# -*- Mode: python; tab-width: 4; indent-tabs-mode:nil; coding:utf-8 -*-
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#
# MDAnalysis --- https://www.mdanalysis.org
# Copyright (c) 2006-2017 The MDAnalysis Development Team and contributors
# (see the file AUTHORS for the full list of names)
#
# Released under the GNU Public Licence, v2 or any higher version
#
# 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"""
Calculating path similarity --- :mod:`pathsimanalysis.psa`
==========================================================================
.. versionadded:: 0.10.0
The module contains code to calculate the geometric similarity of trajectories
using path metrics such as the Hausdorff or Fréchet distances
:footcite:p:`Seyler2015`. The path metrics are functions of two paths and return a
nonnegative number, i.e., a distance. Two paths are identical if their distance
is zero, and large distances indicate dissimilarity. Each path metric is a
function of the individual points (e.g., coordinate snapshots) that comprise
each path and, loosely speaking, identify the two points, one per path of a
pair of paths, where the paths deviate the most. The distance between these
points of maximal deviation is measured by the root mean square deviation
(RMSD), i.e., to compute structural similarity.
One typically computes the pairwise similarity for an ensemble of paths to
produce a symmetric distance matrix, which can be clustered to, at a glance,
identify patterns in the trajectory data. To properly analyze a path ensemble,
one must select a suitable reference structure to which all paths (each
conformer in each path) will be universally aligned using the rotations
determined by the best-fit rmsds. Distances between paths and their structures
are then computed directly with no further alignment. This pre-processing step
is necessary to preserve the metric properties of the Hausdorff and Fréchet
metrics; using the best-fit rmsd on a pairwise basis does not generally
preserve the triangle inequality.
Note
----
The `PSAnalysisTutorial`_ outlines a typical application of PSA to
a set of trajectories, including doing proper alignment,
performing distance comparisons, and generating heat
map-dendrogram plots from hierarchical clustering.
.. _`PSAnalysisTutorial`: https://github.com/Becksteinlab/PSAnalysisTutorial
Helper functions and variables
------------------------------
The following convenience functions are used by other functions in this module.
.. autofunction:: sqnorm
.. autofunction:: get_msd_matrix
.. autofunction:: get_coord_axes
Classes, methods, and functions
-------------------------------
.. autofunction:: get_path_metric_func
.. autofunction:: hausdorff
.. autofunction:: hausdorff_wavg
.. autofunction:: hausdorff_avg
.. autofunction:: hausdorff_neighbors
.. autofunction:: discrete_frechet
.. autofunction:: dist_mat_to_vec
.. autoclass:: Path
:members:
.. attribute:: u_original
:class:`~MDAnalysis.Universe` object with a trajectory
.. attribute:: u_reference
:class:`~MDAnalysis.Universe` object containing a reference structure
.. attribute:: select
string, selection for
:meth:`~MDAnalysis.core.groups.AtomGroup.select_atoms` to select frame
from :attr:`Path.u_reference`
.. attribute:: path_select
string, selection for
:meth:`~MDAnalysis.core.groups.AtomGroup.select_atoms` to select atoms
to compose :attr:`Path.path`
.. attribute:: ref_frame
int, frame index to select frame from :attr:`Path.u_reference`
.. attribute:: u_fitted
:class:`~MDAnalysis.Universe` object with the fitted trajectory
.. attribute:: path
:class:`numpy.ndarray` object representation of the fitted trajectory
.. autoclass:: PSAPair
.. attribute:: npaths
int, total number of paths in the comparison in which *this*
:class:`PSAPair` was generated
.. attribute:: matrix_id
(int, int), (row, column) indices of the location of *this*
:class:`PSAPair` in the corresponding pairwise distance matrix
.. attribute:: pair_id
int, ID of *this* :class:`PSAPair` (the pair_id:math:`^\text{th}`
comparison) in the distance vector corresponding to the pairwise distance
matrix
.. attribute:: nearest_neighbors
dict, contains the nearest neighbors by frame index and the
nearest neighbor distances for each path in *this* :class:`PSAPair`
.. attribute:: hausdorff_pair
dict, contains the frame indices of the Hausdorff pair for each path in
*this* :class:`PSAPair` and the corresponding (Hausdorff) distance
.. autoclass:: PSAnalysis
:members:
.. attribute:: universes
list of :class:`MDAnalysis.Universe` objects containing trajectories
.. attribute:: u_reference
:class:`MDAnalysis.Universe` object containing a reference structure
.. attribute:: select
string, selection for
:meth:`~MDAnalysis.core.groups.AtomGroup.select_atoms` to select frame
from :attr:`PSAnalysis.u_reference`
.. attribute:: path_select
string, selection for
:meth:`~MDAnalysis.core.groups.AtomGroup.select_atoms` to select atoms
to compose :attr:`Path.path`
.. attribute:: ref_frame
int, frame index to select frame from :attr:`Path.u_reference`
.. attribute:: paths
list of :class:`numpy.ndarray` objects representing the set/ensemble of
fitted trajectories
.. attribute:: D
:class:`numpy.ndarray` which stores the calculated distance matrix
.. Markup definitions
.. ------------------
..
.. |3Dp| replace:: :math:`N_p \times N \times 3`
.. |2Dp| replace:: :math:`N_p \times (3N)`
.. |3Dq| replace:: :math:`N_q \times N \times 3`
.. |2Dq| replace:: :math:`N_q \times (3N)`
.. |3D| replace:: :math:`N_p\times N\times 3`
.. |2D| replace:: :math:`N_p\times 3N`
.. |Np| replace:: :math:`N_p`
.. Rubric:: References
.. footbibliography::
"""
import logging
import pickle
import os
import warnings
import numbers
import numpy as np
from scipy import spatial, cluster
from scipy.spatial.distance import directed_hausdorff
import matplotlib
import MDAnalysis
import MDAnalysis.analysis.align
from MDAnalysis import NoDataError
logger = logging.getLogger(__name__)
[docs]
def get_path_metric_func(name):
"""Selects a path metric function by name.
Parameters
----------
name : str
name of path metric
Returns
-------
path_metric : function
The path metric function specified by *name* (if found).
"""
path_metrics = {
'hausdorff' : hausdorff,
'weighted_average_hausdorff' : hausdorff_wavg,
'average_hausdorff' : hausdorff_avg,
'hausdorff_neighbors' : hausdorff_neighbors,
'discrete_frechet' : discrete_frechet
}
try:
return path_metrics[name]
except KeyError as key:
errmsg = (f'Path metric "{key}" not found. Valid selections: '
f'{" ".join(n for n in path_metrics.keys())}')
raise KeyError(errmsg) from None
[docs]
def sqnorm(v, axis=None):
"""Compute the sum of squares of elements along specified axes.
Parameters
----------
v : numpy.ndarray
coordinates
axes : None / int / tuple (optional)
Axes or axes along which a sum is performed. The default
(*axes* = ``None``) performs a sum over all the dimensions of
the input array. The value of *axes* may be negative, in
which case it counts from the last axis to the zeroth axis.
Returns
-------
float
the sum of the squares of the elements of `v` along `axes`
"""
return np.sum(v*v, axis=axis)
[docs]
def get_msd_matrix(P, Q, axis=None):
r"""Generate the matrix of pairwise mean-squared deviations between paths.
The MSDs between all pairs of points in `P` and `Q` are
calculated, each pair having a point from `P` and a point from
`Q`.
`P` (`Q`) is a :class:`numpy.ndarray` of :math:`N_p` (:math:`N_q`) time
steps, :math:`N` atoms, and :math:`3N` coordinates (e.g.,
:attr:`MDAnalysis.core.groups.AtomGroup.positions`). The pairwise MSD
matrix has dimensions :math:`N_p` by :math:`N_q`.
Parameters
----------
P : numpy.ndarray
the points in the first path
Q : numpy.ndarray
the points in the second path
Returns
-------
msd_matrix : numpy.ndarray
matrix of pairwise MSDs between points in `P` and points
in `Q`
Notes
-----
We calculate the MSD matrix
.. math::
M_{ij} = ||p_i - q_j||^2
where :math:`p_i \in P` and :math:`q_j \in Q`.
"""
return np.asarray([sqnorm(p - Q, axis=axis) for p in P])
def reshaper(path, axis):
"""Flatten path when appropriate to facilitate calculations
requiring two dimensional input.
"""
if len(axis) > 1:
path = path.reshape(len(path), -1)
return path
[docs]
def get_coord_axes(path):
"""Return the number of atoms and the axes corresponding to atoms
and coordinates for a given path.
The `path` is assumed to be a :class:`numpy.ndarray` where the 0th axis
corresponds to a frame (a snapshot of coordinates). The :math:`3N`
(Cartesian) coordinates are assumed to be either:
1. all in the 1st axis, starting with the x,y,z coordinates of the
first atom, followed by the *x*,*y*,*z* coordinates of the 2nd, etc.
2. in the 1st *and* 2nd axis, where the 1st axis indexes the atom
number and the 2nd axis contains the *x*,*y*,*z* coordinates of
each atom.
