def fit_ternary_interactions(dbf, phase_name, symmetry, endmembers, datasets, ridge_alpha=None, aicc_phase_penalty=None):
"""
Fit ternary interactions for a database in place
Parameters
----------
dbf : Database
pycalphad Database to add parameters to
phase_name : str
Name of the phase to fit
symmetry : list
List of symmetric sublattices, e.g. [[0, 1, 2], [3, 4]]
endmembers : list
List of endmember tuples, e.g. [('CU', 'MG')]
datasets : PickleableTinyDB
TinyDB database of datasets
ridge_alpha : float
Value of the :math:`\\alpha` hyperparameter used in ridge regression. Defaults to 1.0e-100, which should be degenerate
with ordinary least squares regression. For now, the parameter is applied to all features.
Returns
-------
None
Modified the Database in place
"""
numdigits = 6 # number of significant figures, might cause rounding errors
interactions = generate_interactions(endmembers, order=3, symmetry=symmetry)
_log.trace('%s distinct ternary interactions', len(interactions))
for interaction in interactions:
ixx = interaction
config = tuple(map(tuplify, ixx))
if _param_present_in_database(dbf, phase_name, config, 'L'):
_log.warning('INTERACTION: %s already in Database. Skipping.', ixx)
continue
else:
_log.trace('INTERACTION: %s', ixx)
parameters = fit_formation_energy(dbf, sorted(dbf.elements), phase_name, ixx, symmetry, datasets, ridge_alpha, aicc_phase_penalty=aicc_phase_penalty)
# Organize parameters by polynomial degree
degree_polys = np.zeros(3, dtype=np.object_)
YS = Symbol('YS')
# asymmetric parameters should have Mugiannu V_I/V_J/V_K, while symmetric just has YS
is_asymmetric = any([(k.has(Symbol('V_I'))) and (v != 0) for k, v in parameters.items()])
if is_asymmetric:
params = [(2, YS*Symbol('V_K')), (1, YS*Symbol('V_J')), (0, YS*Symbol('V_I'))] # (excess parameter degree, symbol) tuples
else:
params = [(0, YS)] # (excess parameter degree, symbol) tuples
for degree, check_symbol in params:
keys_to_remove = []
for key, value in sorted(parameters.items(), key=str):
if key.has(check_symbol):
if value != 0:
symbol_name = get_next_symbol(dbf)
dbf.symbols[symbol_name] = sigfigs(parameters[key], numdigits)
parameters[key] = Symbol(symbol_name)
coef = parameters[key] * (key / check_symbol)
try:
coef = float(coef)
except TypeError:
pass
degree_polys[degree] += coef
keys_to_remove.append(key)
for key in keys_to_remove:
parameters.pop(key)
_log.trace('Polynomial coefs: %s', degree_polys)
# Insert into database
symmetric_interactions = generate_symmetric_group(interaction, symmetry)
for degree in np.arange(degree_polys.shape[0]):
if degree_polys[degree] != 0:
for syminter in symmetric_interactions:
dbf.add_parameter('L', phase_name, tuple(map(tuplify, syminter)), degree, degree_polys[degree])
def phase_fit(dbf, phase_name, symmetry, datasets, refdata, ridge_alpha, aicc_penalty=None, aliases=None):
"""Generate an initial CALPHAD model for a given phase and sublattice model.
Parameters
----------
dbf : Database
pycalphad Database to add parameters to.
phase_name : str
Name of the phase.
symmetry : [[int]]
Sublattice model symmetry.
datasets : PickleableTinyDB
All datasets to consider for the calculation.
refdata : dict
Maps tuple(element, phase_name) -> SymPy object defining
energy relative to SER
ridge_alpha : float
Value of the :math:`\\alpha` hyperparameter used in ridge regression. Defaults to 1.0e-100, which should be degenerate
with ordinary least squares regression. For now, the parameter is applied to all features.
aicc_penalty : dict
Map of phase name to feature to a multiplication factor for the AICc's parameter penalty.
aliases : Dict[str, str]
Mapping of possible aliases to the Database phase names.
Returns
-------
None
Modifies the dbf.
