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 calculate(dbf,
comps,
phases,
mode=None,
output='GM',
fake_points=False,
**kwargs):
"""
Sample the property surface of 'output' 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 : str or sequence
Names of components to consider in the calculation.
phases : str or sequence
Names of phases to consider in the calculation.
mode : string, optional
See 'make_callable' docstring for details.
output : string, optional
Model attribute to sample.
fake_points : bool, optional (Default: False)
If True, the first few points of the output surface will be fictitious
points used to define an equilibrium hyperplane guaranteed to be above
all the other points. This is used for convex hull computations.
points : ndarray or a dict of phase names to ndarray, optional
Columns of ndarrays must be internal degrees of freedom (site fractions), sorted.
If this is not specified, points will be generated automatically.
pdens : int, a dict of phase names to int, or a seq of both, optional
Number of points to sample per degree of freedom.
model : Model, a dict of phase names to Model, or a seq of both, optional
Model class to use for each phase.
Returns
-------
xray.Dataset of the sampled attribute as a function of state variables
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)
points_dict = unpack_kwarg(kwargs.pop('points', None), default_arg=None)
model_dict = unpack_kwarg(kwargs.pop('model', Model), default_arg=Model)
callable_dict = unpack_kwarg(kwargs.pop('callables', None),
default_arg=None)
if isinstance(phases, str):
phases = [phases]
if isinstance(comps, str):
comps = [comps]
components = [x for x in sorted(comps) if not x.startswith('VA')]
# Convert keyword strings to proper state variable objects
# If we don't do this, sympy will get confused during substitution
statevar_dict = collections.OrderedDict((v.StateVariable(key), unpack_condition(value)) \
for (key, value) in sorted(kwargs.items()))
str_statevar_dict = collections.OrderedDict((str(key), unpack_condition(value)) \
for (key, value) in statevar_dict.items())
all_phase_data = []
comp_sets = {}
largest_energy = -np.inf
maximum_internal_dof = 0
# Consider only the active phases
active_phases = dict((name.upper(), dbf.phases[name.upper()]) \
for name in unpack_phases(phases))
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:
model_dict[phase_name] = 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
if points_dict[phase_name] is None:
try:
out = getattr(mod, output)
maximum_internal_dof = max(maximum_internal_dof,
len(out.atoms(v.SiteFraction)))
except AttributeError:
raise AttributeError(
'Missing Model attribute {0} specified for {1}'.format(
output, mod.__class__))
else:
maximum_internal_dof = max(
maximum_internal_dof,
np.asarray(points_dict[phase_name]).shape[-1])
for phase_name, phase_obj in sorted(active_phases.items()):
try:
mod = model_dict[phase_name]
except KeyError:
continue
# Construct an ordered list of the variables
variables, sublattice_dof = generate_dof(phase_obj, mod.components)
# Build the "fast" representation of that model
if callable_dict[phase_name] is None:
out = getattr(mod, output)
# 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(out.atoms(Symbol) - out.atoms(v.StateVariable))
for undef in undefs:
out = out.xreplace({undef: float(0)})
logger.warning(
'Setting undefined symbol %s for phase %s to zero', undef,
phase_name)
comp_sets[phase_name] = make_callable(out, \
list(statevar_dict.keys()) + variables, mode=mode)
else:
comp_sets[phase_name] = callable_dict[phase_name]
points = points_dict[phase_name]
if points is None:
# Eliminate pure vacancy endmembers from the calculation
vacancy_indices = list()
for idx, sublattice in enumerate(phase_obj.constituents):
active_in_subl = sorted(
set(phase_obj.constituents[idx]).intersection(comps))
if 'VA' in active_in_subl and 'VA' in sorted(comps):
vacancy_indices.append(active_in_subl.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)
