"""Module for canonical ensemble of mixture.
.. codeauthor:: Yicheng Qiang <yicheng.qiang@ds.mpg.de>
"""
from __future__ import annotations
import logging
import numpy as np
from numba import float64, int32
from numba.experimental import jitclass
from .base import EnsembleBase, EnsembleBaseCompiled
[docs]
@jitclass(
[
("_num_comp", int32), # a scalar
("_phi_means", float64[::1]), # a C-continuous array
]
)
class CanonicalEnsembleCompiled(EnsembleBaseCompiled):
r"""Compiled class for canonical ensemble.
In canonical ensemble, the average volume fractions of the components are fixed.
Therefore, the volume fractions distribution of the components in compartments can be
obtained by normalizing the Boltzmann factors according to the average volume
fractions,
.. math::
\phi_i^{(m)} &= \frac{\bar{\phi}_i}{Q_i} p_i^{(m)} \\
Q_i &= \sum_m p_i^{(m)} J_m .
Since (translational) entropy is always defined for each component, this class is only
aware of the component-based description of the system.
"""
def __init__(self, phi_means: np.ndarray):
r"""
Args:
phi_means:
1D array with the size of :math:`N_\mathrm{C}`, containing the mean volume
fractions of the components, :math:`\bar{\phi}_i`. The number of
components :math:`N_\mathrm{C}` is inferred from this array.
"""
self._num_comp = phi_means.shape[0]
self._phi_means = phi_means # do not affect chis
@property
def num_comp(self):
return self._num_comp
[docs]
def normalize(
self, phis_comp: np.ndarray, Qs: np.ndarray, masks: np.ndarray
) -> np.ndarray:
incomp = -1.0 * np.ones_like(phis_comp[0])
for itr_comp in range(self._num_comp):
factor = self._phi_means[itr_comp] / Qs[itr_comp]
phis_comp[itr_comp] = factor * phis_comp[itr_comp] * masks
incomp += phis_comp[itr_comp]
incomp *= masks
return incomp
[docs]
class CanonicalEnsemble(EnsembleBase):
r"""Class for an canonical ensemble that the average volume fractions are conserved.
The particular form of the conservation law reads
.. math::
\bar{\phi}_i = \frac{\sum_m \phi_i^{(m)} J_m }{\sum_m J_m}.
"""
def __init__(
self,
num_comp: int,
phi_means: np.ndarray,
):
r"""
Args:
num_comp:
Number of components :math:`N_\mathrm{C}`.
phi_means:
The average volume fractions of the components :math:`\bar{\phi}_i`.
"""
super().__init__(num_comp)
self._logger = logging.getLogger(self.__class__.__name__)
phi_means = np.atleast_1d(phi_means)
shape = (num_comp,)
self._phi_means = np.array(np.broadcast_to(phi_means, shape))
if not np.allclose(self._phi_means.sum(), 1.0):
self._logger.warning(
"The sum of phi_means is not 1. In incompressible system the iteration may never converge."
)
@property
def phi_means(self) -> np.ndarray:
r"""The average volume fractions of the components :math:`\bar{\phi}_i`."""
return self._phi_means
@phi_means.setter
def phi_means(self, phi_means_new: np.ndarray):
phi_means_new = np.atleast_1d(phi_means_new)
shape = (self.num_comp,)
self._phi_means = np.array(np.broadcast_to(phi_means_new, shape))
if not np.allclose(self._phi_means.sum(), 1.0):
self._logger.warning(
"The sum of phi_means is not 1. In incompressible system the iteration may never converge."
)
[docs]
def _compiled_impl(self) -> CanonicalEnsembleCompiled:
"""Implementation of creating a compiled ensemble instance.
This method overwrites the interface
:meth:`~flory.ensemble.base.EnsembleBase._compiled_impl` in
:class:`~flory.ensemble.base.EnsembleBase`.
Returns:
: Instance of :class:`CanonicalEnsembleCompiled`.
"""
return CanonicalEnsembleCompiled(self._phi_means)