Source code for MDAnalysis.analysis.psa

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# MDAnalysis --- http://www.MDAnalysis.org
# Copyright (c) 2006-2015 Naveen Michaud-Agrawal, Elizabeth J. Denning, Oliver Beckstein
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# Released under the GNU Public Licence, v2 or any higher version
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# Please cite your use of MDAnalysis in published work:
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# 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
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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.

.. SeeAlso:: 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:: PDBToBinaryTraj
   :members:

   .. attribute:: universe

      :class:`MDAnalysis.Universe` object with a trajectory

   .. attribute:: frames

      :attr:`MDAnalysis.Universe.trajectory`

   .. attribute:: newname

      string, filename for converted trajectory, including file extension

.. 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:: ref_select

      string, selection for
      :meth:`~MDAnalysis.core.AtomGroup.AtomGroup.select_atoms` to select frame
      from :attr:`Path.u_reference`

   .. attribute:: path_select

      string, selection for
      :meth:`~MDAnalysis.core.AtomGroup.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:: ref_select

      string, selection for
      :meth:`~MDAnalysis.core.AtomGroup.AtomGroup.select_atoms` to select frame
      from :attr:`PSAnalysis.u_reference`

   .. attribute:: path_select

      string, selection for
      :meth:`~MDAnalysis.core.AtomGroup.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:: filename

      string, name of file to store calculated distance matrix
      (:attr:`PSAnalysis.D`)

   .. attribute:: paths

      list of :class:`numpy.ndarray` objects representing the set/ensemble of
      fitted trajectories

   .. attribute:: D

      string, name of file to store calculated distance matrix
      (:attr:`PSAnalysis.D`)


.. 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 six
from six.moves import range, cPickle

import numpy as np

import MDAnalysis
import MDAnalysis.analysis.align
from MDAnalysis import NoDataError

