, Mvr[p])
t("copy_hop")
A[p][:, :, :, :, :, i] = oproj[:]
# fast diagonal term: apply full matrix to both block cbs separately and discard hops into other cb
t("apply_self")
tmp @= (blockevenmask * fmat * vr * blockevenmask +
blockoddmask * fmat * vr * blockoddmask)
# coarsen diagonal term
t("coarsen_self")
fullbm.project(selfproj, tmp)
# write to self link
t("copy_self")
A[selflink][:, :, :, :, :, i] = selfproj[:]
if verbose:
gpt.message("coarsen: done with vector %d" % i)
# communicate opposite links
if save_links:
t("comm")
communicate_links(A, dirdisps_forward, make_hermitian)
t()
if verbose:
gpt.message(t)
# basis
n = 30
res = None
tmpf_prev = None
for dtype in [msc, vc12]:
g.message(f"Data type {dtype.__name__}")
basis = [dtype() for i in range(n)]
rng = g.random("block_seed_string_13")
rng.cnormal(basis)
for i in range(2):
g.message("Ortho step %d" % i)
g.block.orthonormalize(coarse_grid, basis)
# test coarse vector
lcoarse = g.vcomplex(coarse_grid, n)
rng.cnormal(lcoarse)
# temporary fine and coarse vectors
tmpf = g.lattice(basis[0])
lcoarse2 = g.lattice(lcoarse)
# coarse-to-fine-to-coarse
g.block.promote(lcoarse, tmpf, basis)
g.block.project(lcoarse2, tmpf, basis)
# report error
err2 = g.norm2(lcoarse - lcoarse2) / g.norm2(lcoarse)
g.message(err2)
assert err2 < 1e-12
def __call__(self, mat, src, ckpt=None):
# verbosity
verbose = g.default.is_verbose("irl")
# checkpointer
if ckpt is None:
ckpt = g.checkpointer_none()
ckpt.grid = src.grid
self.ckpt = ckpt
# first approximate largest eigenvalue
pit = g.algorithms.eigen.power_iteration(eps=0.05,
maxiter=10,
real=True)
lambda_max = pit(mat, src)[0]
# parameters
Nm = self.params["Nm"]
Nk = self.params["Nk"]
Nstop = self.params["Nstop"]
assert Nm >= Nk and Nstop <= Nk
# tensors
dtype = np.float64
lme = np.empty((Nm, ), dtype)
lme2 = np.empty((Nm, ), dtype)
ev = np.empty((Nm, ), dtype)
ev2 = np.empty((Nm, ), dtype)
ev2_copy = np.empty((Nm, ), dtype)
# fields
f = g.lattice(src)
v = g.lattice(src)
evec = [g.lattice(src) for i in range(Nm)]
# advice memory storage
if not self.params["advise"] is None:
g.advise(evec, self.params["advise"])
# scalars
k1 = 1
k2 = Nk
beta_k = 0.0
# set initial vector
evec[0] @= src / g.norm2(src)**0.5
# initial Nk steps
for k in range(Nk):
self.step(mat, ev, lme, evec, f, Nm, k)
# restarting loop
for it in range(self.params["maxiter"]):
if verbose:
g.message("Restart iteration %d" % it)
for k in range(Nk, Nm):
self.step(mat, ev, lme, evec, f, Nm, k)
f *= lme[Nm - 1]
# eigenvalues
for k in range(Nm):
ev2[k] = ev[k + k1 - 1]
lme2[k] = lme[k + k1 - 1]
# diagonalize
t0 = g.time()
Qt = np.identity(Nm, dtype)
self.diagonalize(ev2, lme2, Nm, Qt)
t1 = g.time()
if verbose:
g.message("Diagonalization took %g s" % (t1 - t0))
# sort
ev2_copy = ev2.copy()
ev2 = list(reversed(sorted(ev2)))
# implicitly shifted QR transformations
Qt = np.identity(Nm, dtype)
t0 = g.time()
for ip in range(k2, Nm):
g.qr_decomposition(ev, lme, Nm, Nm, Qt, ev2[ip], k1, Nm)
t1 = g.time()
if verbose:
g.message("QR took %g s" % (t1 - t0))
# rotate
t0 = g.time()
g.rotate(evec, Qt, k1 - 1, k2 + 1, 0, Nm)
t1 = g.time()
if verbose:
g.message("Basis rotation took %g s" % (t1 - t0))
# compression
f *= Qt[k2 - 1, Nm - 1]
f += lme[k2 - 1] * evec[k2]
beta_k = g.norm2(f)**0.5
betar = 1.0 / beta_k
evec[k2] @= betar * f
lme[k2 - 1] = beta_k
if verbose:
g.message("beta_k = ", beta_k)
# convergence test
if it >= self.params["Nminres"]:
if verbose:
g.message("Rotation to test convergence")
# diagonalize
for k in range(Nm):
ev2[k] = ev[k]
lme2[k] = lme[k]
Qt = np.identity(Nm, dtype)
t0 = g.time()
self.diagonalize(ev2, lme2, Nk, Qt)
t1 = g.time()
if verbose:
g.message("Diagonalization took %g s" % (t1 - t0))
