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# MDAnalysis --- https://www.mdanalysis.org
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#
# Please cite your use of MDAnalysis in published work:
#
# R. J. Gowers, M. Linke, J. Barnoud, T. J. E. Reddy, M. N. Melo, S. L. Seyler,
# D. L. Dotson, J. Domanski, S. Buchoux, I. M. Kenney, and O. Beckstein.
# MDAnalysis: A Python package for the rapid analysis of molecular dynamics
# simulations. In S. Benthall and S. Rostrup editors, Proceedings of the 15th
# Python in Science Conference, pages 102-109, Austin, TX, 2016. SciPy.
# doi: 10.25080/majora-629e541a-00e
#
# N. Michaud-Agrawal, E. J. Denning, T. B. Woolf, and O. Beckstein.
# MDAnalysis: A Toolkit for the Analysis of Molecular Dynamics Simulations.
# J. Comput. Chem. 32 (2011), 2319--2327, doi:10.1002/jcc.21787
#
r"""Radial Distribution Functions --- :mod:`MDAnalysis.analysis.rdf`
====================================================================
This module contains two classes to calculate radial
`pair distribution functions`_ (`radial distribution functions`_ or "RDF").
The RDF :math:`g_{ab}(r)` between types of particles :math:`a` and :math:`b` is
.. _equation-gab:
.. math::
g_{ab}(r) = (N_{a} N_{b})^{-1} \sum_{i=1}^{N_a} \sum_{j=1}^{N_b}
\langle \delta(|\mathbf{r}_i - \mathbf{r}_j| - r) \rangle
which is normalized so that the RDF becomes 1 for large separations in a
homogenous system. The RDF effectively counts the average number of :math:`b`
neighbours in a shell at distance :math:`r` around a :math:`a` particle and
represents it as a density.
The radial cumulative distribution function is
.. math::
G_{ab}(r) = \int_0^r \!\!dr' 4\pi r'^2 g_{ab}(r')
and the average number of :math:`b` particles within radius :math:`r`
.. _equation-countab:
.. math::
N_{ab}(r) = \rho G_{ab}(r)
(with the appropriate density :math:`\rho`). The latter function can be used to
compute, for instance, coordination numbers such as the number of neighbors in
the first solvation shell :math:`N(r_1)` where :math:`r_1` is the position of
the first minimum in :math:`g(r)`.
We provide options for calculating the density of particle :math:`b`
in a shell at distance :math:`r` around a :math:`a` particle, which is
.. _equation-nab:
.. math::
n_{ab}(r) = \rho g_{ab}(r)
.. _`pair distribution functions`:
https://en.wikipedia.org/wiki/Pair_distribution_function
.. _`radial distribution functions`:
https://en.wikipedia.org/wiki/Radial_distribution_function
.. Not Implemented yet:
.. - Structure factor?
.. - Coordination number
"""
import warnings
import numpy as np
from ..lib import distances
from .base import AnalysisBase
[docs]class InterRDF(AnalysisBase):
r"""Radial distribution function
:class:`InterRDF` is a tool to calculate average radial distribution
functions between two groups of atoms. Suppose we have two AtomGroups ``A``
and ``B``. ``A`` contains atom ``A1``, ``A2``, and ``B`` contains ``B1``,
``B2``. Given ``A`` and ``B`` to :class:`InterRDF`, the output will be the
average of RDFs between ``A1`` and ``B1``, ``A1`` and ``B2``, ``A2`` and
``B1``, ``A2`` and ``B2``. A typical application is to calculate the RDF of
solvent with itself or with another solute.
The :ref:`radial distribution function<equation-gab>` is calculated by
histogramming distances between all particles in `g1` and `g2` while taking
periodic boundary conditions into account via the minimum image
convention.
The `exclusion_block` keyword may be used to exclude a set of distances
from the calculations.
Results are available in the attributes :attr:`results.rdf`
and :attr:`results.count`.
Parameters
----------
g1 : AtomGroup
First AtomGroup
g2 : AtomGroup
Second AtomGroup
nbins : int
Number of bins in the histogram
range : tuple or list
The size of the RDF
norm : str, {'rdf', 'density', 'none'}
For 'rdf' calculate :math:`g_{ab}(r)`. For
'density' the :ref:`single particle density<equation-nab>`
:math:`n_{ab}(r)` is computed. 'none' computes the number of
particles occurences in each spherical shell.
