def _build_objective_functions(self):
"Construct objective function callables for each phase."
for phase_name, phase_obj in self._phases.items():
# Get the symbolic representation of the energy
mod = self._models[phase_name]
undefs = list(mod.ast.atoms(Symbol) - mod.ast.atoms(v.StateVariable))
for undef in undefs:
mod.ast = mod.ast.xreplace({undef: float(0)})
logger.warning('Setting undefined symbol %s for phase %s to zero',
undef, phase_name)
# Construct an ordered list of the variables
self._variables[phase_name], self._sublattice_dof[phase_name] = \
generate_dof(phase_obj, self.components)
molefrac_dict = dict([(x, molefrac_ast(phase_obj, x)) \
for x in self.components if x != 'VA'])
molefrac_jac_dict = dict()
# Generate callables for the mole fractions
for comp in self.components:
if comp == 'VA':
continue
molefrac_jac_dict[comp] = [ \
make_callable(molefrac_dict[comp].diff(vx), \
self._variables[phase_name], \
) for vx in self._variables[phase_name]]
molefrac_dict[comp] = make_callable(molefrac_dict[comp], \
self._variables[phase_name])
# Build the "fast" representation of energy model
subbed_ast = mod.ast.subs(self.statevars)
self._phase_callables[phase_name] = \
make_callable(subbed_ast, \
self._variables[phase_name])
self._gradient_callables[phase_name] = [ \
make_callable(subbed_ast.diff(vx), \
self._variables[phase_name], \
) for vx in self._variables[phase_name]]
self._molefrac_callables[phase_name] = molefrac_dict
self._molefrac_jac_callables[phase_name] = molefrac_jac_dict
def energy_surf(dbf, comps, phases, mode=None, **kwargs):
"""
Sample the energy surface of a system containing the specified
components and phases. Model parameters are taken from 'dbf' and any
state variables (T, P, etc.) can be specified as keyword arguments.
Parameters
----------
dbf : Database
Thermodynamic database containing the relevant parameters.
comps : list
Names of components to consider in the calculation.
phases : list
Names of phases to consider in the calculation.
pdens : int, a dict of phase names to int, or a list of both, optional
Number of points to sample per degree of freedom.
Returns
-------
DataFrame of the energy as a function of composition, temperature, etc.
Examples
--------
None yet.
"""
# Here we check for any keyword arguments that are special, i.e.,
# there may be keyword arguments that aren't state variables
pdens_dict = unpack_kwarg(kwargs.pop('pdens', 2000), default_arg=2000)
model_dict = unpack_kwarg(kwargs.pop('model', Model), default_arg=Model)
# Convert keyword strings to proper state variable objects
# If we don't do this, sympy will get confused during substitution
statevar_dict = \
dict((v.StateVariable(key), value) \
for (key, value) in kwargs.items())
# Generate all combinations of state variables for 'map' calculation
# Wrap single values of state variables in lists
# Use 'kwargs' because we want state variable names to be stringified
statevar_values = [_listify(val) for val in kwargs.values()]
statevars_to_map = [dict(zip(kwargs.keys(), prod)) \
for prod in itertools.product(*statevar_values)]
# Consider only the active phases
active_phases = dict((name.upper(), dbf.phases[name.upper()]) \
for name in phases)
comp_sets = {}
# Construct a list to hold all the data
all_phase_data = []
for phase_name, phase_obj in sorted(active_phases.items()):
# Build the symbolic representation of the energy
mod = model_dict[phase_name]
# if this is an object type, we need to construct it
if isinstance(mod, type):
try:
mod = mod(dbf, comps, phase_name)
except DofError:
# we can't build the specified phase because the
# specified components aren't found in every sublattice
# we'll just skip it
logger.warning("""Suspending specified phase %s due to
some sublattices containing only unspecified components""",
phase_name)
continue
# As a last resort, treat undefined symbols as zero
# But warn the user when we do this
# This is consistent with TC's behavior
undefs = list(mod.ast.atoms(Symbol) - mod.ast.atoms(v.StateVariable))
for undef in undefs:
mod.ast = mod.ast.xreplace({undef: float(0)})
logger.warning('Setting undefined symbol %s for phase %s to zero',
undef, phase_name)
# Construct an ordered list of the variables
variables, sublattice_dof = generate_dof(phase_obj, mod.components)
