def check_domain():
""" Check sensible subdomain strategy """
if len(boundaries) != Ns + 1 or len(bins) != Ns or len(rules) != Ns:
error(this_file, "Mismatch between number of subdomains and number of boundaries/bins/rules. \nMake sure there are Ns + 1 boundaries, Ns bins and Ns rules in params.py!")
for i in range(len(boundaries)-1):
if boundaries[i+1] <= boundaries[i]:
error(this_file, "Mu boundaries do not increase monotonically from left to right.")
# These are center-of-bin values
mu_s_cross = dom.get_local_mu_bins(dom.s_cross)
# Want a bin centered on mu=0
mu_hi = mu_s_cross[dom.i_cross]
mu_lo = mu_s_cross[dom.i_cross - 1]
# If we've failed to get a bin centered on mu=0
if np.allclose(mu_hi,0.0) == False: # rtol=1e-5, atol=1e-8
print "Error:", this_file
print "mu = 0 falls into a bin centered on mu = %1.8f, rather than 0." %mu_hi
bound_hi = boundaries[dom.s_cross + 1]
bound_lo = boundaries[dom.s_cross]
rnd_bin_width = np.around(dom.subdom[dom.s_cross]['bin_width'],decimals=10)
hbw = 0.5*rnd_bin_width
bins_lo = dom.i_cross - dom.subdom[dom.s_cross]['l_bin_olap']
bins_hi = bins[dom.s_cross] - bins_lo
prop_bound_hi = bins_hi * rnd_bin_width
prop_bound_lo = bins_lo * rnd_bin_width * -1
print "Try %.10f --> %.10f, %.10f --> %.10f" \
%(bound_lo,prop_bound_lo+hbw,bound_hi,prop_bound_hi+hbw)
print "Or %.10f --> %.10f, %.10f --> %.10f" \
%(bound_lo,prop_bound_lo-hbw,bound_hi,prop_bound_hi-hbw)
print "Or change the number of bins and try again."
exit(1)
print "Subdomain strategy OK."
return
##############################
## Set up fine-grained grid ##
##############################
""" Sets up 'windows' centered on each regular bin, containing 'mini-bins'.
This allows more precise measurement of local transition probabilities,
while keeping relatively thick bins for everything else. """
# ------------------------- #
# Iterate over subdomains #
# ------------------------- #
subdom = []
for s in range(Ns):
# These are the centres of the windows
mu_bins = dom.get_local_mu_bins(s)
# Widths in terms of mu
minibin_width = dom.subdom[s]['bin_width'] / float(minibins_per_bin)
window_width = minibin_width * minibins_per_window
# Dictionary of info for this subdomain, including a list of dictionaries
# containing info about individual windows
windows = {
'mbin_width': minibin_width,
'win_width': window_width,
'win_info': []
}
# ---------------------------------- #
# Iterate over regular bin indices #
def run(atoms_alpha,
atoms_beta,
disp,
binned_data,
dyn_data,
p,
s,
F=1,
relax=False):
# ------------------------------------------------- #
# Set simulation parameters and useful quantities #
# ------------------------------------------------- #
lendata = len(binned_data['w']) # length of weights
kTlogF = kT * np.log(F)
# Convert frequency parameters from sweeps to steps
if relax == True:
Nsteps = sweeps_relax * Natoms
else:
Nsteps = alg.Nsteps
save_step = sweeps_save * Natoms
series_step = int(sweeps_series * Natoms)
recalc_step = sweeps_recalc * Natoms
refresh_step = sweeps_refresh * Natoms
# Set boundaries for this simulation
if TRAP == True: # restrict to subdomain 's'; local bin indices
global_mu_min = dom.subdom[s]['min']
global_mu_max = dom.subdom[s]['max']
get_index = dom.get_local_index
mu_bins = dom.get_local_mu_bins(s)
else: # can access entire domain; global bin indices
global_mu_min = boundaries[0]
global_mu_max = boundaries[-1]
get_index = dom.get_global_index
mu_bins = dom.get_global_mu_bins()
# Set weights function
if use_interpolated_weights == True:
get_weight = interpolated_weight
# Need to add bins to the edges of mu and weights for extrapolation
mu_bins = np.concatenate((mu_bins, [0, 0]))
extrapolate(mu_bins)
binned_data['w'] = np.concatenate((binned_data['w'], [0, 0]))
extrapolate(binned_data['w'])