.. versionadded:: 2.3.0
exclusion_block : tuple
A tuple representing the tile to exclude from the distance array.
verbose : bool
Show detailed progress of the calculation if set to `True`
Attributes
----------
results.bins : numpy.ndarray
:class:`numpy.ndarray` of the centers of the `nbins` histogram
bins.
.. versionadded:: 2.0.0
bins : numpy.ndarray
Alias to the :attr:`results.bins` attribute.
.. deprecated:: 2.0.0
This attribute will be removed in 3.0.0.
Use :attr:`results.bins` instead.
results.edges : numpy.ndarray
:class:`numpy.ndarray` of the `nbins + 1` edges of the histogram
bins.
.. versionadded:: 2.0.0
edges : numpy.ndarray
Alias to the :attr:`results.edges` attribute.
.. deprecated:: 2.0.0
This attribute will be removed in 3.0.0.
Use :attr:`results.edges` instead.
results.rdf : numpy.ndarray
:class:`numpy.ndarray` of the :ref:`radial distribution
function<equation-gab>` values for the :attr:`results.bins`.
.. versionadded:: 2.0.0
rdf : numpy.ndarray
Alias to the :attr:`results.rdf` attribute.
.. deprecated:: 2.0.0
This attribute will be removed in 3.0.0.
Use :attr:`results.rdf` instead.
results.count : numpy.ndarray
:class:`numpy.ndarray` representing the radial histogram, i.e.,
the raw counts, for all :attr:`results.bins`.
.. versionadded:: 2.0.0
count : numpy.ndarray
Alias to the :attr:`results.count` attribute.
.. deprecated:: 2.0.0
This attribute will be removed in 3.0.0.
Use :attr:`results.count` instead.
Example
-------
First create the :class:`InterRDF` object, by supplying two
AtomGroups then use the :meth:`run` method ::
rdf = InterRDF(ag1, ag2)
rdf.run()
Results are available through the :attr:`results.bins` and
:attr:`results.rdf` attributes::
plt.plot(rdf.results.bins, rdf.results.rdf)
The `exclusion_block` keyword allows the masking of pairs from
within the same molecule. For example, if there are 7 of each
atom in each molecule, the exclusion mask ``(7, 7)`` can be used.
.. versionadded:: 0.13.0
.. versionchanged:: 1.0.0
Support for the `start`, `stop`, and `step` keywords has been
removed. These should instead be passed to :meth:`InterRDF.run`.
.. versionchanged:: 2.0.0
Store results as attributes `bins`, `edges`, `rdf` and `count`
of the `results` attribute of
:class:`~MDAnalysis.analysis.AnalysisBase`.
"""
def __init__(self,
g1,
g2,
nbins=75,
range=(0.0, 15.0),
norm="rdf",
exclusion_block=None,
**kwargs):
super(InterRDF, self).__init__(g1.universe.trajectory, **kwargs)
self.g1 = g1
self.g2 = g2
self.norm = str(norm).lower()
self.rdf_settings = {'bins': nbins,
'range': range}
self._exclusion_block = exclusion_block
if self.norm not in ['rdf', 'density', 'none']:
raise ValueError(f"'{self.norm}' is an invalid norm. "
"Use 'rdf', 'density' or 'none'.")