# Build the "fast" representation of that model
comp_sets[phase_name] = make_callable(mod.ast, \
list(statevar_dict.keys()) + variables, mode=mode)
# Get the site ratios in each sublattice
site_ratios = list(phase_obj.sublattices)
# Eliminate pure vacancy endmembers from the calculation
vacancy_indices = list()
for idx, sublattice in enumerate(phase_obj.constituents):
if 'VA' in sorted(sublattice) and 'VA' in sorted(comps):
vacancy_indices.append(sorted(sublattice).index('VA'))
if len(vacancy_indices) != len(phase_obj.constituents):
vacancy_indices = None
logger.debug('vacancy_indices: %s', vacancy_indices)
# Add all endmembers to guarantee their presence
points = endmember_matrix(sublattice_dof,
vacancy_indices=vacancy_indices)
# Sample composition space for more points
if sum(sublattice_dof) > len(sublattice_dof):
points = np.concatenate((points,
point_sample(sublattice_dof,
pdof=pdens_dict[phase_name])
))
# If there are nontrivial sublattices with vacancies in them,
# generate a set of points where their fraction is zero and renormalize
for idx, sublattice in enumerate(phase_obj.constituents):
if 'VA' in set(sublattice) and len(sublattice) > 1:
var_idx = variables.index(v.SiteFraction(phase_name, idx, 'VA'))
addtl_pts = np.copy(points)
# set vacancy fraction to log-spaced between 1e-10 and 1e-6
addtl_pts[:, var_idx] = np.power(10.0, -10.0*(1.0 - addtl_pts[:, var_idx]))
# renormalize site fractions
cur_idx = 0
for ctx in sublattice_dof:
end_idx = cur_idx + ctx
addtl_pts[:, cur_idx:end_idx] /= \
addtl_pts[:, cur_idx:end_idx].sum(axis=1)[:, None]
cur_idx = end_idx
# add to points matrix
points = np.concatenate((points, addtl_pts), axis=0)
data_dict = {'Phase': phase_name}
# Generate input d.o.f matrix for all state variable combinations
for statevars in statevars_to_map:
# Prefill the state variable arguments to the energy function
energy_func = \
lambda *args: comp_sets[phase_name](
*itertools.chain(list(statevars.values()),
args))
# Get the stable points and energies for this configuration
# Set max refinements equal to the number of independent dof
mxr = sum(phase_obj.sublattices) - len(phase_obj.sublattices)
refined_points, energies = \
refine_energy_surf(points, None, phase_obj, comps,
variables, energy_func, max_iterations=-1)
try:
data_dict['GM'].extend(energies)
for statevar in kwargs.keys():
data_dict[statevar].extend(
list(np.repeat(list(statevars.values()),
len(refined_points))))
except KeyError:
data_dict['GM'] = list(energies)
for statevar in kwargs.keys():
data_dict[statevar] = \
list(np.repeat(list(statevars.values()),
len(refined_points)))
# Map the internal degrees of freedom to global coordinates
# Normalize site ratios
# Normalize by the sum of site ratios times a factor
# related to the site fraction of vacancies
site_ratio_normalization = np.zeros(len(refined_points))
for idx, sublattice in enumerate(phase_obj.constituents):
vacancy_column = np.ones(len(refined_points))
if 'VA' in set(sublattice):
var_idx = variables.index(v.SiteFraction(phase_name, idx, 'VA'))
vacancy_column -= refined_points[:, var_idx]
site_ratio_normalization += site_ratios[idx] * vacancy_column
for comp in sorted(comps):
if comp == 'VA':
continue
avector = [float(cur_var.species == comp) * \
site_ratios[cur_var.sublattice_index] for cur_var in variables]
try:
data_dict['X('+comp+')'].extend(list(np.divide(np.dot(
refined_points[:, :], avector), site_ratio_normalization)))
except KeyError:
data_dict['X('+comp+')'] = list(np.divide(np.dot(
refined_points[:, :], avector), site_ratio_normalization))
# Copy coordinate information into data_dict
# TODO: Is there a more memory-efficient way to deal with this?
# Perhaps with hierarchical indexing...
try:
for column_idx, data in enumerate(refined_points.T):
data_dict[str(variables[column_idx])].extend(list(data))
except KeyError:
for column_idx, data in enumerate(refined_points.T):
data_dict[str(variables[column_idx])] = list(data)
all_phase_data.append(pd.DataFrame(data_dict))
# all_phases_data now contains energy surface information for the system
return pd.concat(all_phase_data, axis=0, join='outer', \
ignore_index=True, verify_integrity=False)