# Filter out nan's that may have slipped in if we sampled too high a vacancy concentration
# Issues with this appear to be platform-dependent
points = points[~np.isnan(points).any(axis=-1)]
# Ensure that points has the correct dimensions and dtype
points = np.atleast_2d(np.asarray(points, dtype=np.float))
phase_ds = _compute_phase_values(phase_obj, components, variables,
str_statevar_dict, points,
comp_sets[phase_name], output,
maximum_internal_dof)
# largest_energy is really only relevant if fake_points is set
if fake_points:
largest_energy = max(phase_ds[output].max(), largest_energy)
all_phase_data.append(phase_ds)
if fake_points:
if output != 'GM':
raise ValueError(
'fake_points=True should only be used with output=\'GM\'')
phase_ds = _generate_fake_points(components, statevar_dict,
largest_energy, output,
maximum_internal_dof)
final_ds = xray.concat(itertools.chain([phase_ds], all_phase_data),
dim='points')
else:
# speedup for single-phase case (found by profiling)
if len(all_phase_data) > 1:
final_ds = xray.concat(all_phase_data, dim='points')
else:
final_ds = all_phase_data[0]
if (not fake_points) and (len(all_phase_data) == 1):
pass
else:
# Reset the points dimension to use a single global index
final_ds['points'] = np.arange(len(final_ds.points))
return final_ds
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)
def calculate(dbf, comps, phases, mode=None, output='GM', fake_points=False, broadcast=True, tmpman=None, **kwargs):
"""
Sample the property surface of 'output' 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 : str or sequence
Names of components to consider in the calculation.
phases : str or sequence
Names of phases to consider in the calculation.
mode : string, optional
See 'make_callable' docstring for details.
output : string, optional
Model attribute to sample.
fake_points : bool, optional (Default: False)
If True, the first few points of the output surface will be fictitious
points used to define an equilibrium hyperplane guaranteed to be above
all the other points. This is used for convex hull computations.
broadcast : bool, optional
If True, broadcast given state variable lists against each other to create a grid.
If False, assume state variables are given as equal-length lists.
tmpman : TempfileManager, optional
Context manager for temporary file creation during the calculation.
points : ndarray or a dict of phase names to ndarray, optional
Columns of ndarrays must be internal degrees of freedom (site fractions), sorted.
If this is not specified, points will be generated automatically.
pdens : int, a dict of phase names to int, or a seq of both, optional
Number of points to sample per degree of freedom.
model : Model, a dict of phase names to Model, or a seq of both, optional
Model class to use for each phase.
sampler : callable, a dict of phase names to callable, or a seq of both, optional
Function to sample phase constitution space.
Must have same signature as 'pycalphad.core.utils.point_sample'
grid_points : bool, a dict of phase names to bool, or a seq of both, optional (Default: True)
Whether to add evenly spaced points between end-members.
The density of points is determined by 'pdens'
Returns
-------
Dataset of the sampled attribute as a function of state variables
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)
points_dict = unpack_kwarg(kwargs.pop('points', None), default_arg=None)
model_dict = unpack_kwarg(kwargs.pop('model', Model), default_arg=Model)
callable_dict = unpack_kwarg(kwargs.pop('callables', None), default_arg=None)
sampler_dict = unpack_kwarg(kwargs.pop('sampler', None), default_arg=None)
fixedgrid_dict = unpack_kwarg(kwargs.pop('grid_points', True), default_arg=True)
if isinstance(phases, str):
phases = [phases]
if isinstance(comps, str):
comps = [comps]
if points_dict is None and broadcast is False:
raise ValueError('The \'points\' keyword argument must be specified if broadcast=False is also given.')