"""
aicc_penalty = aicc_penalty if aicc_penalty is not None else {}
aicc_phase_penalty = aicc_penalty.get(phase_name, {})
if not hasattr(dbf, 'varcounter'):
dbf.varcounter = 0
phase_obj = dbf.phases[phase_name]
# TODO: assumed pure elements - add proper support for Species objects
subl_model = [sorted([sp.name for sp in subl]) for subl in phase_obj.constituents]
site_ratios = phase_obj.sublattices
# First fit endmembers
all_em_count = len(generate_endmembers(subl_model)) # number of total endmembers
endmembers = generate_endmembers(subl_model, symmetry)
# Number of significant figures in parameters, might cause rounding errors
numdigits = 6
em_dict = {}
# TODO: use the global aliases dictionary passed in as-is instead of converting it to a phase-local dict
# TODO: use the aliases dictionary in dataset queries to find relevant data
if aliases is None:
aliases = [phase_name]
else:
aliases = sorted([alias for alias, database_phase in aliases.items() if database_phase == phase_name])
_log.info('FITTING: %s', phase_name)
_log.trace('%s endmembers (%s distinct by symmetry)', all_em_count, len(endmembers))
all_endmembers = []
for endmember in endmembers:
symmetric_endmembers = generate_symmetric_group(endmember, symmetry)
all_endmembers.extend(symmetric_endmembers)
if _param_present_in_database(dbf, phase_name, endmember, 'G'):
_log.trace('ENDMEMBER: %s already in Database. Skipping.', endmember)
continue
else:
_log.trace('ENDMEMBER: %s', endmember)
# Some endmembers are fixed by our choice of standard lattice stabilities, e.g., SGTE91
# If a (phase, pure component endmember) tuple is fixed, we should use that value instead of fitting
endmember_comps = list(set(endmember))
fit_eq = None
# only one non-VA component, or two components but the other is VA and its only the last sublattice
if ((len(endmember_comps) == 1) and (endmember_comps[0] != 'VA')) or\
((len(endmember_comps) == 2) and (endmember[-1] == 'VA') and (len(set(endmember[:-1])) == 1)):
# this is a "pure component endmember"
# try all phase name aliases until we get run out or get a hit
em_comp = list(set(endmember_comps) - {'VA'})[0]
sym_name = None
for name in aliases:
sym_name = 'G'+name[:3].upper()+em_comp.upper()
stability = refdata.get((em_comp.upper(), name.upper()), None)
if stability is not None:
if isinstance(stability, sympy.Piecewise):
# Default zero required for the compiled backend
if (0, True) not in stability.args:
new_args = stability.args + ((0, True),)
stability = sympy.Piecewise(*new_args)
dbf.symbols[sym_name] = stability
break
if dbf.symbols.get(sym_name, None) is not None:
num_moles = sum([sites for elem, sites in zip(endmember, site_ratios) if elem != 'VA'])
fit_eq = num_moles * Symbol(sym_name)
_log.trace("Found lattice stability: %s", sym_name)
_log.debug("%s = %s", sym_name, dbf.symbols[sym_name])
if fit_eq is None:
# No reference lattice stability data -- we have to fit it
parameters = fit_formation_energy(dbf, sorted(dbf.elements), phase_name, endmember, symmetry, datasets, ridge_alpha, aicc_phase_penalty=aicc_phase_penalty)
for key, value in sorted(parameters.items(), key=str):
if value == 0:
continue
symbol_name = get_next_symbol(dbf)
dbf.symbols[symbol_name] = sigfigs(value, numdigits)
parameters[key] = Symbol(symbol_name)
fit_eq = sympy.Add(*[value * key for key, value in parameters.items()])
