def test_anapot_lanczos():
geom = AnaPot.get_geom((-0.5767, 1.6810, 0.))
guess = (0.4, 0.3, 0.0)
w_min, v_min = geom_lanczos(geom, guess=guess, dx=1e-5, dl=1e-5, logger=logger)
H = geom.hessian
w, v = np.linalg.eigh(H)
w_ref = w[0]
v_ref = v[:,0]
assert w_min == pytest.approx(w_ref, abs=1e-4)
assert any([np.allclose(v, v_ref, atol=5e-2) for v in (v_min, -v_min)])
def test_hcn_iso_lanczos(coord_type, guess):
geom = geom_loader("lib:hcn_iso_hf_sto3g_ts_opt.xyz", coord_type=coord_type)
calc = PySCF(pal=2, basis="sto3g")
geom.set_calculator(calc)
w_min, v_min = geom_lanczos(geom, guess=guess, logger=logger)
# Reference values
H = geom.hessian
w, v = np.linalg.eigh(H)
w_ref = w[0]
v_ref = v[:,0]
assert w_min == pytest.approx(w_ref, abs=1e-2)
assert any([np.allclose(v, v_ref, atol=5e-2) for v in (v_min, -v_min)])
def get_tangent(self, i, kind="upwinding", lanczos_guess=None):
""" [1] Equations (8) - (11)"""
tangent_kinds = ("upwinding", "simple", "bisect", "lanczos")
assert kind in tangent_kinds, \
"Invalid kind! Valid kinds are: {tangent_kinds}"
prev_index = max(i - 1, 0)
next_index = min(i + 1, len(self.images) - 1)
prev_image = self.images[prev_index]
ith_image = self.images[i]
next_image = self.images[next_index]
# If (i == 0) or (i == len(self.images)-1) then one
# of this tangents is zero.
tangent_plus = next_image - ith_image
tangent_minus = ith_image - prev_image
# Handle first and last image
if i == 0:
return tangent_plus / np.linalg.norm(tangent_plus)
elif i == (len(self.images) - 1):
return tangent_minus / np.linalg.norm(tangent_minus)
# [1], Eq. (1)
if kind == "simple":
tangent = next_image - prev_image
# [1], Eq. (2)
elif kind == "bisect":
first_term = tangent_minus / np.linalg.norm(tangent_minus)
sec_term = tangent_plus / np.linalg.norm(tangent_plus)
tangent = first_term + sec_term
# Upwinding tangent from [1] Eq. (8) and so on
elif kind == "upwinding":
prev_energy = prev_image.energy
ith_energy = ith_image.energy
next_energy = next_image.energy
next_energy_diff = abs(next_energy - ith_energy)
prev_energy_diff = abs(prev_energy - ith_energy)
delta_energy_max = max(next_energy_diff, prev_energy_diff)
delta_energy_min = min(next_energy_diff, prev_energy_diff)
# Uphill
if next_energy > ith_energy > prev_energy:
tangent = tangent_plus
# Downhill
elif next_energy < ith_energy < prev_energy:
tangent = tangent_minus
# Minimum or Maximum
else:
if next_energy >= prev_energy:
tangent = (tangent_plus * delta_energy_max +
tangent_minus * delta_energy_min)
# next_energy < prev_energy
else:
tangent = (tangent_plus * delta_energy_min +
tangent_minus * delta_energy_max)
elif kind == "lanczos":
# Calculating a lanczos tangent is costly, so we store the
# tangent in a dictionary. The current coordinates are
# stringified with precision=4 and then hashed. The tangent
# is stored/looked up with this hash.
cur_hash = hash_arr(ith_image.coords, precision=4)
try:
tangent = self.lanczos_tangents[cur_hash]
self.log(
"Returning previously calculated Lanczos tangent with "
f"hash={cur_hash}")
except KeyError:
# Try to use previous Lanczos tangent
guess = lanczos_guess
if (guess is None) and (self.prev_lanczos_hash is not None):
guess = self.lanczos_tangents[self.prev_lanczos_hash]
self.log(
f"Using tangent with hash={self.prev_lanczos_hash} "
"as initial guess for Lanczos algorithm.")
w_min, tangent = geom_lanczos(ith_image,
guess=guess,
logger=self.logger)
self.lanczos_tangents[cur_hash] = tangent
# Update hash
self.prev_lanczos_hash = cur_hash
tangent /= np.linalg.norm(tangent)
return tangent