Parameters
----------
path : numpy.ndarray
representing a path
Returns
-------
(int, (int, ...))
the number of atoms and the axes containing coordinates
"""
path_dimensions = len(path.shape)
if path_dimensions == 3:
N = path.shape[1]
axis = (1,2) # 1st axis: atoms, 2nd axis: x,y,z coords
elif path_dimensions == 2:
# can use mod to check if total # coords divisible by 3
N = path.shape[1] / 3
axis = (1,) # 1st axis: 3N structural coords (x1,y1,z1,...,xN,xN,zN)
else:
raise ValueError("Path must have 2 or 3 dimensions; the first "
"dimensions (axis 0) must correspond to frames, "
"axis 1 (and axis 2, if present) must contain atomic "
"coordinates.")
return N, axis
[docs]
def hausdorff(P, Q):
r"""Calculate the symmetric Hausdorff distance between two paths.
The metric used is RMSD, as opposed to the more conventional L2
(Euclidean) norm, because this is convenient for i.e., comparing
protein configurations.
*P* (*Q*) is a :class:`numpy.ndarray` of :math:`N_p` (:math:`N_q`) time
steps, :math:`N` atoms, and :math:`3N` coordinates (e.g.,
:attr:`MDAnalysis.core.groups.AtomGroup.positions`). *P* (*Q*) has
either shape |3Dp| (|3Dq|), or |2Dp| (|2Dq|) in flattened form.
Note that reversing the path does not change the Hausdorff distance.
Parameters
----------
P : numpy.ndarray
the points in the first path
Q : numpy.ndarray
the points in the second path
Returns
-------
float
the Hausdorff distance between paths `P` and `Q`
Example
-------
Calculate the Hausdorff distance between two halves of a trajectory:
>>> import MDAnalysis as mda
>>> import numpy
>>> from MDAnalysis.tests.datafiles import PSF, DCD
>>> import pathsimanalysis as psa
>>> u = mda.Universe(PSF,DCD)
>>> mid = int(len(u.trajectory)/2)
>>> ca = u.select_atoms('name CA')
>>> P = numpy.array([
... ca.positions for _ in u.trajectory[:mid:]
... ]) # first half of trajectory
>>> Q = numpy.array([
... ca.positions for _ in u.trajectory[mid::]
... ]) # second half of trajectory
>>> psa.hausdorff(P,Q)
4.778663899862152
>>> psa.hausdorff(P,Q[::-1]) # hausdorff distance w/ reversed 2nd trajectory
4.778663899862152
Notes
-----
:func:`scipy.spatial.distance.directed_hausdorff` is an optimized
implementation of the early break algorithm of :footcite:p:`Taha2015`; the
latter code is used here to calculate the symmetric Hausdorff
distance with an RMSD metric
"""
N_p, axis_p = get_coord_axes(P)
N_q, axis_q = get_coord_axes(Q)
if N_p != N_q:
raise ValueError("P and Q must have matching sizes")
P = reshaper(P, axis_p)
Q = reshaper(Q, axis_q)
return max(directed_hausdorff(P, Q)[0],
directed_hausdorff(Q, P)[0]) / np.sqrt(N_p)
[docs]
def hausdorff_wavg(P, Q):
r"""Calculate the weighted average Hausdorff distance between two paths.
*P* (*Q*) is a :class:`numpy.ndarray` of :math:`N_p` (:math:`N_q`) time
steps, :math:`N` atoms, and :math:`3N` coordinates (e.g.,
:attr:`MDAnalysis.core.groups.AtomGroup.positions`). *P* (*Q*) has
either shape |3Dp| (|3Dq|), or |2Dp| (|2Dq|) in flattened form. The nearest
neighbor distances for *P* (to *Q*) and those of *Q* (to *P*) are averaged
individually to get the average nearest neighbor distance for *P* and
likewise for *Q*. These averages are then summed and divided by 2 to get a
measure that gives equal weight to *P* and *Q*.
Parameters
----------
P : numpy.ndarray
the points in the first path
Q : numpy.ndarray
the points in the second path
Returns
-------
float
the weighted average Hausdorff distance between paths `P` and `Q`
Example
-------
>>> import MDAnalysis as mda
>>> from MDAnalysis import Universe
>>> from MDAnalysis.tests.datafiles import PSF, DCD
>>> import pathsimanalysis as psa
>>> u = mda.Universe(PSF,DCD)
>>> mid = int(len(u.trajectory)/2)
>>> ca = u.select_atoms('name CA')
>>> P = numpy.array([
... ca.positions for _ in u.trajectory[:mid:]
... ]) # first half of trajectory
>>> Q = numpy.array([
... ca.positions for _ in u.trajectory[mid::]
... ]) # second half of trajectory
>>> psa.hausdorff_wavg(P,Q)
2.5669644353703447
>>> psa.hausdorff_wavg(P,Q[::-1]) # weighted avg hausdorff dist w/ Q reversed
2.5669644353703447
Notes
-----
The weighted average Hausdorff distance is not a true metric (it does not
obey the triangle inequality); see :footcite:p:`Seyler2015` for further
details.
"""
N, axis = get_coord_axes(P)
d = get_msd_matrix(P, Q, axis=axis)
out = 0.5*( np.mean(np.amin(d,axis=0)) + np.mean(np.amin(d,axis=1)) )
return ( out / N )**0.5
[docs]
def hausdorff_avg(P, Q):
r"""Calculate the average Hausdorff distance between two paths.
*P* (*Q*) is a :class:`numpy.ndarray` of :math:`N_p` (:math:`N_q`) time
steps, :math:`N` atoms, and :math:`3N` coordinates (e.g.,
:attr:`MDAnalysis.core.groups.AtomGroup.positions`). *P* (*Q*) has
either shape |3Dp| (|3Dq|), or |2Dp| (|2Dq|) in flattened form. The nearest
neighbor distances for *P* (to *Q*) and those of *Q* (to *P*) are all
averaged together to get a mean nearest neighbor distance. This measure
biases the average toward the path that has more snapshots, whereas weighted
average Hausdorff gives equal weight to both paths.
Parameters
----------
P : numpy.ndarray
the points in the first path
Q : numpy.ndarray
the points in the second path
Returns
-------
float
the average Hausdorff distance between paths `P` and `Q`
Example
-------
>>> import MDAnalysis as mda
>>> from MDAnalysis.tests.datafiles import PSF, DCD
>>> import pathsimanalysis as psa
>>> u = mda.Universe(PSF,DCD)
>>> mid = int(len(u.trajectory)/2)
>>> ca = u.select_atoms('name CA')
>>> P = numpy.array([
... ca.positions for _ in u.trajectory[:mid:]
... ]) # first half of trajectory
>>> Q = numpy.array([
... ca.positions for _ in u.trajectory[mid::]
... ]) # second half of trajectory
>>> psa.hausdorff_avg(P,Q)
2.5669646575869005
>>> psa.hausdorff_avg(P,Q[::-1]) # hausdorff distance w/ reversed 2nd trajectory
2.5669646575869005
Notes
-----
The average Hausdorff distance is not a true metric (it does not obey the
triangle inequality); see :footcite:p:`Seyler2015` for further details.
"""
N, axis = get_coord_axes(P)
d = get_msd_matrix(P, Q, axis=axis)
out = np.mean( np.append( np.amin(d,axis=0), np.amin(d,axis=1) ) )
return ( out / N )**0.5
[docs]
def hausdorff_neighbors(P, Q):
r"""Find the Hausdorff neighbors of two paths.
*P* (*Q*) is a :class:`numpy.ndarray` of :math:`N_p` (:math:`N_q`) time
steps, :math:`N` atoms, and :math:`3N` coordinates (e.g.,
:attr:`MDAnalysis.core.groups.AtomGroup.positions`). *P* (*Q*) has
either shape |3Dp| (|3Dq|), or |2Dp| (|2Dq|) in flattened form.
Parameters
----------
P : numpy.ndarray
the points in the first path
Q : numpy.ndarray
the points in the second path
Returns
-------
dict
dictionary of two pairs of numpy arrays, the first pair (key
"frames") containing the indices of (Hausdorff) nearest
neighbors for `P` and `Q`, respectively, the second (key
"distances") containing (corresponding) nearest neighbor
distances for `P` and `Q`, respectively
Notes
-----
- Hausdorff neighbors are those points on the two paths that are separated by
the Hausdorff distance. They are the farthest nearest neighbors and are
maximally different in the sense of the Hausdorff distance
:footcite:p:`Seyler2015`.
- :func:`scipy.spatial.distance.directed_hausdorff` can also provide the
hausdorff neighbors.
"""
N, axis = get_coord_axes(P)
d = get_msd_matrix(P, Q, axis=axis)
nearest_neighbors = {
'frames' : (np.argmin(d, axis=1), np.argmin(d, axis=0)),
'distances' : ((np.amin(d,axis=1)/N)**0.5, (np.amin(d, axis=0)/N)**0.5)
}
return nearest_neighbors
[docs]
def discrete_frechet(P, Q):
r"""Calculate the discrete Fréchet distance between two paths.
*P* (*Q*) is a :class:`numpy.ndarray` of :math:`N_p` (:math:`N_q`) time
steps, :math:`N` atoms, and :math:`3N` coordinates (e.g.,
:attr:`MDAnalysis.core.groups.AtomGroup.positions`). *P* (*Q*) has
either shape |3Dp| (|3Dq|), or :|2Dp| (|2Dq|) in flattened form.
Parameters
----------
P : numpy.ndarray
the points in the first path
Q : numpy.ndarray
the points in the second path
Returns
-------
float
the discrete Fréchet distance between paths *P* and *Q*
Example
-------
Calculate the discrete Fréchet distance between two halves of a
trajectory.