B = g.copy(evec[0])
allconv = True
if beta_k >= self.params["betastp"]:
jj = 1
while jj <= Nstop:
j = Nstop - jj
g.linear_combination(B, evec[0:Nk], Qt[j, 0:Nk])
B *= 1.0 / g.norm2(B)**0.5
if not ckpt.load(v):
mat(v, B)
ckpt.save(v)
ev_test = g.inner_product(B, v).real
eps2 = g.norm2(v - ev_test * B) / lambda_max**2.0
if verbose:
g.message("%-65s %-45s %-50s" % (
"ev[ %d ] = %s" % (j, ev2_copy[j]),
"<B|M|B> = %s" % (ev_test),
"|M B - ev B|^2 / ev_max^2 = %s" % (eps2),
))
if eps2 > self.params["resid"]:
allconv = False
if jj == Nstop:
break
jj = min([Nstop, 2 * jj])
if allconv:
if verbose:
g.message("Converged in %d iterations" % it)
break
t0 = g.time()
g.rotate(evec, Qt, 0, Nstop, 0, Nk)
t1 = g.time()
if verbose:
g.message("Final basis rotation took %g s" % (t1 - t0))
return (evec[0:Nstop], ev2_copy[0:Nstop])
for s1 in range(4):
for s2 in range(4):
eps = np.linalg.norm(
msc[0, 0, 0, 0].array[s1, s2, :, :] - xs[s1, s2][0, 0, 0, 0].array
)
assert eps < 1e-13
for c1 in range(3):
for c2 in range(3):
eps = np.linalg.norm(
msc[0, 0, 0, 0].array[:, :, c1, c2] - xc[c1, c2][0, 0, 0, 0].array
)
assert eps < 1e-13
msc2 = g.lattice(msc)
g.merge_spin(msc2, xs)
assert g.norm2(msc2 - msc) < 1e-13
g.merge_color(msc2, xc)
assert g.norm2(msc2 - msc) < 1e-13
assert (
g.norm2(g.separate_color(xs[1, 2])[2, 0] - g.separate_spin(xc[2, 0])[1, 2]) < 1e-13
)
################################################################################
# Setup lattices
################################################################################
grid = g.grid(g.default.get_ivec("--grid", [16, 16, 16, 32], 4), precision)
N = 10
Nwarmup = 5
g.message(f"""
Matrix Multiply Benchmark with
fdimensions : {grid.fdimensions}
precision : {precision.__name__}
""")
# Source and destination
for tp in [
g.ot_matrix_color(3),
g.ot_matrix_spin(4),
g.ot_matrix_spin_color(4, 3)
]:
one = g.lattice(grid, tp)
two = g.lattice(grid, tp)
three = g.lattice(grid, tp)
rng.cnormal([one, two])
# Rank inner product
nbytes = 3.0 * one.global_bytes() * N
# Time
dt = 0.0
for it in range(N + Nwarmup):
if it >= Nwarmup:
dt -= g.time()
g.eval(three, one * two)
if it >= Nwarmup:
dt += g.time()
for precision in [g.single, g.double]:
grid = g.grid(g.default.get_ivec("--grid", [16, 16, 16, 32], 4), precision)
N = 100
Nwarmup = 5
g.message(
f"""
Inner Product Benchmark with
fdimensions : {grid.fdimensions}
precision : {precision.__name__}
"""
)
# Source and destination
for tp in [g.ot_singlet(), g.ot_vector_spin_color(4, 3), g.ot_vector_singlet(12)]:
for n in [1, 4]:
one = [g.lattice(grid, tp) for i in range(n)]
two = [g.lattice(grid, tp) for i in range(n)]
rng.cnormal([one, two])
# Rank inner product
nbytes = (one[0].global_bytes() + two[0].global_bytes()) * N * n * n
for use_accelerator, compute_name, access in [
(False, "host", access_host),
(True, "accelerator", access_accelerator),
]:
# Time
dt = 0.0
cgpt.timer_begin()
for it in range(N + Nwarmup):
access(one)
# now define coarse-grid operator
g.message("Test precision of promote-project chain: %g" %
(g.norm2(cstart - b.project * b.promote * cstart) / g.norm2(cstart)))
g.mem_report()
try:
cevec, cev = g.load("cevec", {"grids": cgrid})
except g.LoadError:
cevec, cev = irl(cop, cstart, params["checkpointer"])
g.save("cevec", (cevec, cev))
# smoother
smoother = params["smoother"](q.NDagN)
nsmoother = params["nsmoother"]
v_fine = g.lattice(basis[0])
v_fine_smooth = g.lattice(basis[0])
try:
ev3 = g.load("ev3")
except g.LoadError:
ev3 = [0.0] * len(cevec)
for i, v in enumerate(cevec):
v_fine @= b.promote * v
for j in range(nsmoother):
v_fine_smooth @= smoother * v_fine
v_fine @= v_fine_smooth / g.norm2(v_fine_smooth)**0.5