# Need to do the same for cuts since it uses mu_bins
if track_dynamics == True:
dyn_data['cu'] = np.concatenate((dyn_data['cu'], [0, 0]))
else:
get_weight = discrete_weight
# ------------------------ #
# Initialise usual stuff #
# ------------------------ #
# Get initial lattice energies and difference between them
old_E_alpha, old_E_beta = lattice_energies(atoms_alpha, atoms_beta)
old_mu = old_E_alpha - old_E_beta
new_mu = old_mu
# For a global simulation, the initial subdomain (corresponding to the
# input disp vector) needs to be computed
if TRAP != True:
s = dom.get_subdomain(old_mu)
# Initial index and weight
old_index = get_index(old_mu, s)
old_weight = get_weight(old_mu, old_index, mu_bins, binned_data['w'])
# Active lattice
if s < dom.s_cross: # start with lattice alpha(1) active
ACT = 1
elif s > dom.s_cross: # start with lattice beta(-1) active
ACT = -1
else: # randomise
ACT = np.random.choice([-1, 1])
# Flag for histogram flatness
FLAT = 1 # start with 1 < f if wang-landau, otherwise f = 1 = FLAT
# Initialise counters
step = 1
moves = 0
retakes = 0
switches = 0
# ---------------------------- #
# Initialise 'dynamics' info #
# ---------------------------- #
if track_dynamics == True:
cuts = {'counter': 0, 'old_mu': old_mu, 'new_mu': old_mu}
if TRAP == True:
rt_min = 0
rt_max = lendata - 1
else:
rt_min = np.argmax(binned_data['w'][mu_bins < 0])
rt_max = np.argmax(binned_data['w'][mu_bins > 0]) + len(
mu_bins[mu_bins < 0])
rtrips = {
'minmax': (0, rt_min, rt_max),
'counts': 0,
'flag': int(dyn_data['rt'][4])
}
# Mini transition matrix only works for TRAP == True (due to indexing)
if TRAP == True:
minimat = {
'counter': 0,
'root_index': old_index,
'old_index': dyn.get_minibin_index(old_mu, s, old_index),
'Pprod': 1
}
# --------------------------- #
# Open file for data series #
# --------------------------- #
if track_series == True:
series_file = alg.file_names('output', s, p)['s']
series = open(series_file, 'a')
# ------------------------------------------------------------ #
# Main loop over individual particle moves + switch attempts #
# ------------------------------------------------------------ #
while FLAT < F or step <= Nsteps: # Flat condition only relevant for Wang Landau
# Refresh weights with eigenvector of transition matrix (TM only)
if step % refresh_step == 0:
alg.refresh_func(binned_data)
# Write values from this step to the series file. Note high precision needed for mu
if track_series == True:
if step % series_step == 0:
E_active = (0, old_E_alpha, old_E_beta)[ACT]
series.write("%d %.10f %f %f \n" \
%(s, old_mu, old_weight, E_active) )
# --------------------------------------------------- #
# Move a single particle and compute energy changes #
# --------------------------------------------------- #
# Pick a random particle
ipart = np.random.randint(0, Natoms)
# Calculate old local energies for the two lattices before trial move
old_local_energies = local_energy(atoms_alpha, atoms_beta, ipart)
# Pick a random displacement and update lattice positions
dr = (np.random.random(3) * 2.0 - 1.0) * dr_max
dr_alpha = np.dot(dr, atoms_alpha.get_cell())
dr_beta = np.dot(dr, atoms_beta.get_cell())
atoms_alpha.positions[ipart, :] += dr_alpha
atoms_beta.positions[ipart, :] += dr_beta
# Calculate new local energies after trial move
new_local_energies = local_energy(atoms_alpha, atoms_beta, ipart)
# Calculate energy difference
delta_local_energies = new_local_energies - old_local_energies
# New energy difference between lattices
if step % recalc_step == 1: # full calculation
new_E_alpha, new_E_beta = lattice_energies(atoms_alpha, atoms_beta)
# Sanity check - don't want to be below ideal lattice energy!
if new_E_alpha < E_ideal or new_E_beta < E_ideal:
error(this_file,
"Oh no! Energy is less than that of an Ideal lattice.")