>>> import MDAnalysis as mda
>>> import numpy as np
>>> from MDAnalysis.tests.datafiles import PSF, DCD
>>> import pathsimanalysis as psa
>>> u = mda.Universe(PSF,DCD)
>>> mid = int(len(u.trajectory)/2)
>>> ca = u.select_atoms('name CA')
>>> P = np.array([
... ca.positions for _ in u.trajectory[:mid:]
... ]) # first half of trajectory
>>> Q = np.array([
... ca.positions for _ in u.trajectory[mid::]
... ]) # second half of trajectory
>>> psa.discrete_frechet(P,Q)
4.778663984013591
>>> psa.discrete_frechet(P,Q[::-1]) # frechet distance w/ 2nd trj reversed 2nd
6.842901117711383
Note that reversing the direction increased the Fréchet distance:
it is sensitive to the direction of the path.
Notes
-----
The discrete Fréchet metric is an approximation to the continuous Fréchet
metric :footcite:p:`Frechet1906,Alt1995`. The calculation of the continuous
Fréchet distance is implemented with the dynamic programming algorithm of
:footcite:p:`EiterMannila1994,EiterMannila1997`.
"""
N, axis = get_coord_axes(P)
Np, Nq = len(P), len(Q)
d = get_msd_matrix(P, Q, axis=axis)
ca = -np.ones((Np, Nq))
def c(i, j):
"""Compute the coupling distance for two partial paths formed by *P* and
*Q*, where both begin at frame 0 and end (inclusive) at the respective
frame indices :math:`i-1` and :math:`j-1`. The partial path of *P* (*Q*)
up to frame *i* (*j*) is formed by the slicing ``P[0:i]`` (``Q[0:j]``).
:func:`c` is called recursively to compute the coupling distance
between the two full paths *P* and *Q* (i.e., the discrete Frechet
distance) in terms of coupling distances between their partial paths.
Parameters
----------
i : int
partial path of *P* through final frame *i-1*
j : int
partial path of *Q* through final frame *j-1*
Returns
-------
dist : float
the coupling distance between partial paths `P[0:i]` and `Q[0:j]`
"""
if ca[i,j] != -1 :
return ca[i,j]
if i > 0:
if j > 0:
ca[i,j] = max( min(c(i-1,j),c(i,j-1),c(i-1,j-1)), d[i,j] )
else:
ca[i,j] = max( c(i-1,0), d[i,0] )
elif j > 0:
ca[i,j] = max( c(0,j-1), d[0,j] )
else:
ca[i,j] = d[0,0]
return ca[i,j]
return (c(Np-1, Nq-1) / N)**0.5
[docs]
def dist_mat_to_vec(N, i, j):
"""Convert distance matrix indices (in the upper triangle) to the index of
the corresponding distance vector.
This is a convenience function to locate distance matrix elements (and the
pair generating it) in the corresponding distance vector. The row index *j*
should be greater than *i+1*, corresponding to the upper triangle of the
distance matrix.
Parameters
----------
N : int
size of the distance matrix (of shape *N*-by-*N*)
i : int
row index (starting at 0) of the distance matrix
j : int
column index (starting at 0) of the distance matrix
Returns
-------
int
index (of the matrix element) in the corresponding distance vector
"""
if not (isinstance(N, numbers.Integral) and isinstance(i, numbers.Integral)
and isinstance(j, numbers.Integral)):
raise ValueError("N, i, j all must be of type int")
if i < 0 or j < 0 or N < 2:
raise ValueError("Matrix indices are invalid; i and j must be greater "
"than 0 and N must be greater the 2")
if (j > i and (i > N - 1 or j > N)) or (j < i and (i > N or j > N - 1)):
raise ValueError("Matrix indices are out of range; i and j must be "
"less than N = {0:d}".format(N))
if j > i:
return (N*i) + j - (i+2)*(i+1) // 2 # old-style division for int output
elif j < i:
warnings.warn("Column index entered (j = {:d} is smaller than row "
"index (i = {:d}). Using symmetric element in upper "
"triangle of distance matrix instead: i --> j, "
"j --> i".format(j, i))
return (N*j) + i - (j+2)*(j+1) // 2 # old-style division for int output
else:
raise ValueError("Error in processing matrix indices; i and j must "
"be integers less than integer N = {0:d} such that"
" j >= i+1.".format(N))
[docs]
class Path(object):
"""Represent a path based on a :class:`~MDAnalysis.core.universe.Universe`.
Pre-process a :class:`Universe` object: (1) fit the trajectory to a
reference structure, (2) convert fitted time series to a
:class:`numpy.ndarray` representation of :attr:`Path.path`.
The analysis is performed with :meth:`PSAnalysis.run` and stores the result
in the :class:`numpy.ndarray` distance matrix :attr:`PSAnalysis.D`.
:meth:`PSAnalysis.run` also generates a fitted trajectory and path from
alignment of the original trajectories to a reference structure.
.. versionadded:: 0.9.1
"""
def __init__(self, universe, reference, select='name CA',
path_select='all', ref_frame=0):
"""Setting up trajectory alignment and fitted path generation.
Parameters
----------
universe : Universe
:class:`MDAnalysis.Universe` object containing a trajectory
reference : Universe
reference structure (uses `ref_frame` from the trajectory)
select : str or dict or tuple (optional)
The selection to operate on for rms fitting; can be one of:
1. any valid selection string for
:meth:`~MDAnalysis.core.groups.AtomGroup.select_atoms` that
produces identical selections in *mobile* and *reference*; or
2. a dictionary ``{'mobile':sel1, 'reference':sel2}`` (the
:func:`MDAnalysis.analysis.align.fasta2select` function returns
such a dictionary based on a ClustalW_ or STAMP_ sequence
alignment); or
3. a tuple ``(sel1, sel2)``
When using 2. or 3. with *sel1* and *sel2* then these selections
can also each be a list of selection strings (to generate an
AtomGroup with defined atom order as described under
:ref:`ordered-selections-label`).
ref_frame : int
frame index to select the coordinate frame from
`select.trajectory`
path_select : selection_string
atom selection composing coordinates of (fitted) path; if ``None``
then `path_select` is set to `select` [``None``]
"""
self.u_original = universe
self.u_reference = reference
self.select = select
self.ref_frame = ref_frame
self.path_select = path_select
self.top_name = self.u_original.filename
self.trj_name = self.u_original.trajectory.filename
self.newtrj_name = None
self.u_fitted = None
self.path = None
self.natoms = None
[docs]
def fit_to_reference(self, filename=None, prefix='', postfix='_fit',
rmsdfile=None, targetdir=os.path.curdir,
weights=None, tol_mass=0.1):
"""Align each trajectory frame to the reference structure
Parameters
----------
filename : str (optional)
file name for the RMS-fitted trajectory or pdb; defaults to the
original trajectory filename (from :attr:`Path.u_original`) with
`prefix` prepended
prefix : str (optional)
prefix for auto-generating the new output filename
rmsdfile : str (optional)
file name for writing the RMSD time series [``None``]
weights : {"mass", ``None``} or array_like (optional)
choose weights. With ``"mass"`` uses masses as weights; with
``None`` weigh each atom equally. If a float array of the same
length as the selected AtomGroup is provided, use each element of
the `array_like` as a weight for the corresponding atom in the
AtomGroup.
tol_mass : float (optional)
Reject match if the atomic masses for matched atoms differ by more
than `tol_mass` [0.1]
Returns
-------
Universe
:class:`MDAnalysis.Universe` object containing a fitted trajectory
Notes
-----
Uses :class:`MDAnalysis.analysis.align.AlignTraj` for the fitting.
.. deprecated:: 0.16.1
Instead of ``mass_weighted=True`` use new ``weights='mass'``;
refactored to fit with AnalysisBase API
.. versionchanged:: 0.17.0
Deprecated keyword `mass_weighted` was removed.
"""
head, tail = os.path.split(self.trj_name)
oldname, ext = os.path.splitext(tail)
filename = filename or oldname
self.newtrj_name = os.path.join(targetdir, filename + postfix + ext)
self.u_reference.trajectory[self.ref_frame] # select frame from ref traj
aligntrj = MDAnalysis.analysis.align.AlignTraj(self.u_original,
self.u_reference,
select=self.select,
filename=self.newtrj_name,
prefix=prefix,
weights=weights,
tol_mass=tol_mass).run()
if rmsdfile is not None:
aligntrj.save(rmsdfile)
return MDAnalysis.Universe(self.top_name, self.newtrj_name)
[docs]
def to_path(self, fitted=False, select=None, flat=False):
r"""Generates a coordinate time series from the fitted universe
trajectory.
Given a selection of *N* atoms from *select*, the atomic positions for
each frame in the fitted universe (:attr:`Path.u_fitted`) trajectory
(with |Np| total frames) are appended sequentially to form a 3D or 2D
(if *flat* is ``True``) :class:`numpy.ndarray` representation of the
fitted trajectory (with dimensions |3D| or |2D|, respectively).