ev_smooth = g.algorithms.eigen.evals(q.NDagN, [v_fine],
check_eps2=1e-2,
real=True)
ev3[i] = ev_smooth[0]
g.message("Eigenvalue %d = %.15g" % (i, ev3[i]))
def gpt_object(first, ot):
if type(first) == gpt.grid:
return gpt.lattice(first, ot)
return gpt.tensor(numpy.array(first, dtype=numpy.complex128), ot)
def __call__(self, mat, src, ckpt=None):
# verbosity
verbose = g.default.is_verbose("irl")
# checkpointer
if ckpt is None:
ckpt = g.checkpointer_none()
ckpt.grid = src.grid
self.ckpt = ckpt
# first approximate largest eigenvalue
pit = g.algorithms.eigen.power_iteration(eps=0.05, maxiter=10, real=True)
lambda_max = pit(mat, src)[0]
# parameters
Nm = self.params["Nm"]
Nu = self.params["Nu"]
Nk = self.params["Nk"]
Nstop = self.params["Nstop"]
Np = Nm-Nk
MaxIter=self.params["maxiter"]
Np /= MaxIter
assert Nm >= Nk and Nstop <= Nk
print ( 'Nm=',Nm,'Nu=',Nu,'Nk=',Nk )
# tensors
dtype = np.float64
ctype = np.complex128
lme = np.zeros((Nu,Nm), ctype)
lmd = np.zeros((Nu,Nm), ctype)
lme2 = np.zeros((Nu,Nm), ctype)
lmd2 = np.empty((Nu,Nm), ctype)
Qt = np.zeros((Nm,Nm),ctype)
Q = np.zeros((Nm,Nm),ctype)
ev = np.empty((Nm,), dtype)
ev2_copy = np.empty((Nm,), dtype)
# fields
f = g.lattice(src)
v = g.lattice(src)
evec = [g.lattice(src) for i in range(Nm)]
w = [g.lattice(src) for i in range(Nu)]
w_copy = [g.lattice(src) for i in range(Nu)]
# advice memory storage
if not self.params["advise"] is None:
g.advise(evec, self.params["advise"])
# scalars
k1 = 1
k2 = Nk
beta_k = 0.0
rng=g.random("test")
# set initial vector
# rng.zn(w)
for i in range(Nu):
rng.zn(w[i])
if i > 0:
g.orthogonalize(w[i],evec[0:i])
evec[i]=g.copy(w[i])
evec[i] *= 1.0/ g.norm2(evec[i]) ** 0.5
g.message("norm(evec[%d]=%e "%(i,g.norm2(evec[i])))
if i > 0:
for j in range(i):
ip=g.innerProduct(evec[j],w[i])
if np.abs(ip) >1e-6:
g.message("inner(evec[%d],w[%d])=%e %e"% (j,i,ip.real,ip.imag))
# evec[i] @= src[i] / g.norm2(src[i]) ** 0.5
# initial Nk steps
Nblock_k = int(Nk/Nu)
for b in range(Nblock_k):
self.blockStep(mat, lmd, lme, evec, w, w_copy, Nm, b,Nu)
Nblock_p = int(Np/Nu)
# restarting loop
# for it in range(self.params["maxiter"]):
for it in range(MaxIter):
if verbose:
g.message("Restart iteration %d" % it)
Nblock_l = Nblock_k + it*Nblock_p;
Nblock_r = Nblock_l + Nblock_p;
Nl = Nblock_l*Nu
Nr = Nblock_r*Nu
# ev2.resize(Nr)
ev2 = np.empty((Nr,), dtype)
for b in range(Nblock_l, Nblock_r):
self.blockStep(mat, lmd, lme, evec, w, w_copy, Nm, b,Nu)
for u in range(Nu):
for k in range(Nr):
lmd2[u,k]=lmd[u,k]
lme2[u,k]=lme[u,k]
Qt = np.identity(Nr, ctype)
# diagonalize
t0 = g.time()
# self.diagonalize(ev2, lme2, Nm, Qt)
self.diagonalize(ev2,lmd2,lme2,Nu,Nr,Qt)
# def diagonalize(self, eval, lmd, lme, Nu, Nk, Nm, Qt):
t1 = g.time()
if verbose:
g.message("Diagonalization took %g s" % (t1 - t0))
# sort
ev2_copy = ev2.copy()
ev2 = list(reversed(sorted(ev2)))
for i in range(Nr):
g.message("Rval[%d]= %e"%(i,ev2[i]))
# rotate
# t0 = g.time()
# g.rotate(evec, Qt, k1 - 1, k2 + 1, 0, Nm)
# t1 = g.time()
# if verbose:
# g.message("Basis rotation took %g s" % (t1 - t0))
# convergence test
if it >= self.params["Nminres"]:
if verbose:
g.message("Rotation to test convergence")
# diagonalize
for k in range(Nr):
ev2[k] = ev[k]
# lme2[k] = lme[k]
for u in range(Nu):
for k in range(Nr):
lmd2[u,k]=lmd[u,k]
lme2[u,k]=lme[u,k]
Qt = np.identity(Nm, ctype)
t0 = g.time()
# self.diagonalize(ev2, lme2, Nk, Qt)
self.diagonalize(ev2,lmd2,lme2,Nu,Nr,Qt)
t1 = g.time()
if verbose:
g.message("Diagonalization took %g s" % (t1 - t0))
B = g.copy(evec[0])
allconv = True
if beta_k >= self.params["betastp"]:
jj = 1
while jj <= Nstop:
j = Nstop - jj
g.linear_combination(B, evec[0:Nr], Qt[j, 0:Nr])