else: # update with local energy difference
new_E_alpha = old_E_alpha + delta_local_energies[1]
new_E_beta = old_E_beta + delta_local_energies[-1]
new_mu = new_E_alpha - new_E_beta
# ---------------- #
# Switch attempt #
# ---------------- #
# Attempt a switch here 50% of the time - before any move evaluation
coin = coinflip()
ACT, switches = ((ACT, switches),
attempt_switch(new_mu, ACT, switches))[coin]
# --------------------------------------- #
# Check if boundaries have been crossed #
# --------------------------------------- #
# 'Global' boundaries are those that the simulation may not cross
if new_mu < global_mu_min or new_mu > global_mu_max:
# Update the bin from which the move was attempted
old_weight, FLAT = alg.update_func(
step,
binned_data,
delta_local_energies[ACT],
old_index,
old_index,
old_index, # only update edge bin
old_mu,
mu_bins,
old_weight,
get_weight,
lendata,
kTlogF,
s)
if track_dynamics == True:
# Update data on simulation dynamics / mobility
dyn.update_func(dyn_data, mu_bins, old_mu, old_index, s, cuts,
rtrips, False, abs(new_mu - old_mu),
abs(delta_local_energies[ACT]))
if TRAP == True:
dyn.update_minimat(dyn_data, mu_bins, old_mu, old_index, s,
minimat, True, 0)
# Undo lattice positions update
atoms_alpha.positions[ipart, :] -= dr_alpha
atoms_beta.positions[ipart, :] -= dr_beta
retakes += 1
step += 1
# Go back to the start of the while loop
continue
# Check if subdomain boundary crossed
old_s = s
if new_mu < dom.subdom[s]['min']:
s -= 1
elif new_mu > dom.subdom[s]['max']:
s += 1
# ---------------------- #
# Evaluate move result #
# ---------------------- #
# Get index for arrays using mu
new_index = get_index(new_mu, s)
# Difference in weights augments delta_local_energy
new_weight = get_weight(new_mu, new_index, mu_bins, binned_data['w'])
augment = new_weight - old_weight
# Accept/reject trial move with weighted energy difference
expnt = -B * (delta_local_energies[ACT] + augment)
accepted = accept_move(expnt)
""" #Difference between bin-averaged weight and interpolated
intra_bin_weight = old_weight - weights[old_index]
#sampling_adjust = np.exp( B*intra_bin_weight ) # doesn't work: centre of bins?"""
old_index_copy = old_index # to update Cmat and extra info after move evaluation
dmu = abs(new_mu - old_mu) # to update dynamics
# Update things according to whether move accepted
if accepted == True:
disp[ipart, :] += dr
old_E_alpha = new_E_alpha
old_E_beta = new_E_beta
old_index = new_index
old_weight = new_weight
old_mu = new_mu
moves += 1
cuts_new_mu = new_mu
else:
atoms_alpha.positions[ipart, :] -= dr_alpha
atoms_beta.positions[ipart, :] -= dr_beta
s = old_s # Account for possible subdomain change
cuts_new_mu = old_mu
# ------------------------ #
# Update bin information #
# ------------------------ #
old_weight, FLAT = alg.update_func(step, binned_data,
delta_local_energies[ACT],
new_index, old_index,
old_index_copy, old_mu, mu_bins,
old_weight, get_weight, lendata,
kTlogF, s)
# ------------------------------------ #
# Update data on simulation dynamics #
# ------------------------------------ #
if track_dynamics == True:
# Update data on simulation dynamics / mobility
cuts['new_mu'] = cuts_new_mu
dyn.update_func(dyn_data, mu_bins, old_mu, old_index, s, cuts,
rtrips, accepted, dmu,
abs(delta_local_energies[ACT]))
if TRAP == True:
dyn.update_minimat(dyn_data, mu_bins, old_mu, old_index, s,
minimat, accepted, expnt)
