import numpy as np
from ._base import Descriptor
from ._graph_matrix import DistanceMatrix
from ._atomic_property import AtomicProperty, get_properties
__all__ = ("ATS", "AATS", "ATSC", "AATSC", "MATS", "GATS",)
class AutocorrelationBase(Descriptor):
__slots__ = "_prop", "_order"
explicit_hydrogens = True
def __str__(self):
return "{}{}{}".format(
self.__class__.__name__,
self._order,
self._avec.as_argument,
)
def description(self):
return "{} of lag {} weighted by {}".format(
self._description_name, self._order, self._avec.get_long())
def parameters(self):
return self._order, self._prop
def __init__(self, order=0, prop="m"):
self._prop = prop
self._order = order
@property
def _avec(self):
return AtomicProperty(self.explicit_hydrogens, self._prop)
@property
def _cavec(self):
return CAVec(self._prop)
@property
def _gmat(self):
return GMat(self._order)
@property
def _gsum(self):
return GSum(self._order)
@property
def _ATS(self):
return ATS(self._order, self._prop)
@property
def _ATSC(self):
return ATSC(self._order, self._prop)
@property
def _AATSC(self):
return AATSC(self._order, self._prop)
rtype = float
class AutocorrelationProp(AutocorrelationBase):
__slots__ = ()
def parameters(self):
return self._prop,
def __init__(self, prop):
self._prop = prop
rtype = None
class AutocorrelationOrder(AutocorrelationBase):
__slots__ = ()
def _prop(self):
pass
def parameters(self):
return self._order,
def __init__(self, order):
self._order = order
rtype = None
class CAVec(AutocorrelationProp):
__slots__ = ()
_order = 0
def dependencies(self):
return {"avec": self._avec}
def calculate(self, avec):
return avec - avec.mean()
class GMat(AutocorrelationOrder):
__slots__ = ()
def dependencies(self):
return {"dmat": DistanceMatrix(self.explicit_hydrogens)}
def calculate(self, dmat):
return dmat == self._order
class GSum(AutocorrelationOrder):
__slots__ = ()
def dependencies(self):
return {"gmat": GMat(self._order)}
def calculate(self, gmat):
s = gmat.sum()
return s if self._order == 0 else 0.5 * s
MAX_DISTANCE = 8
[docs]class ATS(AutocorrelationBase):
r"""Autocorrelation of Topological Structure descriptor.
a.k.a. Moreau-Broto autocorrelation descriptor
.. math::
{\rm ATS}_0 = \sum^{A}_{i=1} {\boldsymbol w}_i^2
{\rm ATS}_k = \frac{1}{2}
\left(
{\boldsymbol w}^{\rm T} \cdot
{}^k{\boldsymbol B} \cdot
{\boldsymbol w}
\right)
{}^k{\boldsymbol B} =
\begin{cases}
1 & (d_{ij} = k) \\
0 & (d_{ij} \neq k)
\end{cases}
where
:math:`{\boldsymbol w}` is atomic property vector,
:math:`d_{ij}` is graph distance(smallest number of bonds between atom i and j).
:type order: int
:param order: order(:math:`k`)
:type property: str, function
:param property: :ref:`atomic_properties`
:returns: NaN when any properties are NaN
"""
__slots__ = ()
_description_name = "moreau-broto autocorrelation"
@classmethod
def preset(cls):
return (
cls(d, a)
for a in get_properties(valence=True)
for d in range(MAX_DISTANCE + 1)
)
def dependencies(self):
return {"avec": self._avec, "gmat": self._gmat}
def calculate(self, avec, gmat):
if self._order == 0:
return (avec ** 2).sum().astype("float")
return 0.5 * avec.dot(gmat).dot(avec)
[docs]class AATS(ATS):
r"""averaged ATS descriptor.
.. math::
{\rm AATS}_k = \frac{{\rm ATS}_k}{\Delta_k}
where
:math:`\Delta_k` is number of vertex pairs at order equal to :math:`k`.
:Parameters: see :py:class:`ATS`
:returns: NaN when
* :math:`\Delta_k = 0`
* some properties are NaN
"""
__slots__ = ()
_description_name = "averaged moreau-broto autocorrelation"
def dependencies(self):
return {"ATS": self._ATS, "gsum": self._gsum}
def calculate(self, ATS, gsum):
with self.rethrow_zerodiv():
return ATS / gsum
[docs]class ATSC(AutocorrelationBase):
r"""centered ATS descriptor.
ATS with :math:`{\boldsymbol w}_{\rm c}` property
.. math::
{\boldsymbol w}_{\rm c} = {\boldsymbol w} - \bar{\boldsymbol w}
:Parameters: see :py:class:`ATS`
:returns: NaN when any properties are NaN
"""
__slots__ = ()
_description_name = "centered moreau-broto autocorrelation"
@classmethod
def preset(cls):
return (
cls(d, a)
for a in get_properties(charge=True, valence=True)
for d in range(MAX_DISTANCE + 1)
)
def dependencies(self):
return {"cavec": self._cavec, "gmat": self._gmat}
def calculate(self, cavec, gmat):
if self._order == 0:
return (cavec ** 2).sum().astype("float")
return 0.5 * cavec.dot(gmat).dot(cavec)
[docs]class AATSC(ATSC):
r"""averaged ATSC descriptor.
.. math::
{\rm AATSC}_k = \frac{{\rm ATSC}_k}{\Delta_k}
where
:math:`\Delta_k` is number of vertex pairs at order equal to :math:`k`.
:Parameters: see :py:class:`ATS`
:returns: NaN when
* :math:`\Delta_k = 0`
* any properties are NaN
"""
__slots__ = ()
_description_name = "averaged and centered moreau-broto autocorrelation"
def dependencies(self):
return {"ATSC": self._ATSC, "gsum": self._gsum}
def calculate(self, ATSC, gsum):
with self.rethrow_zerodiv():
return ATSC / gsum
[docs]class MATS(AutocorrelationBase):
r"""Moran coefficient descriptor.
.. math::
{\rm MATS}_k = \frac{
{\rm AATSC}_k
}{
\frac{1}{A} \cdot \sum {\boldsymbol w}_{\rm c}^2
}
:Parameters: see :py:class:`ATS`
:returns: NaN when
* some properties are NaN
* denominator = 0
"""
__slots__ = ()
_description_name = "moran coefficient"
@classmethod
def preset(cls):
return (
cls(d, a)
for a in get_properties(charge=True, valence=True)
for d in range(1, MAX_DISTANCE + 1)
)
def dependencies(self):
return {
"AATSC": self._AATSC,
"avec": self._avec,
"cavec": self._cavec,
}
def calculate(self, avec, AATSC, cavec):
with self.rethrow_zerodiv():
return len(avec) * AATSC / (cavec ** 2).sum()
[docs]class GATS(MATS):
r"""Geary coefficient descriptor.
:Parameters: see :py:class:`ATS`
:returns: NaN when
* :math:`\Delta_k = 0`
* any properties are NaN
* denominator = 0
"""
__slots__ = ()
_description_name = "geary coefficient"
def dependencies(self):
return {
"avec": self._avec,
"cavec": self._cavec,
"gmat": self._gmat,
"gsum": self._gsum,
}
def calculate(self, avec, gmat, gsum, cavec):
if len(avec) <= 1:
self.fail(ValueError("no bond"))
with self.rethrow_zerodiv():
n = (gmat * (avec[:, np.newaxis] - avec) ** 2).sum() / (4 * gsum)
d = (cavec ** 2).sum() / (len(avec) - 1)
return n / d