ref = 0
for subl, ratio in zip(endmember, site_ratios):
if subl == 'VA':
continue
subl = (subl.upper()*2)[:2]
ref = ref + ratio * Symbol('GHSER'+subl)
fit_eq += ref
_log.trace('SYMMETRIC_ENDMEMBERS: %s', symmetric_endmembers)
for em in symmetric_endmembers:
em_dict[em] = fit_eq
dbf.add_parameter('G', phase_name, tuple(map(tuplify, em)), 0, fit_eq)
_log.trace('FITTING BINARY INTERACTIONS')
bin_interactions = generate_interactions(all_endmembers, order=2, symmetry=symmetry)
_log.trace('%s distinct binary interactions', len(bin_interactions))
for interaction in bin_interactions:
ixx = []
for i in interaction:
if isinstance(i, (tuple, list)):
ixx.append(tuple(i))
else:
ixx.append(i)
ixx = tuple(ixx)
config = tuple(map(tuplify, ixx))
if _param_present_in_database(dbf, phase_name, config, 'L'):
_log.trace('INTERACTION: %s already in Database', ixx)
continue
else:
_log.trace('INTERACTION: %s', ixx)
parameters = fit_formation_energy(dbf, sorted(dbf.elements), phase_name, ixx, symmetry, datasets, ridge_alpha, aicc_phase_penalty=aicc_phase_penalty)
# Organize parameters by polynomial degree
degree_polys = np.zeros(10, dtype=np.object_)
for degree in reversed(range(10)):
check_symbol = Symbol('YS') * Symbol('Z')**degree
keys_to_remove = []
for key, value in sorted(parameters.items(), key=str):
if key.has(check_symbol):
if value != 0:
symbol_name = get_next_symbol(dbf)
dbf.symbols[symbol_name] = sigfigs(parameters[key], numdigits)
parameters[key] = Symbol(symbol_name)
coef = parameters[key] * (key / check_symbol)
try:
coef = float(coef)
except TypeError:
pass
degree_polys[degree] += coef
keys_to_remove.append(key)
for key in keys_to_remove:
parameters.pop(key)
_log.trace('Polynomial coefs: %s', degree_polys.tolist())
# Insert into database
symmetric_interactions = generate_symmetric_group(interaction, symmetry)
for degree in np.arange(degree_polys.shape[0]):
if degree_polys[degree] != 0:
for syminter in symmetric_interactions:
dbf.add_parameter('L', phase_name, tuple(map(tuplify, syminter)), degree, degree_polys[degree])
_log.trace('FITTING TERNARY INTERACTIONS')
fit_ternary_interactions(dbf, phase_name, symmetry, all_endmembers, datasets, aicc_phase_penalty=aicc_phase_penalty)
if hasattr(dbf, 'varcounter'):
del dbf.varcounter
def phase_fit(dbf,
phase_name,
symmetry,
subl_model,
site_ratios,
datasets,
refdata,
ridge_alpha,
aliases=None):
"""Generate an initial CALPHAD model for a given phase and sublattice model.
Parameters
----------
dbf : Database
pycalphad Database to add parameters to.
phase_name : str
Name of the phase.
symmetry : [[int]]
Sublattice model symmetry.
subl_model : [[str]]
Sublattice model for the phase of interest.
site_ratios : [float]
Number of sites in each sublattice, normalized to one atom.
datasets : PickleableTinyDB
All datasets to consider for the calculation.
refdata : dict
Maps tuple(element, phase_name) -> SymPy object defining
energy relative to SER
ridge_alpha : float
Value of the $alpha$ hyperparameter used in ridge regression. Defaults to 1.0e-100, which should be degenerate
with ordinary least squares regression. For now, the parameter is applied to all features.
aliases : [str]
Alternative phase names. Useful for matching against
reference data or other datasets. (Default value = None)
Returns
-------
None
Modifies the dbf.