components = [x for x in sorted(comps) if not x.startswith('VA')]
# Convert keyword strings to proper state variable objects
# If we don't do this, sympy will get confused during substitution
statevar_dict = collections.OrderedDict((v.StateVariable(key), unpack_condition(value)) \
for (key, value) in sorted(kwargs.items()))
str_statevar_dict = collections.OrderedDict((str(key), unpack_condition(value)) \
for (key, value) in statevar_dict.items())
all_phase_data = []
comp_sets = {}
largest_energy = -np.inf
maximum_internal_dof = 0
# Consider only the active phases
active_phases = dict((name.upper(), dbf.phases[name.upper()]) \
for name in unpack_phases(phases))
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:
model_dict[phase_name] = 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
if points_dict[phase_name] is None:
try:
out = getattr(mod, output)
maximum_internal_dof = max(maximum_internal_dof, len(out.atoms(v.SiteFraction)))
except AttributeError:
raise AttributeError('Missing Model attribute {0} specified for {1}'
.format(output, mod.__class__))
else:
maximum_internal_dof = max(maximum_internal_dof, np.asarray(points_dict[phase_name]).shape[-1])
for phase_name, phase_obj in sorted(active_phases.items()):
try:
mod = model_dict[phase_name]
except KeyError:
continue
# Construct an ordered list of the variables
variables, sublattice_dof = generate_dof(phase_obj, mod.components)
# Build the "fast" representation of that model
if callable_dict[phase_name] is None:
out = getattr(mod, output)
# 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(out.atoms(Symbol) - out.atoms(v.StateVariable))
for undef in undefs:
out = out.xreplace({undef: float(0)})
logger.warning('Setting undefined symbol %s for phase %s to zero',
undef, phase_name)
comp_sets[phase_name] = build_functions(out, list(statevar_dict.keys()) + variables, tmpman=tmpman,
include_obj=True, include_grad=False, include_hess=False)
else:
comp_sets[phase_name] = callable_dict[phase_name]
points = points_dict[phase_name]
if points is None:
# Eliminate pure vacancy endmembers from the calculation
vacancy_indices = list()
for idx, sublattice in enumerate(phase_obj.constituents):
active_in_subl = sorted(set(phase_obj.constituents[idx]).intersection(comps))
if 'VA' in active_in_subl and 'VA' in sorted(comps):
vacancy_indices.append(active_in_subl.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)
if fixedgrid_dict[phase_name] is True:
# Sample along the edges of the endmembers
# These constitution space edges are often the equilibrium points!
em_pairs = list(itertools.combinations(points, 2))
for first_em, second_em in em_pairs:
extra_points = first_em * np.linspace(0, 1, pdens_dict[phase_name])[np.newaxis].T + \
second_em * np.linspace(0, 1, pdens_dict[phase_name])[::-1][np.newaxis].T
points = np.concatenate((points, extra_points))
# Sample composition space for more points
if sum(sublattice_dof) > len(sublattice_dof):
sampler = sampler_dict[phase_name]
if sampler is None:
sampler = point_sample
points = np.concatenate((points,
sampler(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)
# Filter out nan's that may have slipped in if we sampled too high a vacancy concentration
# Issues with this appear to be platform-dependent
points = points[~np.isnan(points).any(axis=-1)]
# Ensure that points has the correct dimensions and dtype
points = np.atleast_2d(np.asarray(points, dtype=np.float))
phase_ds = _compute_phase_values(phase_obj, components, variables, str_statevar_dict,
points, comp_sets[phase_name], output,
maximum_internal_dof, broadcast=broadcast)
# largest_energy is really only relevant if fake_points is set
if fake_points:
largest_energy = max(phase_ds[output].max(), largest_energy)
all_phase_data.append(phase_ds)
if fake_points:
if output != 'GM':
raise ValueError('fake_points=True should only be used with output=\'GM\'')
phase_ds = _generate_fake_points(components, statevar_dict, largest_energy, output,
maximum_internal_dof, broadcast)
final_ds = concat(itertools.chain([phase_ds], all_phase_data),
dim='points')
else:
# speedup for single-phase case (found by profiling)
if len(all_phase_data) > 1:
final_ds = concat(all_phase_data, dim='points')
else:
final_ds = all_phase_data[0]
if (not fake_points) and (len(all_phase_data) == 1):
pass
else:
# Reset the points dimension to use a single global index
final_ds['points'] = np.arange(len(final_ds.points))
return final_ds
def energy_surf(dbf, comps, phases, mode=None, output='GM', **kwargs):
"""
Sample the property surface of 'output' 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.
mode : string, optional
See 'make_callable' docstring for details.
output : string, optional
Model attribute to sample.
pdens : int, a dict of phase names to int, or a list of both, optional
Number of points to sample per degree of freedom.
model : Model, a dict of phase names to Model, or a list of both, optional
Model class to use for each phase.