# ---------------- #
# Switch attempt #
# ---------------- #
# 50/50 chance of attempting a switch after the move
ACT, switches = (attempt_switch(old_mu, ACT,
switches), (ACT, switches))[coin]
# ------------------- #
# Save periodically #
# ------------------- #
if step % save_step == 0:
alg.save_func(binned_data, mu_bins, step, s, p)
# Take this opportunity to reset centre of mass
atoms_alpha.positions = atoms_alpha.positions - atoms_alpha.get_center_of_mass(
)
atoms_beta.positions = atoms_beta.positions - atoms_beta.get_center_of_mass(
)
step += 1
# End main loop
print "- Steps: ", step
print "- Moves: ", moves
print "- Retakes: ", retakes
print "- Switches: ", switches
# --------------------------------------------- #
# Finalise things before returning to main.py #
# --------------------------------------------- #
# Close series file
if track_series == True:
series.close()
if track_dynamics == True:
# Round trip output file
dyn_data['rt'][0] += step
dyn_data['rt'][1] += switches
dyn_data['rt'][2] += rtrips['counts'] # half round trips
rt_rate = float(0.5 * dyn_data['rt'][2] *
Natoms) / dyn_data['rt'][0] # rtrips per sweep
dyn_data['rt'][3] = 1.0 / rt_rate # sweeps per rtrip
dyn_data['rt'][4] = rtrips['flag'] # to be picked up by next iteration
# Compute eigenvector and refresh weights
alg.refresh_func(binned_data)
# If interpolated weights used, remove those extrapolated bins / 'ghost points'
if len(binned_data['w']) != len(binned_data['h']):
binned_data['w'] = binned_data['w'][:-2]
if track_dynamics == True:
dyn_data['cu'] = dyn_data['cu'][:-2]
# Only care about difference in weights, set minimum to zero
binned_data['w'] -= np.min(binned_data['w'])
return step
input_files = alg.file_names('output', s, p)
extra_input_files = dyn.file_names('output', s, p)
# Load input files
this_hist = np.loadtxt(input_files['h'])
this_cuts = np.loadtxt(extra_input_files['cu'])
# Add to combined
hist = hist + this_hist
cuts = cuts + this_cuts
if TRAP == True:
# Scale by bin width
cuts = cuts * dom.subdom[s]['bin_width']
# Load mu subdomain
mu_bins = dom.get_local_mu_bins(s) * B / float(Natoms)
else:
# Scale global data by bin widths for each subdomain
bin_low = 0
bin_high = 0
for ss in range(Ns):
bin_high += bins[ss]
cuts[bin_low:bin_high] = cuts[bin_low:bin_high] * dom.subdom[ss]['bin_width']
bin_low = bin_high
# Formula given in Tian et a. (2014), though coefficient is arbitrary in this case
cuts = 0.5*cuts
diffusivity = np.pi / dyn.cuts_step * (cuts**2) / (hist**2)
# The edge bins are not well estimated with the cuts method implemented
diffusivity[0] = diffusivity[1] + 0.25*(diffusivity[1] - diffusivity[4])
error(this_file, "No file name found in list of argument variables.")
# Load data
input_data = np.loadtxt(input_file[1]) # index 0 is the plot script itself
# Extract subdomain index if provided as argument variable
# This will be the first int given in the argv list
s = [v for v in argv if v.isdigit()]
# If no subdomain given as argument variable, plot global data
if len(s) == 0:
mu_bins = dom.get_global_mu_bins() * B / float(Natoms)
s = 'all'
else:
s = s[0]
mu_bins = dom.get_local_mu_bins(int(s)) * B / float(Natoms)
# Check data and mu are the same size
if len(input_data) != len(mu_bins):
error(this_file, "Length of input data does not match number of mu bins in subdomain: "+s)
# Plot parameters
plt.rc('text',usetex=True)
font = {'family' : 'serif',
'size' : 14}
plt.rc('font', **font)
plt.rcParams['axes.linewidth'] = 2
# Create plot
fig, ax = plt.subplots()