Parameters
----------
fitted : bool (optional)
construct a :attr:`Path.path` from the :attr:`Path.u_fitted`
trajectory; if ``False`` then :attr:`Path.path` is generated with
the trajectory from :attr:`Path.u_original` [``False``]
select : str (optional)
the selection for constructing the coordinates of each frame in
:attr:`Path.path`; if ``None`` then :attr:`Path.path_select`
is used, else it is overridden by *select* [``None``]
flat : bool (optional)
represent :attr:`Path.path` as a 2D (|2D|) :class:`numpy.ndarray`;
if ``False`` then :attr:`Path.path` is a 3D (|3D|)
:class:`numpy.ndarray` [``False``]
Returns
-------
numpy.ndarray
representing a time series of atomic positions of an
:class:`MDAnalysis.core.groups.AtomGroup` selection from
:attr:`Path.u_fitted.trajectory`
"""
select = select if select is not None else self.path_select
if fitted:
if not isinstance(self.u_fitted, MDAnalysis.Universe):
raise TypeError("Fitted universe not found. Generate a fitted " +
"universe with fit_to_reference() first, or explicitly "+
"set argument \"fitted\" to \"False\" to generate a " +
"path from the original universe.")
u = self.u_fitted
else:
u = self.u_original
frames = u.trajectory
atoms = u.select_atoms(select)
self.natoms = len(atoms)
frames.rewind()
if flat:
return np.array([atoms.positions.flatten() for _ in frames])
else:
return np.array([atoms.positions for _ in frames])
[docs]
def run(self, align=False, filename=None, postfix='_fit', rmsdfile=None,
targetdir=os.path.curdir, weights=None, tol_mass=0.1,
flat=False):
r"""Generate a path from a trajectory and reference structure.
As part of the path generation, the trajectory can be superimposed
("aligned") to a reference structure if specified.
This is a convenience method to generate a fitted trajectory from an
inputted universe (:attr:`Path.u_original`) and reference structure
(:attr:`Path.u_reference`). :meth:`Path.fit_to_reference` and
:meth:`Path.to_path` are used consecutively to generate a new universe
(:attr:`Path.u_fitted`) containing the fitted trajectory along with the
corresponding :attr:`Path.path` represented as an
:class:`numpy.ndarray`. The method returns a tuple of the topology name
and new trajectory name, which can be fed directly into an
:class:`MDAnalysis.Universe` object after unpacking the tuple using the
``*`` operator, as in
``MDAnalysis.Universe(*(top_name, newtraj_name))``.
Parameters
----------
align : bool (optional)
Align trajectory to atom selection :attr:`Path.select` of
:attr:`Path.u_reference`. If ``True``, a universe containing an
aligned trajectory is produced with :meth:`Path.fit_to_reference`
[``False``]
filename : str (optional)
filename for the RMS-fitted trajectory or pdb; defaults to the
original trajectory filename (from :attr:`Path.u_original`) with
*prefix* prepended
postfix : str (optional)
prefix for auto-generating the new output filename
rmsdfile : str (optional)
file name for writing the RMSD time series [``None``]
weights : {"mass", ``None``} or array_like (optional)
choose weights. With ``"mass"`` uses masses as weights; with
``None`` weigh each atom equally. If a float array of the same
length as the selected AtomGroup is provided, use each element of
the `array_like` as a weight for the corresponding atom in the
AtomGroup.
tol_mass : float (optional)
Reject match if the atomic masses for matched atoms differ by more
than *tol_mass* [0.1]
flat : bool (optional)
represent :attr:`Path.path` with 2D (|2D|) :class:`numpy.ndarray`;
if ``False`` then :attr:`Path.path` is a 3D (|3D|)
:class:`numpy.ndarray` [``False``]
Returns
-------
topology_trajectory : tuple
A tuple of the topology name and new trajectory name.
.. deprecated:: 0.16.1
Instead of ``mass_weighted=True`` use new ``weights='mass'``;
refactored to fit with AnalysisBase API
.. versionchanged:: 0.17.0
Deprecated keyword `mass_weighted` was removed.
"""
if align:
self.u_fitted = self.fit_to_reference(
filename=filename, postfix=postfix,
rmsdfile=rmsdfile, targetdir=targetdir,
weights=weights, tol_mass=0.1)
self.path = self.to_path(fitted=align, flat=flat)
return self.top_name, self.newtrj_name
[docs]
def get_num_atoms(self):
"""Return the number of atoms used to construct the :class:`Path`.
Must run :meth:`Path.to_path` prior to calling this method.
Returns
-------
int
the number of atoms in the :class:`Path`
"""
if self.natoms is None:
raise ValueError("No path data; do 'Path.to_path()' first.")
return self.natoms
[docs]
class PSAPair(object):
"""Generate nearest neighbor and Hausdorff pair information between a pair
of paths from an all-pairs comparison generated by :class:`PSA`.
The nearest neighbors for each path of a pair of paths is generated by
:meth:`PSAPair.compute_nearest_neighbors` and stores the result
in a dictionary (:attr:`nearest_neighbors`): each path has a
:class:`numpy.ndarray` of the frames of its nearest neighbors, and a
:class:`numpy.ndarray` of its nearest neighbor distances
:attr:`PSAnalysis.D`. For example, *nearest_neighbors['frames']* is a pair
of :class:`numpy.ndarray`, the first being the frames of the nearest
neighbors of the first path, *i*, the second being those of the second path,
*j*.
The Hausdorff pair for the pair of paths is found by calling
:meth:`find_hausdorff_pair` (locates the nearest neighbor pair having the
largest overall distance separating them), which stores the result in a
dictionary (:attr:`hausdorff_pair`) containing the frames (indices) of the
pair along with the corresponding (Hausdorff) distance.
*hausdorff_pair['frame']* contains a pair of frames in the first path, *i*,
and the second path, *j*, respectively, that correspond to the Hausdorff
distance between them.
.. versionadded:: 0.11
"""
def __init__(self, npaths, i, j):
"""Set up a :class:`PSAPair` for a pair of paths that are part of a
:class:`PSA` comparison of *npaths* total paths.
Each unique pair of paths compared using :class:`PSA` is related by
their nearest neighbors (and corresponding distances) and the Hausdorff
pair and distance. :class:`PSAPair` is a convenience class for
calculating and encapsulating nearest neighbor and Hausdorff pair
information for one pair of paths.
Given *npaths*, :class:`PSA` performs and all-pairs comparison among all
paths for a total of :math:`\text{npaths}*(\text{npaths}-1)/2` unique
comparisons. If distances between paths are computed, the all-pairs
comparison can be summarized in a symmetric distance matrix whose upper
triangle can be mapped to a corresponding distance vector form in a
one-to-one manner. A particular comparison of a pair of paths in a
given instance of :class:`PSAPair` is thus unique identified by the row
and column indices in the distance matrix representation (whether or not
distances are actually computed), or a single ID (index) in the
corresponding distance vector.
Parameters
----------
npaths : int
total number of paths in :class:`PSA` used to generate *this*
:class:`PSAPair`
i : int
row index (starting at 0) of the distance matrix
j : int
column index (starting at 0) of the distance matrix
"""
self.npaths = npaths
self.matrix_idx = (i,j)
self.pair_idx = self._dvec_idx(i,j)
# Set by calling hausdorff_nn
self.nearest_neighbors = {'frames' : None, 'distances' : None}
# Set by self.getHausdorffPair
self.hausdorff_pair = {'frames' : (None, None), 'distance' : None}
def _dvec_idx(self, i, j):
"""Convert distance matrix indices (in the upper triangle) to the index
of the corresponding distance vector.
This is a convenience function to locate distance matrix elements (and
the pair generating it) in the corresponding distance vector. The row
index *j* should be greater than *i+1*, corresponding to the upper
triangle of the distance matrix.
Parameters
----------
i : int
row index (starting at 0) of the distance matrix
j : int
column index (starting at 0) of the distance matrix
Returns
-------
int
(matrix element) index in the corresponding distance vector
"""
return (self.npaths*i) + j - (i+2)*(i+1)/2
def compute_nearest_neighbors(self, P,Q, N=None):
"""Generates Hausdorff nearest neighbor lists of *frames* (by index) and
*distances* for *this* pair of paths corresponding to distance matrix
indices (*i*,*j*).
:meth:`PSAPair.compute_nearest_neighbors` calls
:func:`hausdorff_neighbors` to populate the dictionary of the nearest
neighbor lists of frames (by index) and distances
(:attr:`PSAPair.nearest_neighbors`). This method must explicitly take as
arguments a pair of paths, *P* and *Q*, where *P* is the
:math:`i^\text{th}` path and *Q* is the :math:`j^\text{th}` path among
the set of *N* total paths in the comparison.
Parameters
----------
P : numpy.ndarray
representing a path
Q : numpy.ndarray
representing a path
N : int
size of the distance matrix (of shape *N*-by-*N*) [``None``]
"""
hn = hausdorff_neighbors(P, Q)
self.nearest_neighbors['frames'] = hn['frames']
self.nearest_neighbors['distances'] = hn['distances']
def find_hausdorff_pair(self):
r"""Find the Hausdorff pair (of frames) for *this* pair of paths.
:meth:`PSAPair.find_hausdorff_pair` requires that
`:meth:`PSAPair.compute_nearest_neighbors` be called first to
generate the nearest neighbors (and corresponding distances) for each
path in *this* :class:`PSAPair`. The Hausdorff pair is the nearest
neighbor pair (of snapshots/frames), one in the first path and one in
the second, with the largest separation distance.