import os

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


[docs]def get_path_metric_func(name): """Selects a path metric function by name. :Arguments: *name* string, name of path metric :Returns: 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: print("Path metric {0} not found. Valid selections: ".format(key)) for name in path_metrics.keys(): print(" \"{0}\"".format(name))
[docs]def sqnorm(v, axis=None): """Compute the sum of squares of elements along specified axes. :Arguments: *v* :class:`numpy.ndarray` of coordinates *axes* None or int or tuple of ints, 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): """Generate the matrix of pairwise mean-squared deviations (MSDs) between all pairs of points in *P* and *Q*, 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., :meth:`MDAnalysis.core.AtomGroup.AtomGroup.coordinates`). The pairwise MSD matrix has dimensions :math:`N_p` by :math:`N_q`. :Arguments: *P* :class:`numpy.ndarray` representing a path *Q* :class:`numpy.ndarray` representing a path :Returns: :class:`numpy.ndarray` of pairwise MSDs between points in *P* and points in *Q* """ return np.asarray([sqnorm(p - Q, axis=axis) for p in P])
[docs]def get_coord_axes(path): """Return the number of atoms and the axes (*axis*) 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. :Arguments: *path* :class:`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: err_str = "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.".format(N) raise ValueError(err_str) return N, axis
[docs]def hausdorff(P, Q): r"""Calculate the 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., :meth:`MDAnalysis.core.AtomGroup.AtomGroup.coordinates`). *P* (*Q*) has either shape |3Dp| (|3Dq|), or |2Dp| (|2Dq|) in flattened form. :Arguments: *P* :class:`numpy.ndarray` representing a path *Q* :class:`numpy.ndarray` representing a path :Returns: float, the 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(P,Q) 4.7786639840135905 >>> hausdorff(P,Q[::-1]) # hausdorff distance w/ reversed 2nd trajectory 4.7786639840135905 """ N, axis = get_coord_axes(P) d = get_msd_matrix(P, Q, axis=axis) return ( max( np.amax(np.amin(d, axis=0)), \ np.amax(np.amin(d, axis=1)) ) / N )**0.5
[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., :meth:`MDAnalysis.core.AtomGroup.AtomGroup.coordinates`). *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*. :Arguments: *P* :class:`numpy.ndarray` representing a path *Q* :class:`numpy.ndarray` representing a 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 """ 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., :meth:`MDAnalysis.core.AtomGroup.AtomGroup.coordinates`). *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. :Arguments: *P* :class:`numpy.ndarray` representing a path *Q* :class:`numpy.ndarray` representing a 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 """ 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"""Calculate the Hausdorff distance between two paths. .. |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)` *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., :meth:`MDAnalysis.core.AtomGroup.AtomGroup.coordinates`). *P* (*Q*) has either shape |3Dp| (|3Dq|), or |2Dp| (|2Dq|) in flattened form. :Arguments: *P* :class:`numpy.ndarray` representing a path *Q* :class:`numpy.ndarray` representing a path :Returns: dictionary of two pairs of numpy arrays, the first pair containing the indices of (Hausdorff) nearest neighbors for *P* and *Q*, respectively, the second containing (corresponding) nearest neighbor distances for *P* and *Q*, respectively """ 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 Frechet 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., :meth:`MDAnalysis.core.AtomGroup.AtomGroup.coordinates`). *P* (*Q*) has either shape |3Dp| (|3Dq|), or :|2Dp| (|2Dq|) in flattened form. :Arguments: *P* :class:`numpy.ndarray` representing a path *Q* :class:`numpy.ndarray` representing a path :Returns: float, the discrete Frechet distance between paths *P* and *Q* Example:: >>> 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 """ 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. :Arguments: *i* int, partial path of *P* through final frame *i-1* *j* int, partial path of *Q* through final frame *j-1* :Returns: 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. :Arguments: *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 i > N or j > N: err_str = "Matrix indices are out of range; i and j must be less than" \ + " N = {0:d}".format(N) raise ValueError(err_str) if j > i: return (N*i) + j - (i+2)*(i+1)/2 elif j < i: warn_str = "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" print(warn_str) return (N*j) + i - (j+2)*(j+1)/2 else: err_str = "Error in processing matrix indices; i and j must be integers"\ + " less than integer N = {0:d} such that j >= i+1.".format(N) raise ValueError(err_str)
[docs]class PDBToBinaryTraj(object): def __init__(self, universe, output_type='.dcd', infix=''): self.universe = universe self.universe.atoms.write('new_top.pdb') # write first frame as topology self.frames = self.universe.trajectory base, ext = os.path.splitext(self.frames.filename) path, name = os.path.split(base) self.newname = name + infix + output_type def convert(self): w = MDAnalysis.Writer(self.newname, self.frames.numatoms) for ts in self.frames: w.write(ts) w.close_trajectory()
