def test_bfgs_multiply_empty_lists():
size = 10
s_list = list()
y_list = list()
forces = np.ones(size)
Hf = bfgs_multiply(s_list, y_list, forces)
np.testing.assert_allclose(Hf, forces)
def optimize(self):
prev_coords = self.coords[-1]
prev_forces = self.forces[-1]
step = bfgs_multiply(self.sigmas, self.grad_diffs, prev_forces)
step = self.scale_by_max_step(step)
new_coords = prev_coords + self.alpha * step
coords_tmp = prev_coords.copy()
forces_tmp = prev_forces.copy()
self.geometry.coords = new_coords
if self.is_cos and self.align:
rot_vecs, rot_vec_lists, _ = fit_rigid(
self.geometry, (prev_coords, prev_forces),
vector_lists=(self.sigmas, self.grad_diffs))
prev_coords, prev_forces = rot_vecs
# self.sigmas, self.grad_diffs = rot_vec_lists
rot_sigmas, rot_grad_diffs = rot_vec_lists
# if sigs:
# import pdb; pdb.set_trace()
np.testing.assert_allclose(np.linalg.norm(rot_sigmas),
np.linalg.norm(self.sigmas))
np.testing.assert_allclose(np.linalg.norm(rot_grad_diffs),
np.linalg.norm(self.grad_diffs))
self.sigmas = rot_sigmas
self.grad_diffs = rot_grad_diffs
new_forces = self.geometry.forces
new_energy = self.geometry.energy
skip = self.backtrack(new_forces, prev_forces)
print("alpha", self.alpha)
if skip:
self.geometry.coords = coords_tmp
return None
sigma = new_coords - prev_coords
self.sigmas.append(sigma)
grad_diff = prev_forces - new_forces
self.grad_diffs.append(grad_diff)
# if len(self.sigmas) == self.keep_last:
# import pdb; pdb.set_trace()
self.sigmas = self.sigmas[-self.keep_last:]
self.grad_diffs = self.grad_diffs[-self.keep_last:]
# Because we add the step later on we restore the original
# coordinates and set the appropriate energies and forces.
self.geometry.coords = prev_coords
self.geometry.forces = new_forces
self.geometry.energy = new_energy
self.forces.append(new_forces)
self.energies.append(new_energy)
return step
def optimize(self):
forces = self.geometry.forces
energy = self.geometry.energy
self.forces.append(forces)
self.energies.append(energy)
norm = np.linalg.norm(forces)
if not self.is_cos:
self.log(f"Current energy={energy:.6f}")
self.log(f"norm(forces)={norm:.6f}")
# Steepest descent fallback
step = forces
# Check for preconditioner update
if (self.precon_update and self.cur_cycle > 0
and self.cur_cycle % self.precon_update == 0):
self.precon_getter = precon_getter(self.geometry,
c_stab=self.c_stab)
# Construct preconditoner if requested
P = None
if self.precon:
P = self.precon_getter(self.geometry.coords)
self.log("Calculated new preconditioner P")
step = spsolve(P, forces)
if self.cur_cycle > 0:
self.grad_diffs.append(-forces - -self.forces[-2])
self.steps_.append(self.steps[-1])
step = bfgs_multiply(self.steps_, self.grad_diffs, forces, P=P)
step_dir = step / np.linalg.norm(step)
if self.line_search_cls is not None:
kwargs = {
"geometry": self.geometry,
"p": step_dir,
"f0": energy,
"g0": -forces,
"alpha_init": self.alpha_init,
}
line_search = self.line_search_cls(**kwargs)
line_search_result = line_search.run()
alpha = line_search_result.alpha
step = alpha * step_dir
else:
max_element = np.abs(step).max()
if max_element > self.max_step_element:
step *= self.max_step_element / max_element
return step
def optimize(self):
if self.is_cos and self.align:
rot_vecs, rot_vec_lists, _ = fit_rigid(
self.geometry,
vector_lists=(self.steps, self.forces, self.coord_diffs,
self.grad_diffs))
rot_steps, rot_forces, rot_coord_diffs, rot_grad_diffs = rot_vec_lists
self.steps = rot_steps
self.forces = rot_forces
self.coord_diffs = rot_coord_diffs
self.grad_diffs = rot_grad_diffs
forces = self.geometry.forces
self.forces.append(forces)
energy = self.geometry.energy
self.energies.append(energy)
norm = np.linalg.norm(forces)
self.log(f"norm(forces)={norm:.6f}")
if self.cur_cycle > 0:
y = self.forces[-2] - forces
s = self.steps[-1]
if self.double_damp:
s, y = double_damp(s,
y,
s_list=self.coord_diffs,
y_list=self.grad_diffs)
self.grad_diffs.append(y)
self.coord_diffs.append(s)
# Drop superfluous oldest vectors
self.coord_diffs = self.coord_diffs[-self.keep_last:]
self.grad_diffs = self.grad_diffs[-self.keep_last:]
step = bfgs_multiply(self.coord_diffs,
self.grad_diffs,
forces,
beta=self.beta,
gamma_mult=self.gamma_mult,
logger=self.logger)
step = scale_by_max_step(step, self.max_step)
return step
def double_damp(s,
y,
H=None,
s_list=None,
y_list=None,
mu_1=0.2,
mu_2=0.2,
logger=None):
"""Double damped step 's' and gradient differences 'y'.