"""
if self.nearest_neighbors['distances'] is None:
raise NoDataError("Nearest neighbors have not been calculated yet;"
" run compute_nearest_neighbors() first.")
nn_idx_P, nn_idx_Q = self.nearest_neighbors['frames']
nn_dist_P, nn_dist_Q = self.nearest_neighbors['distances']
max_nn_dist_P = max(nn_dist_P)
max_nn_dist_Q = max(nn_dist_Q)
if max_nn_dist_P > max_nn_dist_Q:
max_nn_idx_P = np.argmax(nn_dist_P)
self.hausdorff_pair['frames'] = max_nn_idx_P, nn_idx_P[max_nn_idx_P]
self.hausdorff_pair['distance'] = max_nn_dist_P
else:
max_nn_idx_Q = np.argmax(nn_dist_Q)
self.hausdorff_pair['frames'] = nn_idx_Q[max_nn_idx_Q], max_nn_idx_Q
self.hausdorff_pair['distance'] = max_nn_dist_Q
def get_nearest_neighbors(self, frames=True, distances=True):
"""Returns the nearest neighbor frame indices, distances, or both, for
each path in *this* :class:`PSAPair`.
:meth:`PSAPair.get_nearest_neighbors` requires that the nearest
neighbors (:attr:`nearest_neighbors`) be initially computed by first
calling :meth:`compute_nearest_neighbors`. At least one of *frames*
or *distances* must be ``True``, or else a ``NoDataError`` is raised.
Parameters
----------
frames : bool
if ``True``, return nearest neighbor frame indices
[``True``]
distances : bool
if ``True``, return nearest neighbor distances [``True``]
Returns
-------
dict or tuple
If both *frames* and *distances* are ``True``, return the entire
dictionary (:attr:`nearest_neighbors`); if only *frames* is
``True``, return a pair of :class:`numpy.ndarray` containing the
indices of the frames (for the pair of paths) of the nearest
neighbors; if only *distances* is ``True``, return a pair of
:class:`numpy.ndarray` of the nearest neighbor distances (for the
pair of paths).
"""
if self.nearest_neighbors['distances'] is None:
raise NoDataError("Nearest neighbors have not been calculated yet;"
" run compute_nearest_neighbors() first.")
if frames:
if distances:
return self.nearest_neighbors
else:
return self.nearest_neighbors['frames']
elif distances:
return self.nearest_neighbors['distances']
else:
raise NoDataError('Need to select Hausdorff pair "frames" or'
' "distances" or both. "frames" and "distances"'
' cannot both be set to False.')
def get_hausdorff_pair(self, frames=True, distance=True):
"""Returns the Hausdorff pair of frames indices, the Hausdorff distance,
or both, for the paths in *this* :class:`PSAPair`.
:meth:`PSAPair.get_hausdorff_pair` requires that the Hausdorff pair
(and distance) be initially found by first calling
:meth:`find_hausdorff_pair`. At least one of *frames* or *distance*
must be ``True``, or else a ``NoDataError`` is raised.
Parameters
----------
frames : bool
if ``True``, return the indices of the frames
of the Hausdorff pair [``True``]
distances : bool
if ``True``, return Hausdorff distance [``True``]
Returns
-------
dict or tuple
If both *frames* and *distance* are ``True``, return the entire
dictionary (:attr:`hausdorff_pair`); if only *frames* is
``True``, return a pair of ``int`` containing the indices of the
frames (one index per path) of the Hausdorff pair; if only *distance*
is ``True``, return the Hausdorff distance for this path pair.
"""
if self.hausdorff_pair['distance'] is None:
raise NoDataError("Hausdorff pair has not been calculated yet;"
" run find_hausdorff_pair() first.")
if frames:
if distance:
return self.hausdorff_pair
else:
return self.hausdorff_pair['frames']
elif distance:
return self.hausdorff_pair['distance']
else:
raise NoDataError('Need to select Hausdorff pair "frames" or'
' "distance" or both. "frames" and "distance"'
' cannot both be set to False.')
[docs]
class PSAnalysis(object):
"""Perform Path Similarity Analysis (PSA) on a set of trajectories.
The analysis is performed with :meth:`PSAnalysis.run` and stores the result
in the :class:`numpy.ndarray` distance matrix :attr:`PSAnalysis.D`.
:meth:`PSAnalysis.run` also generates a fitted trajectory and path from
alignment of the original trajectories to a reference structure.
.. versionadded:: 0.8
.. versionchanged:: 1.0.0
``save_result()`` method has been removed. You can use ``np.save()`` on
:attr:`PSAnalysis.D` instead.
"""
def __init__(self, universes, reference=None, select='name CA',
ref_frame=0, path_select=None, labels=None,
targetdir=os.path.curdir):
"""Setting up Path Similarity Analysis.
The mutual similarity between all unique pairs of trajectories
are computed using a selected path metric.
Parameters
----------
universes : list
a list of universes (:class:`MDAnalysis.Universe` object), each
containing a trajectory
reference : Universe
reference coordinates; :class:`MDAnalysis.Universe` object; if
``None`` the first time step of the first item in `universes` is used
[``None``]
select : str or dict or tuple
The selection to operate on; can be one of:
1. any valid selection string for
:meth:`~MDAnalysis.core.groups.AtomGroup.select_atoms` that
produces identical selections in *mobile* and *reference*; or
2. a dictionary ``{'mobile':sel1, 'reference':sel2}`` (the
:func:`MDAnalysis.analysis.align.fasta2select` function returns
such a dictionary based on a ClustalW_ or STAMP_ sequence
alignment); or
3. a tuple ``(sel1, sel2)``
When using 2. or 3. with *sel1* and *sel2* then these selections
can also each be a list of selection strings (to generate an
AtomGroup with defined atom order as described under
:ref:`ordered-selections-label`).
tol_mass : float
Reject match if the atomic masses for matched atoms differ by more
than *tol_mass* [0.1]
ref_frame : int
frame index to select frame from *reference* [0]
path_select : str
atom selection composing coordinates of (fitted) path; if ``None``
then *path_select* is set to *select* [``None``]
targetdir : str
output files are saved there; if ``None`` then "./psadata" is
created and used [.]
labels : list
list of strings, names of trajectories to be analyzed
(:class:`MDAnalysis.Universe`); if ``None``, defaults to trajectory
names [``None``]
.. _ClustalW: http://www.clustal.org/
.. _STAMP: http://www.compbio.dundee.ac.uk/manuals/stamp.4.2/
"""
self.universes = universes
self.u_reference = self.universes[0] if reference is None else reference
self.select = select
self.ref_frame = ref_frame
self.path_select = self.select if path_select is None else path_select
if targetdir is None:
try:
targetdir = os.path.join(os.path.curdir, 'psadata')
os.makedirs(targetdir)
except OSError:
if not os.path.isdir(targetdir):
raise
self.targetdir = os.path.realpath(targetdir)
# Set default directory names for storing topology/reference structures,
# fitted trajectories, paths, distance matrices, and plots
self.datadirs = {'fitted_trajs' : 'fitted_trajs',
'paths' : 'paths',
'distance_matrices' : 'distance_matrices',
'plots' : 'plots'}
for dir_name, directory in self.datadirs.items():
try:
full_dir_name = os.path.join(self.targetdir, dir_name)
os.makedirs(full_dir_name)
except OSError:
if not os.path.isdir(full_dir_name):
raise
# Keep track of topology, trajectory, and related files
trj_names = []
for i, u in enumerate(self.universes):
head, tail = os.path.split(u.trajectory.filename)
filename, ext = os.path.splitext(tail)
trj_names.append(filename)
self.trj_names = trj_names
self.fit_trj_names = None
self.path_names = None
self.top_name = self.universes[0].filename if len(universes) != 0 else None
self.labels = labels or self.trj_names
# Names of persistence (pickle) files where topology and trajectory
# filenames are stored--should not be modified by user
self._top_pkl = os.path.join(self.targetdir, "psa_top-name.pkl")
self._trjs_pkl = os.path.join(self.targetdir, "psa_orig-traj-names.pkl")
self._fit_trjs_pkl = os.path.join(self.targetdir, "psa_fitted-traj-names.pkl")
self._paths_pkl = os.path.join(self.targetdir, "psa_path-names.pkl")
self._labels_pkl = os.path.join(self.targetdir, "psa_labels.pkl")
# Pickle topology and trajectory filenames for this analysis to curdir
with open(self._top_pkl, 'wb') as output:
pickle.dump(self.top_name, output)
with open(self._trjs_pkl, 'wb') as output:
pickle.dump(self.trj_names, output)
with open(self._labels_pkl, 'wb') as output:
pickle.dump(self.labels, output)
self.natoms = None
self.npaths = None
self.paths = None
self.D = None # pairwise distances
self._HP = None # (distance vector order) list of all Hausdorff pairs
self._NN = None # (distance vector order) list of all nearest neighbors
self._psa_pairs = None # (distance vector order) list of all PSAPairs
[docs]
def generate_paths(self, align=False, filename=None, infix='', weights=None,
tol_mass=False, ref_frame=None, flat=False, save=True, store=False):
"""Generate paths, aligning each to reference structure if necessary.