g.message("norm=%e"%(g.norm2(B)))
B *= 1.0 / g.norm2(B) ** 0.5
if not ckpt.load(v):
mat(v, B)
ckpt.save(v)
ev_test = g.innerProduct(B, v).real
eps2 = g.norm2(v - ev_test * B) / lambda_max ** 2.0
if verbose:
g.message(
"%-65s %-45s %-50s"
% (
"ev[ %d ] = %s" % (j, ev2_copy[j]),
"<B|M|B> = %s" % (ev_test),
"|M B - ev B|^2 / ev_max^2 = %s" % (eps2),
)
)
if eps2 > self.params["resid"]:
allconv = False
if jj == Nstop:
break
jj = min([Nstop, 2 * jj])
if allconv:
if verbose:
g.message("Converged in %d iterations" % it)
break
t0 = g.time()
g.rotate(evec, Qt, 0, Nstop, 0, Nk)
t1 = g.time()
if verbose:
g.message("Final basis rotation took %g s" % (t1 - t0))
return (evec[0:Nstop], ev2_copy[0:Nstop])
################################################################################
# Test mview
################################################################################
c = g.coordinates(l_dp)
x = l_dp[c]
mv = g.mview(x)
assert mv.itemsize == 1 and mv.shape[0] == len(mv)
assert sys.getrefcount(x) == 3
del mv
assert sys.getrefcount(x) == 2
################################################################################
# Test assignments
################################################################################
pos = l_dp.mview_coordinates()
lhs = g.lattice(l_dp)
def assign_copy():
g.copy(lhs, l_dp)
def assign_pos():
lhs[pos] = l_dp[pos]
def assign_pos_view():
lhs[pos] = l_dp.view[pos]
for method in [assign_copy, assign_pos, assign_pos_view]:
def read_lattice(self, a):
g_desc = a[0]
cv_desc = a[1]
l_desc = a[2]
filepos = [int(x) for x in a[3:]]
# first find grid
if g_desc not in self.params["grids"]:
self.params["grids"][g_desc] = gpt.grid_from_description(g_desc)
g = self.params["grids"][g_desc]
# create a cartesian view and lattice to load
l = gpt.lattice(g, l_desc)
cv0 = gpt.cartesian_view(-1, cv_desc, g.fdimensions, g.cb,
l.checkerboard())
# find tasks for my node
views_for_node = self.views_for_node(cv0, g)
# performance
dt_distr, dt_crc, dt_read = 0.0, 0.0, 0.0
szGB = 0.0
g.barrier()
t0 = gpt.time()
# need to load all views
for xk, iview in enumerate(views_for_node):
g.barrier()
dt_read -= gpt.time()
f, pos = self.open_view(xk, iview, False, cv_desc, g.fdimensions,
g.cb, l.checkerboard())
cache_key = f"{a[0:3]}_{g.obj}_{iview}_read"
if cache_key not in self.cache:
self.cache[cache_key] = {}
if f is not None:
f.seek(filepos[iview], 0)
ntag = int.from_bytes(f.read(4), byteorder="little")
f.read(ntag) # not needed if index is present
crc_exp = int.from_bytes(f.read(4), byteorder="little")
nd = int.from_bytes(f.read(4), byteorder="little")
f.read(8 * nd) # not needed if index is present
sz = int.from_bytes(f.read(8), byteorder="little")
data = memoryview(f.read(sz))
dt_crc -= gpt.time()
crc_comp = gpt.crc32(data)
dt_crc += gpt.time()
assert crc_comp == crc_exp
sys.stdout.flush()
szGB += len(data) / 1024.0**3.0
else:
assert len(pos) == 0
data = None
g.barrier()
dt_read += gpt.time()
dt_distr -= gpt.time()
l[pos, self.cache[cache_key]] = data
g.barrier()
dt_distr += gpt.time()
g.barrier()
t1 = gpt.time()
szGB = g.globalsum(szGB)
if self.verbose and dt_crc != 0.0:
gpt.message(
"Read %g GB at %g GB/s (%g GB/s for distribution, %g GB/s for reading + checksum, %g GB/s for checksum, %d views per node)"
% (
szGB,
szGB / (t1 - t0),
szGB / dt_distr,
szGB / dt_read,
szGB / dt_crc,
len(views_for_node),
))
return l
# start vector
cstart = g.vcomplex(cgrid, nbasis)
cstart[:] = g.vcomplex([1] * nbasis, nbasis)
g.mem_report()
# basis
northo = params["northo"]
for i in range(northo):
g.message("Orthonormalization round %d" % i)
g.block.orthonormalize(cgrid, basis)
g.mem_report()
# now define coarse-grid operator
ftmp = g.lattice(basis[0])