H is the inverse Hessian!
See [6]. Potentially updates s and y. y is only
updated if mu_2 is not None.
Parameters
----------
s : np.array, shape (N, ), floats
Coordiante differences/step.
y : np.array, shape (N, ), floats
Gradient differences
H : np.array, shape (N, N), floats, optional
Inverse Hessian.
s_list : list of nd.array, shape (K, N), optional
List of K previous steps. If no H is supplied and prev_ys is given
the matrix-vector product Hy will be calculated through the
two-loop LBFGS-recursion.
y_list : list of nd.array, shape (K, N), optional
List of K previous gradient differences. See s_list.
mu_1 : float, optional
Parameter for 's' damping.
mu_2 : float, optional
Parameter for 'y' damping.
logger : logging.Logger, optional
Logger to be used.
Returns
-------
s : np.array, shape (N, ), floats
Damped coordiante differences/step.
y : np.array, shape (N, ), floats
Damped gradient differences
"""
sy = s.dot(y)
# Calculate Hy directly
if H is not None:
Hy = H.dot(y)
# Calculate Hy via BFGS_multiply as in LBFGS
else:
Hy = bfgs_multiply(s_list, y_list, y, logger=logger)
yHy = y.dot(Hy)
theta_1 = 1
damped_s = ""
if sy < mu_1 * yHy:
theta_1 = (1 - mu_1) * yHy / (yHy - sy)
s = theta_1 * s + (1 - theta_1) * Hy
if theta_1 < 1.:
damped_s = ", damped s"
msg = f"damped BFGS\n\ttheta_1={theta_1:.4f} {damped_s}"
# Double damping
damped_y = ""
if mu_2 is not None:
sy = s.dot(y)
ss = s.dot(s)
theta_2 = 1
if sy < mu_2 * ss:
theta_2 = (1 - mu_2) * ss / (ss - sy)
y = theta_2 * y + (1 - theta_2) * s
if theta_2 < 1.:
damped_y = ", damped y"
msg = "double " + msg + f"\n\ttheta_2={theta_2:.4f} {damped_y}"
if logger is not None:
logger.debug(msg.capitalize())
return s, y
def optimize(self):
new_image_inds = self.geometry.new_image_inds
string_size_changed = len(new_image_inds) > 0
if self.align and string_size_changed and self.is_cart_opt:
procrustes(self.geometry)
self.log("Aligned string.")
forces = self.geometry.forces
self.energies.append(self.geometry.energy)
self.forces.append(forces)
cur_size = self.geometry.string_size
add_to_list = (
self.keep_last >
0 # Only add to s_list and y_list if we want to keep
and self.cur_cycle >
0 # cycles and if we can actually calculate differences.
and
(not self.
lbfgs_when_full # Add when LBFGS is allowed before fully grown.
or self.lbfgs_when_full and self.geometry.fully_grown and
not string_size_changed # Don't add when string has to be fully grown
# but grew fully in this cycle.
))
if add_to_list:
inds = list(range(cur_size))
try:
y = self.forces[-2] - forces
s = self.coords[-1] - self.coords[-2]
# Will be raised when the string grew in the previous cycle.
except ValueError:
cur_forces = np.delete(forces.reshape(cur_size, -1),
new_image_inds,
axis=0).flatten()
y = self.forces[-2] - cur_forces
cur_coords = np.delete(self.coords[-1].reshape(cur_size, -1),
new_image_inds,
axis=0).flatten()
s = self.coords[-2] - cur_coords
inds = np.delete(inds, new_image_inds)
if self.double_damp:
s, y = double_damp(s,
y,
s_list=self.s_list,
y_list=self.y_list)
self.s_list.append(s)
self.y_list.append(y)
self.inds.append(inds)
# Drop oldest vectors
self.s_list = self.s_list[-self.keep_last:]
self.y_list = self.y_list[-self.keep_last:]
self.inds = self.inds[-self.keep_last:]
# Results in steepest descent step for empty s_list & y_list
step = bfgs_multiply(self.s_list,
self.y_list,
forces,
gamma_mult=self.gamma_mult,
inds=self.inds,
cur_size=cur_size,
logger=self.logger)
# When keep_last == 0 or LBFGS is not yet enabled then s_list and y_list will
# be empty and step will be a simple SD step. We try to improve it via CG.
if ((self.keep_last == 0 and self.cur_cycle > 0
and not string_size_changed)
and (len(self.s_list) == 0 and len(self.y_list) == 0)):
prev_forces = self.forces[-2]
# Fletcher-Reeves
beta = forces.dot(forces) / prev_forces.dot(prev_forces)
# Polar-Ribiere
# beta = forces.dot(forces - prev_forces) / prev_forces.dot(prev_forces)
beta = min(beta, 1)
step = forces + beta * self.steps[-1]
self.log(f"Conjugate gradient correction, β={beta:.6f}")
if self.scale_step == "global":
step = scale_by_max_step(step, self.max_step)
elif self.scale_step == "per_image":
for image_step in step.reshape(len(self.geometry.images), -1):
scale_by_max_step(image_step, self.max_step)
else:
raise Exception("Invalid scale_step={self.scale_step}!")
return step