Parameters
----------
align : bool
Align trajectories to atom selection :attr:`PSAnalysis.select`
of :attr:`PSAnalysis.u_reference` [``False``]
filename : str
strings representing base filename for fitted trajectories and
paths [``None``]
infix : str
additional tag string that is inserted into the output filename of
the fitted trajectory files ['']
weights : {"mass", ``None``} or array_like (optional)
choose weights. With ``"mass"`` uses masses as weights; with
``None`` weigh each atom equally. If a float array of the same
length as the selected AtomGroup is provided, use each element of
the `array_like` as a weight for the corresponding atom in the
AtomGroup [``None``]
tol_mass : float
Reject match if the atomic masses for matched atoms differ by more
than *tol_mass* [``False``]
ref_frame : int
frame index to select frame from *reference* [``None``]
flat : bool
represent :attr:`Path.path` as a 2D (|2D|) :class:`numpy.ndarray`;
if ``False`` then :attr:`Path.path` is a 3D (|3D|)
:class:`numpy.ndarray` [``False``]
save : bool
if ``True``, pickle list of names for fitted trajectories
[``True``]
store : bool
if ``True`` then writes each path (:class:`numpy.ndarray`)
in :attr:`PSAnalysis.paths` to compressed npz (numpy) files
[``False``]
The fitted trajectories are written to new files in the
"/trj_fit" subdirectory in :attr:`PSAnalysis.targetdir` named
"filename(*trajectory*)XXX*infix*_psa", where "XXX" is a number between
000 and 999; the extension of each file is the same as its original.
Optionally, the trajectories can also be saved in numpy compressed npz
format in the "/paths" subdirectory in :attr:`PSAnalysis.targetdir` for
persistence and can be accessed as the attribute
:attr:`PSAnalysis.paths`.
.. deprecated:: 0.16.1
Instead of ``mass_weighted=True`` use new ``weights='mass'``;
refactored to fit with AnalysisBase API
.. versionchanged:: 0.17.0
Deprecated keyword `mass_weighted` was removed.
.. versionchanged:: 1.0.0
Defaults for the `store` and `filename` keywords have been changed
from `True` and `fitted` to `False` and `None` respectively. These
now match the docstring documented defaults.
"""
if ref_frame is None:
ref_frame = self.ref_frame
paths = []
fit_trj_names = []
for i, u in enumerate(self.universes):
p = Path(u, self.u_reference, select=self.select,
path_select=self.path_select, ref_frame=ref_frame)
trj_dir = os.path.join(self.targetdir, self.datadirs['fitted_trajs'])
postfix = '{0}{1}{2:03n}'.format(infix, '_psa', i+1)
top_name, fit_trj_name = p.run(align=align, filename=filename,
postfix=postfix,
targetdir=trj_dir,
weights=weights,
tol_mass=tol_mass, flat=flat)
paths.append(p.path)
fit_trj_names.append(fit_trj_name)
self.natoms, axis = get_coord_axes(paths[0])
self.paths = paths
self.npaths = len(paths)
self.fit_trj_names = fit_trj_names
if save:
with open(self._fit_trjs_pkl, 'wb') as output:
pickle.dump(self.fit_trj_names, output)
if store:
self.save_paths(filename=filename)
[docs]
def run(self, **kwargs):
"""Perform path similarity analysis on the trajectories to compute
the distance matrix.
A number of parameters can be changed from the defaults. The
result is stored as the array :attr:`PSAnalysis.D`.
Parameters
----------
metric : str or callable
selection string specifying the path metric to measure pairwise
distances among :attr:`PSAnalysis.paths` or a callable with the
same call signature as :func:`hausdorff`
[``'hausdorff'``]
start : int
`start` and `stop` frame index with `step` size: analyze
``trajectory[start:stop:step]`` [``None``]
stop : int
step : int
.. versionchanged:: 1.0.0
`store` and `filename` have been removed.
"""
metric = kwargs.pop('metric', 'hausdorff')
start = kwargs.pop('start', None)
stop = kwargs.pop('stop', None)
step = kwargs.pop('step', None)
if isinstance(metric, str):
metric_func = get_path_metric_func(str(metric))
else:
metric_func = metric
numpaths = self.npaths
D = np.zeros((numpaths,numpaths))
for i in range(0, numpaths-1):
for j in range(i+1, numpaths):
P = self.paths[i][start:stop:step]
Q = self.paths[j][start:stop:step]
D[i,j] = metric_func(P, Q)
D[j,i] = D[i,j]
self.D = D
[docs]
def run_pairs_analysis(self, **kwargs):
"""Perform PSA Hausdorff (nearest neighbor) pairs analysis on all unique
pairs of paths in :attr:`PSAnalysis.paths`.
Partial results can be stored in separate lists, where each list is
indexed according to distance vector convention (i.e., element *(i,j)*
in distance matrix representation corresponds to element
:math:`s=N*i+j-(i+1)*(i+2)` in distance vector representation, which is
the :math:`s`:sup:`th` comparison). For each unique pair of paths, the
nearest neighbors for that pair can be stored in :attr:`NN` and the
Hausdorff pair in :attr:`HP`. :attr:`PP` stores the full information
of Hausdorff pairs analysis that is available for each pair of path,
including nearest neighbors lists and the Hausdorff pairs.
The pairwise distances are stored as the array :attr:`PSAnalysis.D`.
Parameters
----------
start : int
`start` and `stop` frame index with `step` size: analyze
``trajectory[start:stop:step]`` [``None``]
stop : int
step : int
neighbors : bool
if ``True``, then stores dictionary of nearest neighbor
frames/distances in :attr:`PSAnalysis.NN` [``False``]
hausdorff_pairs : bool
if ``True``, then stores dictionary of Hausdorff pair
frames/distances in :attr:`PSAnalysis.HP` [``False``]
"""
start = kwargs.pop('start', None)
stop = kwargs.pop('stop', None)
step = kwargs.pop('step', None)
neighbors = kwargs.pop('neighbors', False)
hausdorff_pairs = kwargs.pop('hausdorff_pairs', False)
numpaths = self.npaths
D = np.zeros((numpaths,numpaths))
self._NN = [] # list of nearest neighbors pairs
self._HP = [] # list of Hausdorff pairs
self._psa_pairs = [] # list of PSAPairs
for i in range(0, numpaths-1):
for j in range(i+1, numpaths):
pp = PSAPair(i, j, numpaths)
P = self.paths[i][start:stop:step]
Q = self.paths[j][start:stop:step]
pp.compute_nearest_neighbors(P, Q, self.natoms)
pp.find_hausdorff_pair()
D[i,j] = pp.hausdorff_pair['distance']
D[j,i] = D[i,j]
self._psa_pairs.append(pp)
if neighbors:
self._NN.append(pp.get_nearest_neighbors())
if hausdorff_pairs:
self._HP.append(pp.get_hausdorff_pair())
self.D = D
[docs]
def save_paths(self, filename=None):
"""Save fitted :attr:`PSAnalysis.paths` to numpy compressed npz files.
The data are saved with :func:`numpy.savez_compressed` in the directory
specified by :attr:`PSAnalysis.targetdir`.
Parameters
----------
filename : str
specifies filename [``None``]
Returns
-------
filename : str
See Also
--------
load
"""
filename = filename or 'path_psa'
head = os.path.join(self.targetdir, self.datadirs['paths'])
outfile = os.path.join(head, filename)
if self.paths is None:
raise NoDataError("Paths have not been calculated yet")
path_names = []
for i, path in enumerate(self.paths):
current_outfile = "{0}{1:03n}.npy".format(outfile, i+1)
np.save(current_outfile, self.paths[i])
path_names.append(current_outfile)
logger.info("Wrote path to file %r", current_outfile)
self.path_names = path_names
with open(self._paths_pkl, 'wb') as output:
pickle.dump(self.path_names, output)
return filename
[docs]
def load(self):
"""Load fitted paths specified by 'psa_path-names.pkl' in
:attr:`PSAnalysis.targetdir`.
All filenames are determined by :class:`PSAnalysis`.
See Also
--------
save_paths
"""
if not os.path.exists(self._paths_pkl):
raise NoDataError("Fitted trajectories cannot be loaded; save file" +
"{0} does not exist.".format(self._paths_pkl))
self.path_names = np.load(self._paths_pkl, allow_pickle=True)
self.paths = [np.load(pname) for pname in self.path_names]
if os.path.exists(self._labels_pkl):
self.labels = np.load(self._labels_pkl, allow_pickle=True)
logger.info("Loaded paths from %r", self._paths_pkl)
[docs]
def plot(self, filename=None, linkage='ward', count_sort=False,
distance_sort=False, figsize=4.5, labelsize=12):
"""Plot a clustered distance matrix.
Usese method *linkage* and plots the corresponding dendrogram. Rows
(and columns) are identified using the list of strings specified by
:attr:`PSAnalysis.labels`.
If `filename` is supplied then the figure is also written to file (the
suffix determines the file type, e.g. pdf, png, eps, ...). All other
keyword arguments are passed on to :func:`matplotlib.pyplot.matshow`.