ctmp = g.lattice(cstart)
g.block.promote(cstart, ftmp, basis)
g.block.project(ctmp, ftmp, basis)
g.message(
"Test precision of promote-project chain: %g"
% (g.norm2(cstart - ctmp) / g.norm2(cstart))
)
g.mem_report()
try:
cevec, cev = g.load("cevec", {"grids": cgrid})
except g.LoadError:
cevec, cev = irl(cop, cstart, params["checkpointer"])
g.save("cevec", (cevec, cev))
def inv_lvl(psi, src, lvl):
# assertions
assert psi != src
# neighbors
nc_lvl = s.nc_lvl[lvl]
# aliases
t = self.t[lvl]
r = self.r[lvl]
pp = self.print_prefix[lvl]
r_c = self.r[nc_lvl] if lvl != s.coarsest else None
e_c = self.e[nc_lvl] if lvl != s.coarsest else None
mat_c = s.mat[nc_lvl] if lvl != s.coarsest else None
mat = s.mat[lvl]
bm = s.blockmap[lvl]
slv_s = self.smooth_solver[lvl] if lvl != s.coarsest else None
slv_w = self.wrapper_solver[lvl] if lvl <= s.coarsest - 2 else None
slv_c = self.coarsest_solver if lvl == s.coarsest else None
# start clocks
t("misc")
if self.verbose:
g.message("%s starting inversion routine: psi = %g, src = %g" %
(pp, g.norm2(psi), g.norm2(src)))
inputnorm = g.norm2(src)
if lvl == s.coarsest:
t("invert")
g.default.push_verbose(get_slv_name(slv_c), False)
slv_c(mat)(psi, src)
g.default.pop_verbose()
self.history[lvl]["coarsest"].append(get_slv_history(slv_c))
else:
t("copy")
r @= src
# fine to coarse
t("to_coarser")
bm.project(r_c, r)
if self.verbose:
t("output")
g.message("%s done calling f2c: r_c = %g, r = %g" %
(pp, g.norm2(r_c), g.norm2(r)))
# call method on next level
t("on_coarser")
e_c[:] = 0.0
if slv_w is not None and lvl < s.coarsest - 1:
def prec(matrix):
def ignore_mat(dst_p, src_p):
inv_lvl(dst_p, src_p, nc_lvl)
return ignore_mat
g.default.push_verbose(get_slv_name(slv_w), False)
slv_w.modified(prec=prec)(mat_c)(e_c, r_c)
g.default.pop_verbose()
self.history[lvl]["wrapper"].append(get_slv_history(slv_w))
else:
inv_lvl(e_c, r_c, nc_lvl)
if self.verbose:
t("output")
g.message(
"%s done calling coarser level: e_c = %g, r_c = %g" %
(pp, g.norm2(e_c), g.norm2(r_c)))
# coarse to fine
t("from_coarser")
bm.promote(psi, e_c)
if self.verbose:
t("output")
g.message("%s done calling c2f: psi = %g, e_c = %g" %
(pp, g.norm2(psi), g.norm2(e_c)))
t("residual")
tmp = g.lattice(src)
mat(tmp, psi)
tmp @= src - tmp
res_cgc = (g.norm2(tmp) / inputnorm)**0.5
# smooth
t("smooth")
g.default.push_verbose(get_slv_name(slv_s), False)
slv_s(mat)(psi, src)
g.default.pop_verbose()
self.history[lvl]["smooth"].append(get_slv_history(slv_s))
t("residual")
mat(tmp, psi)
tmp @= src - tmp
res_smooth = (g.norm2(tmp) / inputnorm)**0.5
if self.verbose:
t("output")
g.message(
"%s done smoothing: input norm = %g, coarse residual = %g, smooth residual = %g"
% (pp, inputnorm, res_cgc, res_smooth))
t()
if self.verbose:
t("output")
g.message("%s ending inversion routine: psi = %g, src = %g" %
(pp, g.norm2(psi), g.norm2(src)))
t()
# define coarse-grid operator
cop = b.coarse_operator(c(w.Mpc))
eps2 = g.norm2(cop * cstart -
b.project * c(w.Mpc) * b.promote * cstart) / g.norm2(cstart)
g.message(f"Test coarse-grid promote/project cycle: {eps2}")
assert eps2 < 1e-13
# coarse-grid lanczos
cevec, cev = irl(cop, cstart)
# smoothened evals
smoother = inv.cg({"eps": 1e-6, "maxiter": 10})(w.Mpc)
smoothed_evals = []
g.default.push_verbose("cg", False)
tmpf = g.lattice(basis[0])
for i, cv in enumerate(cevec):
tmpf @= smoother * b.promote * cv
smoothed_evals = smoothed_evals + g.algorithms.eigen.evals(
w.Mpc, [tmpf], calculate_eps2=False, real=True)
g.default.pop_verbose()
# test coarse-grid deflation (re-use fine-grid evals instead of smoothing)
cdefl = inv.sequence(inv.coarse_deflate(cevec, basis, smoothed_evals), cg)
sol_cdefl = g.eval(cdefl(w.Mpc) * start)