def _prepare(self):
# Empty histogram to store the RDF
count, edges = np.histogram([-1], **self.rdf_settings)
count = count.astype(np.float64)
count *= 0.0
self.results.count = count
self.results.edges = edges
self.results.bins = 0.5 * (edges[:-1] + edges[1:])
if self.norm == "rdf":
# Cumulative volume for rdf normalization
self.volume_cum = 0
# Set the max range to filter the search radius
self._maxrange = self.rdf_settings['range'][1]
def _single_frame(self):
pairs, dist = distances.capped_distance(self.g1.positions,
self.g2.positions,
self._maxrange,
box=self._ts.dimensions)
# Maybe exclude same molecule distances
if self._exclusion_block is not None:
idxA = pairs[:, 0]//self._exclusion_block[0]
idxB = pairs[:, 1]//self._exclusion_block[1]
mask = np.where(idxA != idxB)[0]
dist = dist[mask]
count, _ = np.histogram(dist, **self.rdf_settings)
self.results.count += count
if self.norm == "rdf":
self.volume_cum += self._ts.volume
def _conclude(self):
norm = self.n_frames
if self.norm in ["rdf", "density"]:
# Volume in each radial shell
vols = np.power(self.results.edges, 3)
norm *= 4/3 * np.pi * np.diff(vols)
if self.norm == "rdf":
# Number of each selection
nA = len(self.g1)
nB = len(self.g2)
N = nA * nB
# If we had exclusions, take these into account
if self._exclusion_block:
xA, xB = self._exclusion_block
nblocks = nA / xA
N -= xA * xB * nblocks
# Average number density
box_vol = self.volume_cum / self.n_frames
norm *= N / box_vol
self.results.rdf = self.results.count / norm
@property
def edges(self):
wmsg = ("The `edges` attribute was deprecated in MDAnalysis 2.0.0 "
"and will be removed in MDAnalysis 3.0.0. Please use "
"`results.bins` instead")
warnings.warn(wmsg, DeprecationWarning)
return self.results.edges
@property
def count(self):
wmsg = ("The `count` attribute was deprecated in MDAnalysis 2.0.0 "
"and will be removed in MDAnalysis 3.0.0. Please use "
"`results.bins` instead")
warnings.warn(wmsg, DeprecationWarning)
return self.results.count
@property
def bins(self):
wmsg = ("The `bins` attribute was deprecated in MDAnalysis 2.0.0 "
"and will be removed in MDAnalysis 3.0.0. Please use "
"`results.bins` instead")
warnings.warn(wmsg, DeprecationWarning)
return self.results.bins
@property
def rdf(self):
wmsg = ("The `rdf` attribute was deprecated in MDAnalysis 2.0.0 "
"and will be removed in MDAnalysis 3.0.0. Please use "
"`results.rdf` instead")
warnings.warn(wmsg, DeprecationWarning)
return self.results.rdf
[docs]class InterRDF_s(AnalysisBase):
r"""Site-specific radial distribution function
Calculates site-specific radial distribution
functions. Instead of two groups of atoms it takes as input a list of
pairs of AtomGroup, ``[[A, B], [C, D], ...]``. Given the same ``A`` and
``B`` to
:class:`InterRDF_s`, the output will be a list of individual RDFs between
``A1`` and ``B1``, ``A1`` and ``B2``, ``A2`` and ``B1``, ``A2`` and ``B2``
(and
similarly for ``C`` and ``D``). These site-specific radial distribution
functions are typically calculated if one is interested in the solvation
shells of a ligand in a binding site or the solvation of specific residues
in a protein.
Parameters
----------
u : Universe
a Universe that contains atoms in `ags`
.. deprecated:: 2.3.0
This parameter is superflous and will be removed in
MDAnalysis 3.0.0.
ags : list
a list of pairs of :class:`~MDAnalysis.core.groups.AtomGroup`
instances
nbins : int
Number of bins in the histogram
range : tuple or list
The size of the RDF
norm : str, {'rdf', 'density', 'none'}
For 'rdf' calculate :math:`g_{ab}(r)`. For
'density' the :ref:`single particle density<equation-nab>`
:math:`n_{ab}(r)` is computed. 'none' computes the number of
particles occurences in each spherical shell.
.. versionadded:: 2.3.0
density : bool
`False`: calculate :math:`g_{ab}(r)`; `True`: calculate
the true :ref:`single particle density<equation-nab>`
:math:`n_{ab}(r)`. `density` overwrites the `norm` parameter.
.. versionadded:: 1.0.1
This keyword was available since 0.19.0 but was not
documented. Furthermore, it had the opposite
meaning. Since 1.0.1 it is officially supported as
documented.
.. deprecated:: 2.3.0
Instead of `density=True` use `norm='density'`
Attributes
----------
results.bins : numpy.ndarray
:class:`numpy.ndarray` of the centers of the `nbins` histogram
bins; all individual site-specific RDFs have the same bins.
.. versionadded:: 2.0.0
bins : numpy.ndarray
Alias to the :attr:`results.bins` attribute.
.. deprecated:: 2.0.0
This attribute will be removed in 3.0.0.
Use :attr:`results.bins` instead.
results.edges : numpy.ndarray
array of the ``nbins + 1`` edges of the histogram
bins; all individual site-specific RDFs have the same bins.