Parameters
----------
filename : str
save figure to *filename* [``None``]
linkage : str
name of linkage criterion for clustering [``'ward'``]
count_sort : bool
see :func:`scipy.cluster.hierarchy.dendrogram` [``False``]
distance_sort : bool
see :func:`scipy.cluster.hierarchy.dendrogram` [``False``]
figsize : float
set the vertical size of plot in inches [``4.5``]
labelsize : float
set the font size for colorbar labels; font size for path labels on
dendrogram default to 3 points smaller [``12``]
Returns
-------
Z
`Z` from :meth:`cluster`
dgram
`dgram` from :meth:`cluster`
dist_matrix_clus
clustered distance matrix (reordered)
.. versionchanged:: 1.0.0
:attr:`tick1On`, :attr:`tick2On`, :attr:`label1On` and :attr:`label2On`
changed to :attr:`tick1line`, :attr:`tick2line`, :attr:`label1` and
:attr:`label2` due to upstream deprecation (see #2493)
"""
from matplotlib.pyplot import figure, colorbar, cm, savefig, clf
if self.D is None:
raise ValueError(
"No distance data; do 'PSAnalysis.run()' first.")
npaths = len(self.D)
dist_matrix = self.D
dgram_loc, hmap_loc, cbar_loc = self._get_plot_obj_locs()
aspect_ratio = 1.25
clf()
fig = figure(figsize=(figsize*aspect_ratio, figsize))
ax_hmap = fig.add_axes(hmap_loc)
ax_dgram = fig.add_axes(dgram_loc)
Z, dgram = self.cluster(method=linkage, \
count_sort=count_sort, \
distance_sort=distance_sort)
rowidx = colidx = dgram['leaves'] # get row-wise ordering from clustering
ax_dgram.invert_yaxis() # Place origin at up left (from low left)
minDist, maxDist = 0, np.max(dist_matrix)
dist_matrix_clus = dist_matrix[rowidx,:]
dist_matrix_clus = dist_matrix_clus[:,colidx]
im = ax_hmap.matshow(dist_matrix_clus, aspect='auto', origin='lower', \
cmap=cm.YlGn, vmin=minDist, vmax=maxDist)
ax_hmap.invert_yaxis() # Place origin at upper left (from lower left)
ax_hmap.locator_params(nbins=npaths)
ax_hmap.set_xticks(np.arange(npaths), minor=True)
ax_hmap.set_yticks(np.arange(npaths), minor=True)
ax_hmap.tick_params(axis='x', which='both', labelleft='off', \
labelright='off', labeltop='on', labelsize=0)
ax_hmap.tick_params(axis='y', which='both', labelleft='on', \
labelright='off', labeltop='off', labelsize=0)
rowlabels = [self.labels[i] for i in rowidx]
collabels = [self.labels[i] for i in colidx]
ax_hmap.set_xticklabels(collabels, rotation='vertical', \
size=(labelsize-4), multialignment='center', minor=True)
ax_hmap.set_yticklabels(rowlabels, rotation='horizontal', \
size=(labelsize-4), multialignment='left', ha='right', \
minor=True)
ax_color = fig.add_axes(cbar_loc)
colorbar(im, cax=ax_color, ticks=np.linspace(minDist, maxDist, 10), \
format="%0.1f")
ax_color.tick_params(labelsize=labelsize)
# Remove major ticks and labels from both heat map axes
for tic in ax_hmap.xaxis.get_major_ticks():
tic.tick1line.set_visible(False)
tic.tick2line.set_visible(False)
tic.label1.set_visible(False)
tic.label2.set_visible(False)
for tic in ax_hmap.yaxis.get_major_ticks():
tic.tick1line.set_visible(False)
tic.tick2line.set_visible(False)
tic.label1.set_visible(False)
tic.label2.set_visible(False)
# Remove minor ticks from both heat map axes
for tic in ax_hmap.xaxis.get_minor_ticks():
tic.tick1line.set_visible(False)
tic.tick2line.set_visible(False)
for tic in ax_hmap.yaxis.get_minor_ticks():
tic.tick1line.set_visible(False)
tic.tick2line.set_visible(False)
# Remove tickmarks from colorbar
for tic in ax_color.yaxis.get_major_ticks():
tic.tick1line.set_visible(False)
tic.tick2line.set_visible(False)
if filename is not None:
head = os.path.join(self.targetdir, self.datadirs['plots'])
outfile = os.path.join(head, filename)
savefig(outfile, dpi=300, bbox_inches='tight')
return Z, dgram, dist_matrix_clus
[docs]
def plot_annotated_heatmap(self, filename=None, linkage='ward', \
count_sort=False, distance_sort=False, \
figsize=8, annot_size=6.5):
"""Plot a clustered distance matrix.
Uses method `linkage` and plots annotated distances in the matrix. Rows
(and columns) are identified using the list of strings specified by
:attr:`PSAnalysis.labels`.
If `filename` is supplied then the figure is also written to file (the
suffix determines the file type, e.g. pdf, png, eps, ...). All other
keyword arguments are passed on to :func:`matplotlib.pyplot.imshow`.
Parameters
----------
filename : str
save figure to *filename* [``None``]
linkage : str
name of linkage criterion for clustering [``'ward'``]
count_sort : bool
see :func:`scipy.cluster.hierarchy.dendrogram` [``False``]
distance_sort : bool
see :func:`scipy.cluster.hierarchy.dendrogram` [``False``]
figsize : float
set the vertical size of plot in inches [``4.5``]
annot_size : float
font size of annotation labels on heat map [``6.5``]
Returns
-------
Z
`Z` from :meth:`cluster`
dgram
`dgram` from :meth:`cluster`
dist_matrix_clus
clustered distance matrix (reordered)
Note
----
This function requires the seaborn_ package, which can be installed
with `pip install seaborn` or `conda install seaborn`.
.. _seaborn: https://seaborn.pydata.org/
.. versionchanged:: 1.0.0
:attr:`tick1On`, :attr:`tick2On`, :attr:`label1On` and :attr:`label2On`
changed to :attr:`tick1line`, :attr:`tick2line`, :attr:`label1` and
:attr:`label2` due to upstream deprecation (see #2493)
"""
from matplotlib.pyplot import figure, colorbar, cm, savefig, clf
try:
import seaborn as sns
except ImportError:
raise ImportError(
"""ERROR --- The seaborn package cannot be found!
The seaborn API could not be imported. Please install it first.
You can try installing with pip directly from the
internet:
pip install seaborn
Alternatively, download the package from
http://pypi.python.org/pypi/seaborn/
and install in the usual manner.
"""
) from None
if self.D is None:
raise ValueError(
"No distance data; do 'PSAnalysis.run()' first.")
dist_matrix = self.D
Z, dgram = self.cluster(method=linkage, \
count_sort=count_sort, \
distance_sort=distance_sort, \
no_plot=True)
rowidx = colidx = dgram['leaves'] # get row-wise ordering from clustering
dist_matrix_clus = dist_matrix[rowidx,:]
dist_matrix_clus = dist_matrix_clus[:,colidx]
clf()
aspect_ratio = 1.25
fig = figure(figsize=(figsize*aspect_ratio, figsize))
ax_hmap = fig.add_subplot(111)
ax_hmap = sns.heatmap(dist_matrix_clus, \
linewidths=0.25, cmap=cm.YlGn, annot=True, fmt='3.1f', \
square=True, xticklabels=rowidx, yticklabels=colidx, \
annot_kws={"size": 7}, ax=ax_hmap)
# Remove major ticks from both heat map axes
for tic in ax_hmap.xaxis.get_major_ticks():
tic.tick1line.set_visible(False)
tic.tick2line.set_visible(False)
tic.label1.set_visible(False)
tic.label2.set_visible(False)
for tic in ax_hmap.yaxis.get_major_ticks():
tic.tick1line.set_visible(False)
tic.tick2line.set_visible(False)
tic.label1.set_visible(False)
tic.label2.set_visible(False)
# Remove minor ticks from both heat map axes
for tic in ax_hmap.xaxis.get_minor_ticks():
tic.tick1line.set_visible(False)
tic.tick2line.set_visible(False)
for tic in ax_hmap.yaxis.get_minor_ticks():
tic.tick1line.set_visible(False)
tic.tick2line.set_visible(False)
if filename is not None:
head = os.path.join(self.targetdir, self.datadirs['plots'])
outfile = os.path.join(head, filename)
savefig(outfile, dpi=600, bbox_inches='tight')
return Z, dgram, dist_matrix_clus
[docs]
def plot_nearest_neighbors(self, filename=None, idx=0, \
labels=('Path 1', 'Path 2'), figsize=4.5, \
multiplot=False, aspect_ratio=1.75, \
labelsize=12):
"""Plot nearest neighbor distances as a function of normalized frame
number.
The frame number is mapped to the interval *[0, 1]*.
If `filename` is supplied then the figure is also written to file (the
suffix determines the file type, e.g. pdf, png, eps, ...). All other
keyword arguments are passed on to :func:`matplotlib.pyplot.imshow`.
Parameters
----------
filename : str
save figure to *filename* [``None``]
idx : int
index of path (pair) comparison to plot [``0``]
labels : (str, str)
pair of names to label nearest neighbor distance
curves [``('Path 1', 'Path 2')``]
figsize : float
set the vertical size of plot in inches [``4.5``]
multiplot : bool
set to ``True`` to enable plotting multiple nearest
neighbor distances on the same figure [``False``]
aspect_ratio : float
set the ratio of width to height of the plot [``1.75``]
labelsize : float
set the font size for colorbar labels; font size for path labels on
dendrogram default to 3 points smaller [``12``]
Returns
-------
ax : axes
Note
----
This function requires the seaborn_ package, which can be installed
with `pip install seaborn` or `conda install seaborn`.
.. _seaborn: https://seaborn.pydata.org/
"""
from matplotlib.pyplot import figure, savefig, tight_layout, clf, show
try:
import seaborn as sns
except ImportError:
raise ImportError(
"""ERROR --- The seaborn package cannot be found!
The seaborn API could not be imported. Please install it first.
You can try installing with pip directly from the
internet:
pip install seaborn
Alternatively, download the package from
http://pypi.python.org/pypi/seaborn/
and install in the usual manner.
