Source code for MDAnalysis.analysis.psa

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# 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.
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# MDAnalysis: A Toolkit for the Analysis of Molecular Dynamics Simulations.
# J. Comput. Chem. 32 (2011), 2319--2327, doi:10.1002/jcc.21787
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r"""
Calculating path similarity --- :mod:`MDAnalysis.analysis.psa`
==========================================================================

:Author: Sean Seyler
:Year: 2015
:Copyright: GNU Public License v3

.. 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
[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.


.. Rubric:: References


.. [Seyler2015] Seyler SL, Kumar A, Thorpe MF, Beckstein O (2015)
                Path Similarity Analysis: A Method for Quantifying
                Macromolecular Pathways. PLoS Comput Biol 11(10): e1004568.
                doi: `10.1371/journal.pcbi.1004568`_

.. _`10.1371/journal.pcbi.1004568`: http://dx.doi.org/10.1371/journal.pcbi.1004568
.. _`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` whichs store 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`

"""
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
from MDAnalysis.lib.util import deprecate

import logging
logger = logging.getLogger('MDAnalysis.analysis.psa')


from ..due import due, Doi

due.cite(Doi("10.1371/journal.pcbi.1004568"),
         description="Path Similarity Analysis algorithm and implementation",
         path="MDAnalysis.analysis.psa",
         cite_module=True)
del Doi


[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: >>> from MDAnalysis.tests.datafiles import PSF, DCD >>> u = Universe(PSF,DCD) >>> mid = 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 >>> hausdorff(P,Q) 4.7786639840135905 >>> hausdorff(P,Q[::-1]) # hausdorff distance w/ reversed 2nd trajectory 4.7786639840135905 Notes ----- :func:`scipy.spatial.distance.directed_hausdorff` is an optimized implementation of the early break algorithm of [Taha2015]_; the latter code is used here to calculate the symmetric Hausdorff distance with an RMSD metric References ---------- .. [Taha2015] A. A. Taha and A. Hanbury. An efficient algorithm for calculating the exact Hausdorff distance. IEEE Transactions On Pattern Analysis And Machine Intelligence, 37:2153-63, 2015. """ 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 ------- >>> from MDAnalysis import Universe >>> from MDAnalysis.tests.datafiles import PSF, DCD >>> u = Universe(PSF,DCD) >>> mid = 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 >>> hausdorff_wavg(P,Q) 2.5669644353703447 >>> 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 [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 ------- >>> from MDAnalysis.tests.datafiles import PSF, DCD >>> u = Universe(PSF,DCD) >>> mid = 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 >>> hausdorff_avg(P,Q) 2.5669646575869005 >>> 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 [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 [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. >>> u = Universe(PSF,DCD) >>> mid = 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 >>> discrete_frechet(P,Q) 4.7786639840135905 >>> discrete_frechet(P,Q[::-1]) # frechet distance w/ 2nd trj reversed 2nd 6.8429011177113832 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 [Frechet1906]_ [Alt1995]_. The calculation of the continuous Fréchet distance is implemented with the dynamic programming algorithm of [EiterMannila1994]_ [EiterMannila1997]_. References ---------- .. [Frechet1906] M. Fréchet. Sur quelques points du calcul fonctionnel. Rend. Circ. Mat. Palermo, 22(1):1–72, Dec. 1906. .. [Alt1995] H. Alt and M. Godau. Computing the Fréchet distance between two polygonal curves. Int J Comput Geometry & Applications, 5(01n02):75–91, 1995. doi: `10.1142/S0218195995000064`_ .. _`10.1142/S0218195995000064`: http://doi.org/10.1142/S0218195995000064 .. [EiterMannila1994] T. Eiter and H. Mannila. Computing discrete Fréchet distance. Technical Report CD-TR 94/64, Christian Doppler Laboratory for Expert Systems, Technische Universität Wien, Wien, 1994. .. [EiterMannila1997] T. Eiter and H. Mannila. Distance measures for point sets and their computation. Acta Informatica, 34:109–133, 1997. doi: `10.1007/s002360050075`_. .. _10.1007/s002360050075: http://doi.org/10.1007/s002360050075 """ 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^\text{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