"""
The utils module handles helper routines for equilibrium calculation.
"""
import pycalphad.variables as v
from pycalphad.core.halton import halton
from pycalphad.core.constants import MIN_SITE_FRACTION
from sympy.utilities.lambdify import lambdify
from sympy import Symbol
import numpy as np
import operator
import functools
import itertools
import collections
from collections.abc import Iterable, Mapping
try:
# Only available in numpy 1.10 and newer
from numpy import broadcast_to
except ImportError:
def broadcast_to(arr, shape):
"Broadcast an array to a desired shape. Returns a view."
return np.broadcast_arrays(arr, np.empty(shape, dtype=np.bool))[0]
[docs]def point_sample(comp_count, pdof=10):
"""
Sample 'pdof * (sum(comp_count) - len(comp_count))' points in
composition space for the sublattice configuration specified
by 'comp_count'. Points are sampled quasi-randomly from a Halton sequence.
A Halton sequence is like a uniform random distribution, but the
result will always be the same for a given 'comp_count' and 'pdof'.
Note: For systems with only one component, only one point will be
returned, regardless of 'pdof'. This is because the degrees of freedom
are zero for that case.
Parameters
----------
comp_count : list
Number of components in each sublattice.
pdof : int
Number of points to sample per degree of freedom.
Returns
-------
ndarray of generated points satisfying the mass balance.
Examples
--------
>>> comps = [8,1] # 8 components in sublattice 1; only 1 in sublattice 2
>>> pts = point_sample(comps, pdof=20) # 7 d.o.f, returns a 140x7 ndarray
"""
# Generate Halton sequence with appropriate dimensions and size
pts = halton(sum(comp_count),
pdof * (sum(comp_count) - len(comp_count)), scramble=True)
# Convert low-discrepancy sequence to normalized exponential
# This will be uniformly distributed over the simplices
pts = -np.log(pts)
cur_idx = 0
for ctx in comp_count:
end_idx = cur_idx + ctx
pts[:, cur_idx:end_idx] /= pts[:, cur_idx:end_idx].sum(axis=1)[:, None]
cur_idx = end_idx
if len(pts) == 0:
pts = np.atleast_2d([1] * len(comp_count))
return pts
[docs]def make_callable(model, variables, mode=None):
"""
Take a SymPy object and create a callable function.
Parameters
----------
model, SymPy object
Abstract representation of function
variables, list
Input variables, ordered in the way the return function will expect
mode, ['numpy', 'numba', 'sympy'], optional
Method to use when 'compiling' the function. SymPy mode is
slow and should only be used for debugging. If Numba is installed,
it can offer speed-ups when calling the energy function many
times on multi-core CPUs.
Returns
-------
Function that takes arguments in the same order as 'variables'
and returns the energy according to 'model'.
Examples
--------
None yet.
"""
energy = None
if mode is None:
mode = 'numpy'
if mode == 'sympy':
energy = lambda *vs: model.subs(zip(variables, vs)).evalf()
else:
energy = lambdify(tuple(variables), model, dummify=True,
modules=mode)
return energy
[docs]def sizeof_fmt(num, suffix='B'):
"""
Human-readable string for a number of bytes.
http://stackoverflow.com/questions/1094841/reusable-library-to-get-human-readable-version-of-file-size
"""
for unit in ['', 'K', 'M', 'G', 'T', 'P', 'E', 'Z']:
if abs(num) < 1000.0:
return "%3.1f%s%s" % (num, unit, suffix)
num /= 1000.0
return "%.1f%s%s" % (num, 'Y', suffix)
[docs]def unpack_condition(tup):
"""
Convert a condition to a list of values.
Notes
-----
Rules for keys of conditions dicts:
(1) If it's numeric, treat as a point value
(2) If it's a tuple with one element, treat as a point value
(3) If it's a tuple with two elements, treat as lower/upper limits and guess a step size.
(4) If it's a tuple with three elements, treat as lower/upper/step
(5) If it's a list, ndarray or other non-tuple ordered iterable, use those values directly.
"""
if isinstance(tup, tuple):
if len(tup) == 1:
return [float(tup[0])]
elif len(tup) == 2:
return np.arange(tup[0], tup[1], dtype=np.float)
elif len(tup) == 3:
return np.arange(tup[0], tup[1], tup[2], dtype=np.float)
else:
raise ValueError('Condition tuple is length {}'.format(len(tup)))
elif isinstance(tup, Iterable):
return [float(x) for x in tup]
else:
return [float(tup)]
[docs]def unpack_phases(phases):
"Convert a phases list/dict into a sorted list."
active_phases = None
if isinstance(phases, (list, tuple, set)):
active_phases = sorted(phases)
elif isinstance(phases, dict):
active_phases = sorted([phn for phn, status in phases.items() \
if status == 'entered'])
elif type(phases) is str:
active_phases = [phases]
return active_phases
[docs]def generate_dof(phase, active_comps):
"""
Accept a Phase object and a set() of the active components.