eps2 = g.norm2(w.Mpc * sol_cdefl - start) / g.norm2(start)
niter_cdefl = len(cg.history)
g.message("Test resid/iter coarse-grid deflated cg: ", eps2, niter_cdefl)
g.message("Compare fine-grid deflated cg iter: ", niter_defl)
g.message("Compare cg iter: ", niter_cg)
assert eps == 0.0
# test numpy versus lattice tensor multiplication
for a_type in [
g.ot_matrix_spin_color(4, 3),
g.ot_vector_spin_color(4, 3),
g.ot_matrix_spin(4),
g.ot_vector_spin(4),
g.ot_matrix_color(3),
g.ot_vector_color(3),
]:
# mtab
for e in a_type.mtab:
if a_type.mtab[e][1] is not None:
b_type = g.str_to_otype(e)
a = rng.cnormal(g.lattice(grid, a_type))
b = rng.cnormal(g.lattice(grid, b_type))
mul_lat = g(a * b)[0, 0, 0, 0]
mul_np = a[0, 0, 0, 0] * b[0, 0, 0, 0]
eps2 = g.norm2(mul_lat - mul_np) / g.norm2(mul_lat)
g.message(f"Test {a_type.__name__} * {b_type.__name__}: {eps2}")
if eps2 > 1e-12:
g.message(mul_lat)
g.message(
np.tensordot(a[0, 0, 0, 0].array,
b[0, 0, 0, 0].array,
axes=a_type.mtab[e][1]).shape)
assert eps2 < 1e-12
# rmtab
for e in a_type.rmtab:
def jacobian(self, fields, fields_prime, src):
nd = fields[0].grid.nd
U = fields[0:nd]
U_prime = fields_prime[0:nd]
rho = get_rho(U, self.params)
C = g.qcd.gauge.staple_sum(U, rho=rho)
assert len(src) == nd
dst = [g.lattice(s) for s in src]
exp_iQ = [None] * nd
Lambda = [None] * nd
Sigma_prime = [None] * nd
# (75) of https://arxiv.org/pdf/hep-lat/0311018.pdf
for mu in range(nd):
#
# Sigma == g.adj(U) * gradient * 1j
#
Sigma_prime[mu] = g(g.adj(U_prime[mu]) * src[mu] * 1j)
U_Sigma_prime_mu = g(U[mu] * Sigma_prime[mu])
iQ_mu = g.qcd.gauge.project.traceless_anti_hermitian(C[mu] *
g.adj(U[mu]))
exp_iQ[mu], Lambda[mu] = g.matrix.exp.function_and_gradient(
iQ_mu, U_Sigma_prime_mu)
dst[mu] @= Sigma_prime[mu] * exp_iQ[mu] + g.adj(
C[mu]) * 1j * Lambda[mu]
for mu in range(nd):
for nu in range(nd):
if mu == nu:
continue
rho_mu_nu = rho[mu, nu]
rho_nu_mu = rho[nu, mu]
if abs(rho_nu_mu) != 0.0 or abs(rho_mu_nu) != 0.0:
U_nu_x_plus_mu = g.cshift(U[nu], mu, 1)
U_mu_x_plus_nu = g.cshift(U[mu], nu, 1)
Lambda_nu_x_plus_mu = g.cshift(Lambda[nu], mu, 1)
Lambda_mu_x_plus_nu = g.cshift(Lambda[mu], nu, 1)
dst[mu] -= (1j * rho_nu_mu * U_nu_x_plus_mu *
g.adj(U_mu_x_plus_nu) * g.adj(U[nu]) *
Lambda[nu])
dst[mu] += (1j * rho_nu_mu * Lambda_nu_x_plus_mu *
U_nu_x_plus_mu * g.adj(U_mu_x_plus_nu) *
g.adj(U[nu]))
dst[mu] -= (1j * rho_mu_nu * U_nu_x_plus_mu *
g.adj(U_mu_x_plus_nu) * Lambda_mu_x_plus_nu *
g.adj(U[nu]))
dst[mu] += g.cshift(
1j * rho_nu_mu * g.adj(U_nu_x_plus_mu) * g.adj(U[mu]) *
Lambda[nu] * U[nu] -
1j * rho_mu_nu * g.adj(U_nu_x_plus_mu) * g.adj(U[mu]) *
Lambda[mu] * U[nu] -
1j * rho_nu_mu * g.adj(U_nu_x_plus_mu) *
Lambda_nu_x_plus_mu * g.adj(U[mu]) * U[nu],
nu,
-1,
)
for mu in range(nd):
dst[mu] @= U[mu] * dst[mu] * (-1j)
dst[mu] @= g.qcd.gauge.project.traceless_hermitian(dst[mu])
return dst
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)
#
# Authors: Christoph Lehner 2020
#
import gpt as g
import numpy as np
grid = g.grid([8, 4, 4, 4], g.double)
rng = g.random("test")
dims = ["X", "Y", "Z", "T"]
for lat in [g.mspincolor, g.mspin]:
l = lat(grid)
g.message(lat.__name__)
rng.cnormal(l)
dst = g.lattice(l)
ref = g.lattice(l)
assert g.norm2(l) > 1e-7
for i, d1 in enumerate(dims):
for j, d2 in enumerate(dims):
if i < j:
dst @= g.gamma[d1] * g.gamma[d2] * l
dst -= g.gamma[d2] * g.gamma[d1] * l
dst *= 1 / 2.0
ref @= g.gamma["Sigma%s%s" % (d1, d2)] * l
eps = g.norm2(dst - ref) / g.norm2(l)
g.message("Test Sigma%s%s: " % (d1, d2), eps)
assert eps == 0.0
def read_lattice(self, a):
g_desc = a[0]
cv_desc = a[1]
l_desc = a[2]
filepos = [int(x) for x in a[3:]]
# first find grid
if not g_desc in self.params["grids"]:
self.params["grids"][g_desc] = gpt.grid(g_cesc)
g = self.params["grids"][g_desc]
# create a cartesian view and lattice to load
l = gpt.lattice(g, l_desc)
cv0 = gpt.cartesian_view(-1, cv_desc, g.fdimensions, g.cb,
l.checkerboard())
# find tasks for my node
views_for_node = self.views_for_node(cv0, g)
# performance
dt_distr, dt_crc, dt_read, dt_misc = 0.0, 0.0, 0.0, 0.0
szGB = 0.0
g.barrier()
t0 = gpt.time()
# need to load all views
for xk, iview in enumerate(views_for_node):
g.barrier()
dt_read -= gpt.time()
f, pos = self.open_view(xk, iview, False, cv_desc, g.fdimensions,
g.cb, l.checkerboard())
if not f is None:
f.seek(filepos[iview], 0)
ntag = int.from_bytes(f.read(4), byteorder='little')
f.read(ntag) # not needed if index is present
crc_exp = int.from_bytes(f.read(4), byteorder='little')
nd = int.from_bytes(f.read(4), byteorder='little')
f.read(8 * nd) # not needed if index is present
sz = int.from_bytes(f.read(8), byteorder='little')
data = memoryview(f.read(sz))
dt_crc -= gpt.time()
crc_comp = gpt.crc32(data)
dt_crc += gpt.time()
assert (crc_comp == crc_exp)
sys.stdout.flush()
szGB += len(data) / 1024.**3.
else:
assert (len(pos) == 0)
data = None
g.barrier()
dt_read += gpt.time()
dt_distr -= gpt.time()
l[pos] = data
g.barrier()
dt_distr += gpt.time()
g.barrier()
t1 = gpt.time()
szGB = g.globalsum(szGB)
if self.verbose and dt_crc != 0.0:
gpt.message(
"Read %g GB at %g GB/s (%g GB/s for distribution, %g GB/s for reading + checksum, %g GB/s for checksum, %d views per node)"
% (szGB, szGB / (t1 - t0), szGB / dt_distr, szGB / dt_read,
szGB / dt_crc, len(views_for_node)))
# TODO:
# split grid exposure, allow cgpt_distribute to be given a communicator
# and take it in importexport.h, add debug info here
# more benchmarks, useful to create a plan for cgpt_distribute and cache? immutable numpy array returned from coordinates, attach plan
return l
def lattice(self, otype):
return gpt.lattice(self.local_grid, otype)
def __init__(self, op, parity):
self.op = op
self.otype = op.otype[0]
self.parity = gpt.odd if parity is None else parity
self.F_grid_eo = op.F_grid_eo
self.F_grid = op.F_grid
self.U_grid = op.U_grid
self.tmp = gpt.lattice(self.F_grid_eo, self.otype)
self.tmp2 = gpt.lattice(self.F_grid_eo,
self.otype) # need for nested call in R
self.in_p = gpt.lattice(self.F_grid_eo, self.otype)
self.in_np = gpt.lattice(self.F_grid_eo, self.otype)
self.out_p = gpt.lattice(self.F_grid_eo, self.otype)
self.out_np = gpt.lattice(self.F_grid_eo, self.otype)
self.ImportPhysicalFermionSource = self.op.ImportPhysicalFermionSource
self.ExportPhysicalFermionSolution = self.op.ExportPhysicalFermionSolution
self.Dminus = self.op.Dminus
self.ExportPhysicalFermionSource = self.op.ExportPhysicalFermionSource
def _N(op, ip):
self.op.Meooe.mat(self.tmp2, ip)
self.op.Mooee.inv_mat(op, self.tmp2)
self.op.Meooe.mat(self.tmp2, op)
self.op.Mooee.inv_mat(op, self.tmp2)
op @= ip - op
def _NDag(op, ip):
self.op.Mooee.adj_inv_mat(self.tmp2, ip)
self.op.Meooe.adj_mat(op, self.tmp2)
self.op.Mooee.adj_inv_mat(self.tmp2, op)
self.op.Meooe.adj_mat(op, self.tmp2)
op @= ip - op
def _NDagN(op, ip):
_N(self.tmp, ip)
_NDag(op, self.tmp)
def _L(o, ip):
self.out_p @= ip
self.op.Meooe.mat(self.tmp, ip)
self.op.Mooee.inv_mat(self.out_np, self.tmp)
self.out_np @= -self.out_np
self.export_parity(o)
def _L_pseudo_inverse(op, i):
self.import_parity(i)
op @= self.in_p
def _S(o, i):
self.import_parity(i)
self.op.Mooee.inv_mat(self.out_np, self.in_np)
self.out_p[:] = 0
self.out_p.checkerboard(self.parity)
self.export_parity(o)
self.L = gpt.matrix_operator(
mat=_L,
inv_mat=_L_pseudo_inverse,
otype=op.otype,
grid=(self.F_grid, self.F_grid_eo),