Returns
-------
DataFrame of the output as a function of composition, temperature, etc.
Examples
--------
None yet.
"""
warnings.warn('Use pycalphad.calculate() instead', DeprecationWarning, stacklevel=2)
# 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)
callable_dict = unpack_kwarg(kwargs.pop('callables', None), default_arg=None)
# Convert keyword strings to proper state variable objects
# If we don't do this, sympy will get confused during substitution
statevar_dict = \
collections.OrderedDict((v.StateVariable(key), value) \
for (key, value) in sorted(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 statevar_dict.values()]
statevars_to_map = np.array(list(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
try:
out = getattr(mod, output)
except AttributeError:
raise AttributeError('Missing Model attribute {0} specified for {1}'
.format(output, mod.__class__))
# Construct an ordered list of the variables
variables, sublattice_dof = generate_dof(phase_obj, mod.components)
site_ratios = list(phase_obj.sublattices)
# Build the "fast" representation of that model
if callable_dict[phase_name] is None:
# 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(out.atoms(Symbol) - out.atoms(v.StateVariable))
for undef in undefs:
out = out.xreplace({undef: float(0)})
logger.warning('Setting undefined symbol %s for phase %s to zero',
undef, phase_name)
comp_sets[phase_name] = make_callable(out, \
list(statevar_dict.keys()) + variables, mode=mode)
else:
comp_sets[phase_name] = callable_dict[phase_name]
# 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}
# Broadcast compositions and state variables along orthogonal axes
# This lets us eliminate an expensive Python loop
data_dict[output] = \
comp_sets[phase_name](*itertools.chain(
np.transpose(statevars_to_map[:, :, np.newaxis], (1, 2, 0)),
np.transpose(points[:, :, np.newaxis], (1, 0, 2)))).T.ravel()
# Save state variables, with values indexed appropriately
statevar_vals = np.repeat(statevars_to_map, len(points), axis=0).T
data_dict.update({str(statevar): vals for statevar, vals \
in zip(statevar_dict.keys(), statevar_vals)})
# Map the internal degrees of freedom to global coordinates
# Normalize site ratios by the sum of site ratios times a factor
# related to the site fraction of vacancies
site_ratio_normalization = np.zeros(len(points))
for idx, sublattice in enumerate(phase_obj.constituents):
vacancy_column = np.ones(len(points))
if 'VA' in set(sublattice):
var_idx = variables.index(v.SiteFraction(phase_name, idx, 'VA'))
vacancy_column -= points[:, var_idx]
site_ratio_normalization += site_ratios[idx] * vacancy_column
for comp in sorted(comps):
if comp == 'VA':
continue
avector = [float(vxx.species == comp) * \
site_ratios[vxx.sublattice_index] for vxx in variables]
data_dict['X('+comp+')'] = np.tile(np.divide(np.dot(
points[:, :], avector), site_ratio_normalization),
statevars_to_map.shape[0])
# Copy coordinate information into data_dict
# TODO: Is there a more memory-efficient way to deal with this?
# Perhaps with hierarchical indexing...
var_fmt = 'Y({0},{1},{2})'
data_dict.update({var_fmt.format(vxx.phase_name, vxx.sublattice_index,
vxx.species): \
np.tile(vals, statevars_to_map.shape[0]) \
for vxx, vals in zip(variables, points.T)})
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)
def minimize(self, simplex, phase_fractions=None):
"""
Accept a list of simplex vertices and return the values of the
variables that minimize the energy under the constraints.