Return a tuple of variable names and the sublattice degrees of freedom.
"""
variables = []
sublattice_dof = []
for idx, sublattice in enumerate(phase.constituents):
dof = 0
for component in sorted(set(sublattice).intersection(active_comps)):
variables.append(v.SiteFraction(phase.name.upper(), idx, component))
dof += 1
sublattice_dof.append(dof)
return variables, sublattice_dof
[docs]def endmember_matrix(dof, vacancy_indices=None):
"""
Accept the number of components in each sublattice.
Return a matrix corresponding to the compositions of all endmembers.
Parameters
----------
dof : list of int
Number of components in each sublattice.
vacancy_indices, list of list of int, optional
If vacancies are present in every sublattice, specify their indices
in each sublattice to ensure the "pure vacancy" endmembers are excluded.
Examples
--------
Sublattice configuration like: `(AL, NI, VA):(AL, NI, VA):(VA)`
>>> endmember_matrix([3,3,1], vacancy_indices=[[2], [2], [0]])
"""
total_endmembers = functools.reduce(operator.mul, dof, 1)
res_matrix = np.empty((total_endmembers, sum(dof)), dtype=np.float)
dof_arrays = [np.eye(d).tolist() for d in dof]
row_idx = 0
for row in itertools.product(*dof_arrays):
res_matrix[row_idx, :] = np.concatenate(row, axis=0)
row_idx += 1
if vacancy_indices is not None and len(vacancy_indices) == len(dof):
dof_adj = np.array([sum(dof[0:i]) for i in range(len(dof))])
for vacancy_em in itertools.product(*vacancy_indices):
indices = np.array(vacancy_em) + dof_adj
row_idx_to_delete = np.where(np.all(res_matrix[:, indices] == 1,
axis=1))
res_matrix = np.delete(res_matrix, (row_idx_to_delete), axis=0)
# Adjust site fractions to the numerical limit
cur_idx = 0
res_matrix[res_matrix == 0] = MIN_SITE_FRACTION
for ctx in dof:
end_idx = cur_idx + ctx
res_matrix[:, cur_idx:end_idx] /= res_matrix[:, cur_idx:end_idx].sum(axis=1)[:, None]
cur_idx = end_idx
return res_matrix
[docs]def unpack_kwarg(kwarg_obj, default_arg=None):
"""
Keyword arguments in pycalphad can be passed as a constant value, a
dict of phase names and values, or a list containing both of these. If
the latter, then the dict is checked first; if the phase of interest is not
there, then the constant value is used.
This function is a way to construct defaultdicts out of keyword arguments.
Parameters
----------
kwarg_obj : dict, iterable, or None
Argument to unpack into a defaultdict
default_arg : object
Default value to use if iterable isn't specified
Returns
-------
defaultdict for the keyword argument of interest
Examples
--------
>>> test_func = lambda **kwargs: print(unpack_kwarg('opt'))
>>> test_func(opt=100)
>>> test_func(opt={'FCC_A1': 50, 'BCC_B2': 10})
>>> test_func(opt=[{'FCC_A1': 30}, 200])
>>> test_func()
>>> test_func2 = lambda **kwargs: print(unpack_kwarg('opt', default_arg=1))
>>> test_func2()
"""
new_dict = collections.defaultdict(lambda: default_arg)
if isinstance(kwarg_obj, Mapping):
new_dict.update(kwarg_obj)
# kwarg_obj is a list containing a dict and a default
# For now at least, we don't treat ndarrays the same as other iterables
# ndarrays are assumed to be numeric arrays containing "default values", so don't match here
elif isinstance(kwarg_obj, Iterable) and not isinstance(kwarg_obj, np.ndarray):
for element in kwarg_obj:
if isinstance(element, Mapping):
new_dict.update(element)
else:
# element=element syntax to silence var-from-loop warning
new_dict = collections.defaultdict(
lambda element=element: element, new_dict)
elif kwarg_obj is None:
pass
else:
new_dict = collections.defaultdict(lambda: kwarg_obj)
return new_dict
[docs]def unpack_components(dbf, comps):
"""
Parameters
----------
dbf : Database
Thermodynamic database containing elements and species.
comps : list
Names of components to consider in the calculation.
Returns
-------
set
Set of Species objects
"""
# Constrain possible components to those within phase's d.o.f
# Assume for the moment that comps contains a list of pure element strings
# We want to add all the species which can be created by a combination of
# the user-specified pure elements
species_dict = {s.name: s for s in dbf.species}
possible_comps = {v.Species(species_dict.get(x, x)) for x in comps}
desired_active_pure_elements = [list(x.constituents.keys()) for x in possible_comps]
# Flatten nested list
desired_active_pure_elements = [el.upper() for constituents in desired_active_pure_elements for el in constituents]
eligible_species_from_database = {x for x in dbf.species if
set(x.constituents.keys()).issubset(desired_active_pure_elements)}
return eligible_species_from_database
[docs]def get_pure_elements(dbf, comps):
"""
Return a list of pure elements in the system.