"""
) from None
colors = sns.xkcd_palette(["cherry", "windows blue"])
if self._NN is None:
raise ValueError("No nearest neighbor data; run "
"'PSAnalysis.run_pairs_analysis(neighbors=True)' first.")
sns.set_style('whitegrid')
if not multiplot:
clf()
fig = figure(figsize=(figsize*aspect_ratio, figsize))
ax = fig.add_subplot(111)
nn_dist_P, nn_dist_Q = self._NN[idx]['distances']
frames_P = len(nn_dist_P)
frames_Q = len(nn_dist_Q)
progress_P = np.asarray(range(frames_P))/(1.0*frames_P)
progress_Q = np.asarray(range(frames_Q))/(1.0*frames_Q)
ax.plot(progress_P, nn_dist_P, color=colors[0], lw=1.5, label=labels[0])
ax.plot(progress_Q, nn_dist_Q, color=colors[1], lw=1.5, label=labels[1])
ax.legend()
ax.set_xlabel(r'(normalized) progress by frame number', fontsize=12)
ax.set_ylabel(r'nearest neighbor rmsd ($\AA$)', fontsize=12)
ax.tick_params(axis='both', which='major', labelsize=12, pad=4)
sns.despine(bottom=True, left=True, ax=ax)
tight_layout()
if filename is not None:
head = os.path.join(self.targetdir, self.datadirs['plots'])
outfile = os.path.join(head, filename)
savefig(outfile, dpi=300, bbox_inches='tight')
return ax
[docs]
def cluster(self, dist_mat=None, method='ward', count_sort=False, \
distance_sort=False, no_plot=False, no_labels=True, \
color_threshold=4):
"""Cluster trajectories and optionally plot the dendrogram.
This method is used by :meth:`PSAnalysis.plot` to generate a heatmap-
dendrogram combination plot. By default, the distance matrix,
:attr:`PSAnalysis.D`, is assumed to exist, converted to
distance-vector form, and inputted to :func:`cluster.hierarchy.linkage`
to generate a clustering. For convenience in plotting arbitrary
distance matrices, one can also be specify `dist_mat`, which will be
checked for proper distance matrix form by
:func:`spatial.distance.squareform`
Parameters
----------
dist_mat : numpy.ndarray
user-specified distance matrix to be clustered [``None``]
method : str
name of linkage criterion for clustering [``'ward'``]
no_plot : bool
if ``True``, do not render the dendrogram [``False``]
no_labels : bool
if ``True`` then do not label dendrogram [``True``]
color_threshold : float
For brevity, let t be the color_threshold. Colors all the
descendent links below a cluster node k the same color if k is
the first node below the cut threshold t. All links connecting
nodes with distances greater than or equal to the threshold are
colored blue. If t is less than or equal to zero, all nodes are
colored blue. If color_threshold is None or ‘default’,
corresponding with MATLAB(TM) behavior, the threshold is set to
0.7*max(Z[:,2]). [``4``]]
Returns
-------
Z
output from :func:`scipy.cluster.hierarchy.linkage`;
list of indices representing the row-wise order of the objects
after clustering
dgram
output from :func:`scipy.cluster.hierarchy.dendrogram`
"""
# perhaps there is a better way to manipulate the plot... or perhaps it
# is not even necessary? In any case, the try/finally makes sure that
# we are not permanently changing the user's global state
orig_linewidth = matplotlib.rcParams['lines.linewidth']
matplotlib.rcParams['lines.linewidth'] = 0.5
try:
if dist_mat:
dist_vec = spatial.distance.squareform(dist_mat,
force='tovector',
checks=True)
else:
dist_vec = self.get_pairwise_distances(vectorform=True)
Z = cluster.hierarchy.linkage(dist_vec, method=method)
dgram = cluster.hierarchy.dendrogram(
Z, no_labels=no_labels, orientation='left',
count_sort=count_sort, distance_sort=distance_sort,
no_plot=no_plot, color_threshold=color_threshold)
finally:
matplotlib.rcParams['lines.linewidth'] = orig_linewidth
return Z, dgram
def _get_plot_obj_locs(self):
"""Find and return coordinates for dendrogram, heat map, and colorbar.
Returns
-------
tuple
tuple of coordinates for placing the dendrogram, heat map, and
colorbar in the plot.
"""
plot_xstart = 0.04
plot_ystart = 0.04
label_margin = 0.155
dgram_height = 0.2 # dendrogram heights(s)
hmap_xstart = plot_xstart + dgram_height + label_margin
# Set locations for dendrogram(s), matrix, and colorbar
hmap_height = 0.8
hmap_width = 0.6
dgram_loc = [plot_xstart, plot_ystart, dgram_height, hmap_height]
cbar_width = 0.02
cbar_xstart = hmap_xstart + hmap_width + 0.01
cbar_loc = [cbar_xstart, plot_ystart, cbar_width, hmap_height]
hmap_loc = [hmap_xstart, plot_ystart, hmap_width, hmap_height]
return dgram_loc, hmap_loc, cbar_loc
[docs]
def get_num_atoms(self):
"""Return the number of atoms used to construct the :class:`Path` instances in
:class:`PSA`.
Returns
-------
int
the number of atoms in any path
Note
----
Must run :meth:`PSAnalysis.generate_paths` prior to calling this
method.
"""
if self.natoms is None:
raise ValueError(
"No path data; do 'PSAnalysis.generate_paths()' first.")
return self.natoms
[docs]
def get_num_paths(self):
"""Return the number of paths in :class:`PSA`.
Note
----
Must run :meth:`PSAnalysis.generate_paths` prior to calling this method.
Returns
-------
int
the number of paths in :class:`PSA`
"""
if self.npaths is None:
raise ValueError(
"No path data; do 'PSAnalysis.generate_paths()' first.")
return self.npaths
[docs]
def get_paths(self):
"""Return the paths in :class:`PSA`.
Note
----
Must run :meth:`PSAnalysis.generate_paths` prior to calling this
method.
Returns
-------
list
list of :class:`numpy.ndarray` representations of paths in
:class:`PSA`
"""
if self.paths is None:
raise ValueError(
"No path data; do 'PSAnalysis.generate_paths()' first.")
return self.paths
[docs]
def get_pairwise_distances(self, vectorform=False, checks=False):
"""Return the distance matrix (or vector) of pairwise path distances.
Note
----
Must run :meth:`PSAnalysis.run` prior to calling this method.
Parameters
----------
vectorform : bool
if ``True``, return the distance vector instead [``False``]
checks : bool
if ``True``, check that :attr:`PSAnalysis.D` is a proper distance
matrix [``False``]
Returns
-------
numpy.ndarray
representation of the distance matrix (or vector)
"""
if self.D is None:
raise ValueError(
"No distance data; do 'PSAnalysis.run()' first.")
if vectorform:
return spatial.distance.squareform(self.D, force='tovector',
checks=checks)
else:
return self.D
@property
def psa_pairs(self):
"""The list of :class:`PSAPair` instances for each pair of paths.
:attr:`psa_pairs` is a list of all :class:`PSAPair` objects (in
distance vector order). The elements of a :class:`PSAPair` are pairs of
paths that have been compared using
:meth:`PSAnalysis.run_pairs_analysis`. Each :class:`PSAPair` contains
nearest neighbor and Hausdorff pair information specific to a pair of
paths. The nearest neighbor frames and distances for a :class:`PSAPair`
can be accessed in the nearest neighbor dictionary using the keys
'frames' and 'distances', respectively. E.g.,
:attr:`PSAPair.nearest_neighbors['distances']` returns a *pair* of
:class:`numpy.ndarray` corresponding to the nearest neighbor distances
for each path. Similarly, Hausdorff pair information can be accessed
using :attr:`PSAPair.hausdorff_pair` with the keys 'frames' and
'distance'.
Note
----
Must run :meth:`PSAnalysis.run_pairs_analysis` prior to calling this
method.
"""
if self._psa_pairs is None:
raise ValueError("No nearest neighbors data; do"
" 'PSAnalysis.run_pairs_analysis()' first.")
return self._psa_pairs
@property
def hausdorff_pairs(self):
"""The Hausdorff pair for each (unique) pairs of paths.
This attribute contains a list of Hausdorff pair information (in
distance vector order), where each element is a dictionary containing
the pair of frames and the (Hausdorff) distance between a pair of
paths. See :meth:`PSAnalysis.psa_pairs` and
:attr:`PSAPair.hausdorff_pair` for more information about accessing
Hausdorff pair data.
Note
----
Must run :meth:`PSAnalysis.run_pairs_analysis` with
``hausdorff_pairs=True`` prior to calling this method.
"""
if self._HP is None:
raise ValueError("No Hausdorff pairs data; do "
"'PSAnalysis.run_pairs_analysis(hausdorff_pairs=True)' "
"first.")
return self._HP
@property
def nearest_neighbors(self):
"""The nearest neighbors for each (unique) pair of paths.
This attribute contains a list of nearest neighbor information (in
distance vector order), where each element is a dictionary containing
the nearest neighbor frames and distances between a pair of paths. See
:meth:`PSAnalysis.psa_pairs` and :attr:`PSAPair.nearest_neighbors` for
more information about accessing nearest neighbor data.
Note
----
Must run :meth:`PSAnalysis.run_pairs_analysis` with
``neighbors=True`` prior to calling this method.
"""
if self._NN is None:
raise ValueError("No nearest neighbors data; do"
" 'PSAnalysis.run_pairs_analysis(neighbors=True)'"
" first.")
return self._NN