"""
if not hasattr(dbf, 'varcounter'):
dbf.varcounter = 0
# First fit endmembers
all_em_count = len(
generate_endmembers(subl_model)) # number of total endmembers
endmembers = generate_endmembers(subl_model, symmetry)
# Number of significant figures in parameters, might cause rounding errors
numdigits = 6
em_dict = {}
aliases = [] if aliases is None else aliases
aliases = sorted(set(aliases + [phase_name]))
logging.info('FITTING: {}'.format(phase_name))
logging.debug('{0} endmembers ({1} distinct by symmetry)'.format(
all_em_count, len(endmembers)))
all_endmembers = []
for endmember in endmembers:
logging.debug('ENDMEMBER: {}'.format(endmember))
# Some endmembers are fixed by our choice of standard lattice stabilities, e.g., SGTE91
# If a (phase, pure component endmember) tuple is fixed, we should use that value instead of fitting
endmember_comps = list(set(endmember))
fit_eq = None
# only one non-VA component, or two components but the other is VA and its only the last sublattice
if ((len(endmember_comps) == 1) and (endmember_comps[0] != 'VA')) or\
((len(endmember_comps) == 2) and (endmember[-1] == 'VA') and (len(set(endmember[:-1])) == 1)):
# this is a "pure component endmember"
# try all phase name aliases until we get run out or get a hit
em_comp = list(set(endmember_comps) - {'VA'})[0]
sym_name = None
for name in aliases:
sym_name = 'G' + name[:3].upper() + em_comp.upper()
stability = refdata.get((em_comp.upper(), name.upper()), None)
if stability is not None:
if isinstance(stability, sympy.Piecewise):
# Default zero required for the compiled backend
if (0, True) not in stability.args:
new_args = stability.args + ((0, True), )
stability = sympy.Piecewise(*new_args)
dbf.symbols[sym_name] = stability
break
if dbf.symbols.get(sym_name, None) is not None:
num_moles = sum([
sites for elem, sites in zip(endmember, site_ratios)
if elem != 'VA'
])
fit_eq = num_moles * sympy.Symbol(sym_name)
if fit_eq is None:
# No reference lattice stability data -- we have to fit it
parameters = fit_formation_energy(dbf, sorted(dbf.elements),
phase_name, endmember, symmetry,
datasets, ridge_alpha)
for key, value in sorted(parameters.items(), key=str):
if value == 0:
continue
symbol_name = get_next_symbol(dbf)
dbf.symbols[symbol_name] = sigfigs(value, numdigits)
parameters[key] = sympy.Symbol(symbol_name)
fit_eq = sympy.Add(
*[value * key for key, value in parameters.items()])
ref = 0
for subl, ratio in zip(endmember, site_ratios):
if subl == 'VA':
continue
subl = (subl.upper() * 2)[:2]
ref = ref + ratio * sympy.Symbol('GHSER' + subl)
fit_eq += ref
symmetric_endmembers = generate_symmetric_group(endmember, symmetry)
logging.debug('SYMMETRIC_ENDMEMBERS: {}'.format(symmetric_endmembers))
all_endmembers.extend(symmetric_endmembers)
for em in symmetric_endmembers:
em_dict[em] = fit_eq
dbf.add_parameter('G', phase_name, tuple(map(tuplify, em)), 0,
fit_eq)
logging.debug('FITTING BINARY INTERACTIONS')
bin_interactions = generate_interactions(all_endmembers,
order=2,
symmetry=symmetry)
logging.debug('{0} distinct binary interactions'.format(
len(bin_interactions)))
for interaction in bin_interactions:
ixx = []
for i in interaction:
if isinstance(i, (tuple, list)):
ixx.append(tuple(i))
else:
ixx.append(i)
ixx = tuple(ixx)
logging.debug('INTERACTION: {}'.format(ixx))
parameters = fit_formation_energy(dbf, sorted(dbf.elements),
phase_name, ixx, symmetry, datasets,
ridge_alpha)
# Organize parameters by polynomial degree
degree_polys = np.zeros(10, dtype=np.object)
for degree in reversed(range(10)):
check_symbol = sympy.Symbol('YS') * sympy.Symbol('Z')**degree
keys_to_remove = []
for key, value in sorted(parameters.items(), key=str):
if key.has(check_symbol):
if value != 0:
symbol_name = get_next_symbol(dbf)
dbf.symbols[symbol_name] = sigfigs(
parameters[key], numdigits)
parameters[key] = sympy.Symbol(symbol_name)
coef = parameters[key] * (key / check_symbol)
try:
coef = float(coef)
except TypeError:
pass
degree_polys[degree] += coef
keys_to_remove.append(key)
for key in keys_to_remove:
parameters.pop(key)
logging.debug('Polynomial coefs: {}'.format(degree_polys))
# Insert into database
symmetric_interactions = generate_symmetric_group(
interaction, symmetry)
for degree in np.arange(degree_polys.shape[0]):
if degree_polys[degree] != 0:
for syminter in symmetric_interactions:
dbf.add_parameter('L', phase_name,
tuple(map(tuplify, syminter)), degree,
degree_polys[degree])
logging.debug('FITTING TERNARY INTERACTIONS')
fit_ternary_interactions(dbf, phase_name, symmetry, all_endmembers,
datasets)
if hasattr(dbf, 'varcounter'):
del dbf.varcounter