Parameters
----------
dbf : Database
A Database object
comps : list
A list of component names (species and pure elements)
Returns
-------
list
A list of pure elements in the Database
"""
comps = sorted(unpack_components(dbf, comps))
components = [x for x in comps]
desired_active_pure_elements = [list(x.constituents.keys()) for x in components]
desired_active_pure_elements = [el.upper() for constituents in desired_active_pure_elements for el in constituents]
pure_elements = sorted(set([x for x in desired_active_pure_elements if x != 'VA']))
return pure_elements
[docs]def filter_phases(dbf, comps, candidate_phases=None):
"""Return phases that are valid for equilibrium calculations for the given database and components
Filters out phases that
* Have no active components in any sublattice of a phase
* Are disordered phases in an order-disorder model
Parameters
----------
dbf : Database
Thermodynamic database containing the relevant parameters.
comps : list of v.Species
Species to consider in the calculation.
candidate_phases : list
Names of phases to consider in the calculation, if not passed all phases from DBF will be considered
Returns
-------
list
Sorted list of phases that are valid for the Database and components
"""
# TODO: filter phases that can not charge balance
def all_sublattices_active(comps, phase):
active_sublattices = [len(set(comps).intersection(subl)) > 0 for
subl in phase.constituents]
return all(active_sublattices)
if candidate_phases == None:
candidate_phases = dbf.phases.keys()
else:
candidate_phases = set(candidate_phases).intersection(dbf.phases.keys())
disordered_phases = [dbf.phases[phase].model_hints.get('disordered_phase') for phase in candidate_phases]
phases = [phase for phase in candidate_phases if
all_sublattices_active(comps, dbf.phases[phase]) and
(phase not in disordered_phases or (phase in disordered_phases and
dbf.phases[phase].model_hints.get('ordered_phase') not in candidate_phases))]
return sorted(phases)
[docs]def instantiate_models(dbf, comps, phases, model=None, parameters=None, symbols_only=True):
"""
Parameters
----------
dbf : Database
Database used to construct the Model instances.
comps : Iterable
Names of components to consider in the calculation.
phases : Iterable
Names of phases to consider in the calculation.
model : Model class, a dict of phase names to Model, or a Iterable of both
Model class to use for each phase.
parameters : dict, optional
Maps SymPy Symbol to numbers, for overriding the values of parameters in
the Database.
symbols_only : bool
If True, symbols will be extracted from the parameters dict and used to
construct the Model instances.
Returns
-------
dict
Dictionary of Model instances corresponding to the passed phases.
"""
from pycalphad import Model # avoid cyclic imports
parameters = parameters if parameters is not None else {}
if symbols_only:
parameters, _ = extract_parameters(parameters)
if isinstance(model, Model): # Check that this instance is compatible with phases
if len(phases) > 1:
raise ValueError("Cannot instantiate models for multiple phases ({}) using a Model instance ({}, phase: {})".format(phases, model, model.phase_name))
else:
if phases[0] != model.phase_name:
raise ValueError("Cannot instantiate models because the desired {} phase does not match the Model instance () {} phase.".format(phases[0], model.phase_name, model))
models_defaultdict = unpack_kwarg(model, Model)
models_dict = {}
for name in phases:
mod = models_defaultdict[name]
if isinstance(mod, type):
models_dict[name] = mod(dbf, comps, name, parameters=parameters)
else:
models_dict[name] = mod
return models_dict
[docs]def get_state_variables(models=None, conds=None):
"""
Return a set of StateVariables defined Model instances and/or conditions.
Parameters
----------
models : dict, optional
Dictionary mapping phase names to instances of Model objects
conds : dict, optional
Dictionary mapping pycalphad StateVariables to values
Returns
-------
set
State variables that are defined in the models and or conditions.
Examples
--------
>>> from pycalphad import variables as v
>>> from pycalphad.core.utils import get_state_variables
>>> get_state_variables(conds={v.P: 101325, v.N: 1, v.X('AL'): 0.2}) == {v.P, v.N, v.T}
True
"""
state_vars = set()
if models is not None:
for mod in models.values():
state_vars.update(mod.state_variables)
if conds is not None:
for c in conds.keys():
# StateVariable instances are ok (e.g. P, T, N, V, S),
# however, subclasses (X, Y, MU, NP) are not ok.
if type(c) is v.StateVariable:
state_vars.add(c)
return state_vars
[docs]def wrap_symbol(obj):
if isinstance(obj, Symbol):
return obj
else:
return Symbol(obj)
[docs]def wrap_symbol_symengine(obj):
from symengine import Symbol, sympify
from sympy import Symbol as Symbol_sympy
if isinstance(obj, Symbol):
return obj
elif isinstance(obj, Symbol_sympy):
return sympify(obj)
else:
return Symbol(obj)