[docs]class Path(object): """Pre-process a :class:`MDAnalysis.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, ref_select='name CA', path_select='all', ref_frame=0): """Setting up trajectory alignment and fitted path generation. :Arguments: *universe* :class:`MDAnalysis.Universe` object containing a trajectory *reference* reference structure; :class:`MDAnalysis.Universe` object; if ``None`` then *traj* is used (uses the current time step of the object) [``None``] *ref_select* The selection to operate on for rms fitting; can be one of: 1. any valid selection string for :meth:`~MDAnalysis.core.AtomGroup.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`). *path_select* atom selection composing coordinates of (fitted) path; if ``None`` then *path_select* is set to *ref_select* [``None``] .. _ClustalW: http://www.clustal.org/ .. _STAMP: http://www.compbio.dundee.ac.uk/manuals/stamp.4.2/ """ self.u_original = universe self.u_reference = reference self.ref_select = ref_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, mass_weighted=False, tol_mass=0.1): """Align each trajectory frame to the reference structure with :func:`MDAnalysis.analysis.align.rms_fit_trj`. :Arguments: *filename* file name for the RMS-fitted trajectory or pdb; defaults to the original trajectory filename (from :attr:`Path.u_original`) with *prefix* prepended *prefix* prefix for auto-generating the new output filename *rmsdfile* file name for writing the RMSD time series [``None``] *mass_weighted* do a mass-weighted RMSD fit *tol_mass* Reject match if the atomic masses for matched atoms differ by more than *tol_mass* [0.1] :Returns: :class:`MDAnalysis.Universe` object containing a fitted trajectory """ 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 MDAnalysis.analysis.align.rms_fit_trj(self.u_original, self.u_reference,\ select=self.ref_select, filename=self.newtrj_name, \ rmsdfile=rmsdfile, prefix=prefix, mass_weighted=mass_weighted, \ tol_mass=tol_mass) 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). :Arguments: *fitted* 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* 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* 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: :class:`numpy.ndarray` representing a time series of atomic positions of an :class:`MDAnalysis.core.AtomGroup.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, mass_weighted=False, tol_mass=0.1, flat=False): r"""Generate a path from a trajectory and reference structure, aligning 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))``. :Arguments: *align* Align trajectory to atom selection :attr:`Path.ref_select` of :attr:`Path.u_reference`. If ``True``, a universe containing an aligned trajectory is produced with :meth:`Path.fit_to_reference` [``False``] *filename* filename for the RMS-fitted trajectory or pdb; defaults to the original trajectory filename (from :attr:`Path.u_original`) with *prefix* prepended *prefix* prefix for auto-generating the new output filename *rmsdfile* file name for writing the RMSD time series [``None``] *mass_weighted* do a mass-weighted RMSD fit *tol_mass* Reject match if the atomic masses for matched atoms differ by more than *tol_mass* [0.1] *flat* 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: A tuple of the topology name and new trajectory name. """ if align: self.u_fitted = self.fit_to_reference( \ filename=filename, postfix=postfix, \ rmsdfile=rmsdfile, targetdir=targetdir, \ mass_weighted=False, 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 :method:`Path.to_path()` prior to calling this method. :Returns: int, the number of atoms in the :class:`Path` """ if self.natoms is None: err_str = "No path data; do 'Path.to_path()' first." raise ValueError(err_str) 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. :Arguments: *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. :Arguments: *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*). :method:`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. :Arguments: *P* :class:`numpy.ndarray` representing a path *Q* :class:`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. :method:`PSAPair.find_hausdorff_pair` requires that `:method:`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: err_str = "Nearest neighbors have not been calculated yet;" \ + " run compute_nearest_neighbors() first." raise NoDataError(err_str) 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`. :method:`PSAPair.get_nearest_neighbors` requires that the nearest neighbors (:attr:`nearest_neighbors`) be initially computed by first calling :method:`compute_nearest_neighbors`. At least one of *frames* or *distances* must be ``True``, or else a ``NoDataError`` is raised. :Arguments: *frames* boolean; if ``True``, return nearest neighbor frame indices [``True``] *distances* boolean; if ``True``, return nearest neighbor distances [``True``] :Returns: 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: err_str = "Nearest neighbors have not been calculated yet;" \ + " run compute_nearest_neighbors() first." raise NoDataError(err_str) if frames: if distances: return self.nearest_neighbors else: return self.nearest_neighbors['frames'] elif distances: return self.nearest_neighbors['distances'] else: err_str = "Need to select Hausdorff pair \"frames\" or" \ + " \"distances\" or both. \"frames\" and \"distances\" cannot" \ + " both be set