cb=(None, self.parity),
)
self.S = gpt.matrix_operator(
mat=_S,
otype=op.otype,
grid=self.F_grid,
)
self.N = gpt.matrix_operator(mat=_N,
adj_mat=_NDag,
otype=op.otype,
grid=self.F_grid_eo,
cb=self.parity)
self.NDagN = gpt.matrix_operator(
mat=_NDagN,
adj_mat=_NDagN,
otype=op.otype,
grid=self.F_grid_eo,
cb=self.parity,
)
for undressed in ["N", "NDagN"]:
self.__dict__[undressed].split = lambda mpi: eo1_base(
op.split(mpi), parity).__dict__[undressed]
def cartesian(field):
if isinstance(field, list):
return [cartesian(f) for f in field]
return g.lattice(field.grid, field.otype.cartesian()).checkerboard(field.checkerboard())
def __call__(self, mat, src, psi, prec=None):
# verbosity
self.verbose = g.default.is_verbose("fgmres")
checkres = True # for now
# total time
tt0 = time()
# parameters
rlen = self.restartlen
# tensors
dtype = np.complex128
H = np.zeros((rlen + 1, rlen), dtype)
c = np.zeros((rlen + 1), dtype)
s = np.zeros((rlen + 1), dtype)
y = np.zeros((rlen + 1), dtype)
gamma = np.zeros((rlen + 1), dtype)
# fields
mmpsi, r = g.copy(src), g.copy(src),
V = [g.lattice(src) for i in range(rlen + 1)]
if not prec is None: # save vectors if unpreconditioned
Z = [g.lattice(src) for i in range(rlen + 1)]
# residual
ssq = g.norm2(src)
rsq = self.eps**2. * ssq
# initial values
r2 = self.restart(mat, psi, mmpsi, src, r, V, gamma)
for k in range(self.maxiter):
# iteration within current krylov space
i = k % rlen
# iteration criteria
reached_maxiter = (k + 1 == self.maxiter)
need_restart = (i + 1 == rlen)
t0 = time()
if not prec is None:
prec(V[i], Z[i])
t1 = time()
t2 = time()
if not prec is None:
mat(Z[i], V[i + 1])
else:
mat(V[i], V[i + 1])
t3 = time()
t4 = time()
g.orthogonalize(V[i + 1], V[0:i + 1], H[:, i])
t5 = time()
t6 = time()
H[i + 1, i] = g.norm2(V[i + 1])**0.5
if H[i + 1, i] == 0.:
g.message("fgmres breakdown, H[%d, %d] = 0" % (i + 1, i))
break
V[i + 1] /= H[i + 1, i]
t7 = time()
t8 = time()
self.qr_update(s, c, H, gamma, i)
r2 = np.absolute(gamma[i + 1])**2
t9 = time()
if self.verbose:
g.message(
"Timing[s]: Prec = %g, Matrix = %g, Orthog = %g, RestArnoldi = %g, QR = %g"
% (t1 - t0, t3 - t2, t5 - t4, t7 - t6, t9 - t8))
g.message("res^2[ %d, %d ] = %g" % (k, i, r2))
if r2 <= rsq or need_restart or reached_maxiter:
if not prec is None:
self.update_psi(psi, gamma, H, y, Z, i)
else:
self.update_psi(psi, gamma, H, y, V, i)
if r2 <= rsq:
if self.verbose:
tt1 = time()
g.message("Converged in %g s" % (tt1 - tt0))
if checkres:
res = self.calc_res(mat, psi, mmpsi, src, r) / ssq
g.message(
"Computed res = %g, true res = %g, target = %g" %
(r2**0.5, res**0.5, self.eps))
break
if reached_maxiter:
if verbose:
tt1 = time()
g.message("Did NOT converge in %g s" % (tt1 - tt0))
if checkres:
res = self.calc_res(mat, psi, mmpsi, src, r) / ssq
g.message(
"Computed res = %g, true res = %g, target = %g"
% (r2**0.5, res**0.5, self.eps))
if need_restart:
r2 = self.restart(mat, psi, mmpsi, src, r, V, gamma)
if self.verbose:
g.message("Performed restart")
#!/usr/bin/env python3
#
# Authors: Christoph Lehner 2020
#
# Desc.: Illustrate core concepts and features
#
import gpt as g
import numpy as np
# load configuration
rng = g.random("test")
U = g.qcd.gauge.random(g.grid([8, 8, 8, 16], g.double), rng)
V = rng.lie(g.lattice(U[0]))
U_transformed = g.qcd.gauge.transformed(U, V)
# Test gauge invariance of plaquette
P = g.qcd.gauge.plaquette(U)
P_transformed = g.qcd.gauge.plaquette(U_transformed)
eps = abs(P - P_transformed)
g.message(
f"Plaquette before {P} and after {P_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.smear.staple_sum(U, rho=rho)
C_transformed = g.qcd.gauge.smear.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