"""
# Generate phase fraction variables
# Track the multiplicity of phases with a Counter object
composition_sets = Counter()
all_variables = []
# starting point
x_0 = []
# scaling factor -- set to minimum energy of starting simplex
# Scaling the objective to be of order '10' seems to result in
# sufficient precision (at least 5 significant figures).
scaling_factor = abs(simplex['GM'].min()) / 10.0
# a list of tuples for where each phase's variable indices
# start and end
index_ranges = []
#print(list(enumerate(simplex.iterrows())))
#print((simplex.iterrows()))
#print('END')
for m_idx, vertex in enumerate(simplex.iterrows()):
vertex = vertex[1]
# increase multiplicity by one
composition_sets[vertex['Phase']] += 1
# create new phase fraction variable
all_variables.append(
v.PhaseFraction(vertex['Phase'],
composition_sets[vertex['Phase']])
)
start = len(x_0)
# default position is centroid of the simplex
if phase_fractions is None:
x_0.append(1.0/len(list(simplex.iterrows())))
else:
# use the provided guess for the phase fraction
x_0.append(phase_fractions[m_idx])
# add site fraction variables
all_variables.extend(self._variables[vertex['Phase']])
# add starting point for variable
for varname in self._variables[vertex['Phase']]:
x_0.append(vertex[str(varname)])
index_ranges.append([start, len(x_0)])
# Create master objective function
def obj(input_x):
"Objective function. Takes x vector as input. Returns scalar."
objective = 0.0
for idx, vertex in enumerate(simplex.iterrows()):
vertex = vertex[1]
cur_x = input_x[index_ranges[idx][0]+1:index_ranges[idx][1]]
#print('Phase: '+vertex['Phase']+' '+str(cur_x))
# phase fraction times value of objective for that phase
objective += input_x[index_ranges[idx][0]] * \
self._phase_callables[vertex['Phase']](
*list(cur_x))
return objective / scaling_factor
# Create master gradient function
def gradient(input_x):
"Accepts input vector and returns gradient vector."
gradient = np.zeros(len(input_x))
for idx, vertex in enumerate(simplex.iterrows()):
vertex = vertex[1]
cur_x = input_x[index_ranges[idx][0]+1:index_ranges[idx][1]]
#print('grad cur_x: '+str(cur_x))
# phase fraction derivative is just the phase energy
gradient[index_ranges[idx][0]] = \
self._phase_callables[vertex['Phase']](
*list(cur_x))
# gradient for particular phase's variables
# NOTE: We assume all phase d.o.f are independent here,
# and we handle any coupling through the constraints
for g_idx, grad in \
enumerate(self._gradient_callables[vertex['Phase']]):
gradient[index_ranges[idx][0]+1+g_idx] = \
input_x[index_ranges[idx][0]] * \
grad(*list(cur_x))
#print('grad: '+str(gradient / scaling_factor))
return gradient / scaling_factor
# Generate constraint sequence
constraints = []
# phase fraction constraint
def phasefrac_cons(input_x):
"Accepts input vector and returns phase fraction constraint."
output = 1.0 - sum([input_x[i[0]] for i in index_ranges])#** 2
return output
def phasefrac_jac(input_x):
"Accepts input vector and returns Jacobian of constraint."
output_x = np.zeros(len(input_x))
for idx_range in index_ranges:
output_x[idx_range[0]] = -1.0 #\
# -2.0*sum([input_x[i[0]] for i in index_ranges])
return output_x
phasefrac_dict = dict()
phasefrac_dict['type'] = 'eq'
phasefrac_dict['fun'] = phasefrac_cons
phasefrac_dict['jac'] = phasefrac_jac
constraints.append(phasefrac_dict)
# bounds constraint
def nonneg_cons(input_x, idx):
"Accepts input vector and returns non-negativity constraint."