.. versionadded:: 2.0.0
edges : numpy.ndarray
Alias to the :attr:`results.edges` attribute.
.. deprecated:: 2.0.0
This attribute will be removed in 3.0.0.
Use :attr:`results.edges` instead.
results.rdf : list
:class:`list` of the site-specific :ref:`radial distribution
functions<equation-gab>` if `norm='rdf'` or :ref:`density
functions<equation-nab>` for the :attr:`bins`
if `norm='density'`. The list contains
``len(ags)`` entries. Each entry for the ``i``-th pair `[A, B]
= ags[i]` in `ags` is a :class:`numpy.ndarray` with shape
``(len(A), len(B))``, i.e., a stack of RDFs. For example,
``results.rdf[i][0, 2]`` is the RDF between atoms ``A[0]``
and ``B[2]``.
.. versionadded:: 2.0.0
rdf : list
Alias to the :attr:`results.rdf` attribute.
.. deprecated:: 2.0.0
This attribute will be removed in 3.0.0.
Use :attr:`results.rdf` instead.
results.count : list
:class:`list` of the site-specific radial histograms, i.e., the
raw counts, for all :attr:`results.bins`. The data have the same
structure as :attr:`results.rdf` except that the arrays contain
the raw counts.
.. versionadded:: 2.0.0
count : list
Alias to the :attr:`results.count` attribute.
.. deprecated:: 2.0.0
This attribute will be removed in 3.0.0.
Use :attr:`results.count` instead.
results.cdf : list
:class:`list` of the site-specific :ref:`cumulative
counts<equation-countab>`, for all :attr:`results.bins`. The data
have the same structure as :attr:`results.rdf` except that the arrays
contain the cumulative counts.
This attribute only exists after :meth:`get_cdf` has been run.
.. versionadded:: 2.0.0
cdf : list
Alias to the :attr:`results.cdf` attribute.
.. deprecated:: 2.0.0
This attribute will be removed in 3.0.0.
Use :attr:`results.cdf` instead.
Example
-------
First create the :class:`InterRDF_s` object, by supplying one Universe and
one list of pairs of AtomGroups, then use the :meth:`~InterRDF_s.run`
method::
from MDAnalysisTests.datafiles import GRO_MEMPROT, XTC_MEMPROT
u = mda.Universe(GRO_MEMPROT, XTC_MEMPROT)
s1 = u.select_atoms('name ZND and resid 289')
s2 = u.select_atoms('(name OD1 or name OD2) and resid 51 and sphzone 5.0 (resid 289)')
s3 = u.select_atoms('name ZND and (resid 291 or resid 292)')
s4 = u.select_atoms('(name OD1 or name OD2) and sphzone 5.0 (resid 291)')
ags = [[s1, s2], [s3, s4]]
rdf = InterRDF_s(u, ags)
rdf.run()
Results are available through the :attr:`results.bins`
and :attr:`results.rdf` attributes::
plt.plot(rdf.results.bins, rdf.results.rdf[0][0, 0])
(Which plots the rdf between the first atom in ``s1`` and the first atom in
``s2``)
To generate the *cumulative distribution function* (cdf) in the sense of
"particles within radius :math:`r`", i.e., :math:`N_{ab}(r)`, use the
:meth:`~InterRDF_s.get_cdf` method ::
cdf = rdf.get_cdf()
Results are available through the :attr:`results.cdf` attribute::
plt.plot(rdf.results.bins, rdf.results.cdf[0][0, 0])
(Which plots the cdf between the first atom in ``s1`` and the first atom in
``s2``)
.. versionadded:: 0.19.0
.. versionchanged:: 1.0.0
Support for the `start`, `stop`, and `step` keywords has been
removed. These should instead be passed to :meth:`InterRDF_s.run`.
.. versionchanged:: 2.0.0
Store results as attributes `bins`, `edges`, `rdf`, `count`
and `cdf` of the `results` attribute
of :class:`~MDAnalysis.analysis.AnalysisBase`.
.. versionchanged:: 2.3.0
Introduce `norm` and `exclusion_blocks` attributes.
.. deprecated:: 2.3.0
Instead of `density=True` use `norm='density'`
.. deprecated:: 2.3.0
The `universe` parameter is superflous.