output = input_x[idx]
#print('nonneg_cons: '+str(output))
return output
def nonneg_jac(input_x, idx):
"Accepts input vector and returns Jacobian of constraint."
output_x = np.zeros(len(input_x))
output_x[idx] = 1.0
return output_x
for idx in range(len(all_variables)):
nonneg_dict = dict()
nonneg_dict['type'] = 'ineq'
nonneg_dict['fun'] = nonneg_cons
nonneg_dict['jac'] = nonneg_jac
nonneg_dict['args'] = [idx]
constraints.append(nonneg_dict)
# Generate all site fraction constraints
for idx_range in index_ranges:
# need to generate constraint for each sublattice
dofs = self._sublattice_dof[all_variables[idx_range[0]].phase_name]
cur_idx = idx_range[0]+1
for dof in dofs:
sitefrac_dict = dict()
sitefrac_dict['type'] = 'eq'
sitefrac_dict['fun'] = sitefrac_cons
sitefrac_dict['jac'] = sitefrac_jac
sitefrac_dict['args'] = [[cur_idx, cur_idx+dof]]
cur_idx += dof
if dof > 0:
constraints.append(sitefrac_dict)
# All other constraints, e.g., mass balance
def molefrac_cons(input_x, species, fix_val, all_variables, phases):
"""
Accept input vector, species and fixed value.
Returns constraint.
"""
output = -fix_val
for idx, vertex in enumerate(simplex.iterrows()):
vertex = vertex[1]
cur_x = input_x[index_ranges[idx][0]+1:index_ranges[idx][1]]
res = self._molefrac_callables[vertex['Phase']][species](*cur_x)
output += input_x[index_ranges[idx][0]] * res
#print('molefrac_cons: '+str(output))
return output
def molefrac_jac(input_x, species, fix_val, all_variables, phases):
"Accepts input vector and returns Jacobian vector."
output_x = np.zeros(len(input_x))
for idx, vertex in enumerate(simplex.iterrows()):
vertex = vertex[1]
cur_x = input_x[index_ranges[idx][0]+1:index_ranges[idx][1]]
output_x[index_ranges[idx][0]] = \
self._molefrac_callables[vertex['Phase']][species](*cur_x)
for g_idx, grad in \
enumerate(self._molefrac_jac_callables[vertex['Phase']][species]):
output_x[index_ranges[idx][0]+1+g_idx] = \
input_x[index_ranges[idx][0]] * \
grad(*list(cur_x))
#print('molefrac_jac '+str(output_x))
return output_x
eqs = len([x for x in constraints if x['type'] == 'eq'])
if eqs < len(x_0):
for condition, value in self.conditions.items():
if isinstance(condition, v.Composition):
# mass balance constraint for mole fraction
molefrac_dict = dict()
molefrac_dict['type'] = 'eq'
molefrac_dict['fun'] = molefrac_cons
molefrac_dict['jac'] = molefrac_jac
molefrac_dict['args'] = \
[condition.species, value, all_variables,
self._phases]
constraints.append(molefrac_dict)
else:
logger.warning("""Dropping mass balance constraints due to
zero internal degrees of freedom""")
# Run optimization
res = scipy.optimize.minimize(obj, x_0, method='slsqp', jac=gradient,\
constraints=constraints, options={'maxiter': 1000})
# rescale final values back to original
res['raw_fun'] = copy.deepcopy(res['fun'])
res['raw_jac'] = copy.deepcopy(res['jac'])
res['raw_x'] = copy.deepcopy(res['x'])
res['fun'] *= scaling_factor
res['jac'] *= scaling_factor
# force tiny numerical values to be positive
res['x'] = np.maximum(res['x'], np.zeros(1, dtype=np.float64))
logger.debug(res)
if not res['success']:
logger.error('Energy minimization failed')
return None
# Build result object
eq_res = EquilibriumResult(self._phases, self.components,
self.statevars, res['fun'],
zip(all_variables, res['x']))
return eq_res