"""
def __init__(self,
u,
ags,
nbins=75,
range=(0.0, 15.0),
norm="rdf",
density=False,
**kwargs):
super(InterRDF_s, self).__init__(ags[0][0].universe.trajectory,
**kwargs)
warnings.warn("The `u` attribute is superflous and will be removed "
"in MDAnalysis 3.0.0.", DeprecationWarning)
self.ags = ags
self.norm = str(norm).lower()
self.rdf_settings = {'bins': nbins,
'range': range}
if self.norm not in ['rdf', 'density', 'none']:
raise ValueError(f"'{self.norm}' is an invalid norm. "
"Use 'rdf', 'density' or 'none'.")
if density:
warnings.warn("The `density` attribute was deprecated in "
"MDAnalysis 2.3.0 and will be removed in "
"MDAnalysis 3.0.0. Please use `norm=density` "
"instead.", DeprecationWarning)
self.norm = "density"
def _prepare(self):
count, edges = np.histogram([-1], **self.rdf_settings)
self.results.count = [np.zeros((ag1.n_atoms, ag2.n_atoms, len(count)),
dtype=np.float64) for ag1, ag2 in self.ags]
self.results.edges = edges
self.results.bins = 0.5 * (edges[:-1] + edges[1:])
if self.norm == "rdf":
# Cumulative volume for rdf normalization
self.volume_cum = 0
self._maxrange = self.rdf_settings['range'][1]
def _single_frame(self):
for i, (ag1, ag2) in enumerate(self.ags):
pairs, dist = distances.capped_distance(ag1.positions,
ag2.positions,
self._maxrange,
box=self._ts.dimensions)
for j, (idx1, idx2) in enumerate(pairs):
count, _ = np.histogram(dist[j], **self.rdf_settings)
self.results.count[i][idx1, idx2, :] += count
if self.norm == "rdf":
self.volume_cum += self._ts.volume
def _conclude(self):
norm = self.n_frames
if self.norm in ["rdf", "density"]:
# Volume in each radial shell
vols = np.power(self.results.edges, 3)
norm *= 4/3 * np.pi * np.diff(vols)
if self.norm == "rdf":
# Average number density
norm *= 1 / (self.volume_cum / self.n_frames)
# Empty lists to restore indices, RDF
self.results.indices = []
self.results.rdf = []
for i, (ag1, ag2) in enumerate(self.ags):
# Number of each selection
self.results.indices.append([ag1.indices, ag2.indices])
self.results.rdf.append(self.results.count[i] / norm)
[docs] def get_cdf(self):
r"""Calculate the cumulative counts for all sites.
This is the :ref:`cumulative count<equation-countab>` within a given
radius, i.e., :math:`N_{ab}(r)`.
The result is returned and also stored in the attribute
:attr:`results.cdf`.
Returns
-------
cdf : list
list of arrays with the same structure as :attr:`results.rdf`
"""
self.results.cdf = []
for count in self.results.count:
self.results.cdf.append(np.cumsum(count, axis=2) / self.n_frames)
return self.results.cdf
@property
def edges(self):
wmsg = ("The `edges` attribute was deprecated in MDAnalysis 2.0.0 "
"and will be removed in MDAnalysis 3.0.0. Please use "
"`results.bins` instead")
warnings.warn(wmsg, DeprecationWarning)
return self.results.edges
@property
def count(self):
wmsg = ("The `count` attribute was deprecated in MDAnalysis 2.0.0 "
"and will be removed in MDAnalysis 3.0.0. Please use "
"`results.bins` instead")
warnings.warn(wmsg, DeprecationWarning)
return self.results.count
@property
def bins(self):
wmsg = ("The `bins` attribute was deprecated in MDAnalysis 2.0.0 "
"and will be removed in MDAnalysis 3.0.0. Please use "
"`results.bins` instead")
warnings.warn(wmsg, DeprecationWarning)
return self.results.bins
@property
def rdf(self):
wmsg = ("The `rdf` attribute was deprecated in MDAnalysis 2.0.0 "
"and will be removed in MDAnalysis 3.0.0. Please use "
"`results.rdf` instead")
warnings.warn(wmsg, DeprecationWarning)
return self.results.rdf
@property
def cdf(self):
wmsg = ("The `cdf` attribute was deprecated in MDAnalysis 2.0.0 "
"and will be removed in MDAnalysis 3.0.0. Please use "
"`results.cdf` instead")
warnings.warn(wmsg, DeprecationWarning)
return self.results.cdf