to False." raise NoDataError(err_str) 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`. :method:`PSAPair.get_hausdorff_pair` requires that the Hausdorff pair (and distance) be initially found by first calling :method:`find_hausdorff_pair`. At least one of *frames* or *distance* must be ``True``, or else a ``NoDataError`` is raised. :Arguments: *frames* boolean; if ``True``, return the indices of the frames of the Hausdorff pair [``True``] *distances* boolean; if ``True``, return Hausdorff distance [``True``] :Returns: 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: err_str = "Hausdorff pair has not been calculated yet;" \ + " run find_hausdorff_pair() first." raise NoDataError(err_str) if frames: if distance: return self.hausdorff_pair else: return self.hausdorff_pair['frames'] elif distance: return self.hausdorff_pair['distance'] else: err_str = "Need to select Hausdorff pair \"frames\" or" \ + " \"distance\" or both. \"frames\" and \"distance\" cannot" \ + " both be set to False." raise NoDataError(err_str)
[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 """ def __init__(self, universes, reference=None, ref_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. :Arguments: *universes* a list of universes (:class:`MDAnalysis.Universe` object), each containing a trajectory *reference* reference coordinates; :class:`MDAnalysis.Universe` object; if ``None`` the first time step of the first item in *trajs* is used [``None``] *ref_select* The selection to operate on; can be one of: 1. any valid selection string for :meth:`~MDAnalysis.core.AtomGroup.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`). *mass_weighted* do a mass-weighted RMSD fit [``False``] *tol_mass* Reject match if the atomic masses for matched atoms differ by more than *tol_mass* [0.1] *ref_frame* frame index to select frame from *reference* [0] *path_select* atom selection composing coordinates of (fitted) path; if ``None`` then *path_select* is set to *ref_select* [``None``] *targetdir* output files are saved there [.] *labels* list of strings, names of trajectories to be analyzed (:class:`MDAnalysis.Universe`); if ``None``, defaults to trajectory names [``None``] """ self.universes = universes self.u_reference = self.universes[0] if reference is None else reference self.ref_select = ref_select self.ref_frame = ref_frame self.path_select = self.ref_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 six.iteritems(self.datadirs): 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: cPickle.dump(self.top_name, output) with open(self._trjs_pkl, 'wb') as output: cPickle.dump(self.trj_names, output) with open(self._labels_pkl, 'wb') as output: cPickle.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, **kwargs): """Generate paths, aligning each to reference structure if necessary. :Keywords: *align* Align trajectories to atom selection :attr:`PSAnalysis.ref_select` of :attr:`PSAnalysis.u_reference` [``False``] *filename* strings representing base filename for fitted trajectories and paths [``None``] *infix* additional tag string that is inserted into the output filename of the fitted trajectory files [''] *mass_weighted* do a mass-weighted RMSD fit *tol_mass* Reject match if the atomic masses for matched atoms differ by more than *tol_mass* *ref_frame* frame index to select frame from *reference* *flat* 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* boolean; if ``True``, pickle list of names for fitted trajectories [``True``] *store* boolean; 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`. """ align = kwargs.pop('align', False) filename = kwargs.pop('filename', 'fitted') infix = kwargs.pop('infix', '') mass_weighted = kwargs.pop('mass_weighted', False) tol_mass = kwargs.pop('tol_mass', False) ref_frame = kwargs.pop('ref_frame', self.ref_frame) flat = kwargs.pop('flat', False) save = kwargs.pop('save', True) store = kwargs.pop('store', False) paths = [] fit_trj_names = [] for i, u in enumerate(self.universes): p = Path(u, self.u_reference, ref_select=self.ref_select, \ path_select=self.path_select, ref_frame=ref_frame) trj_dir = 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, \ mass_weighted=mass_weighted, \ 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: cPickle.dump(self.fit_trj_names, output) if store: filename = kwargs.pop('filename', None) 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`. :Keywords: *metric* selection string specifying the path metric to measure pairwise distances among :attr:`PSAnalysis.paths` [``'hausdorff'``] *start*, *stop*, *step* start and stop frame index with step size: analyze ``trajectory[start:stop:step]`` [``None``] *store* boolean; if ``True`` then writes :attr:`PSAnalysis.D` to text and compressed npz (numpy) files [``True``] *filename* string, filename to save :attr:`PSAnalysis.D` """ metric = kwargs.pop('metric', 'hausdorff') start = kwargs.pop('start', None) stop = kwargs.pop('stop', None) step = kwargs.pop('step', None) store = kwargs.pop('store', True) if type(metric) is str: metric_func = get_path_metric_func(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 if store: filename = kwargs.pop('filename', str(metric)) self.save_result(filename=filename)
[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. :Keywords: *start*, *stop*, *step* start and stop frame index with step size: analyze ``trajectory[start:stop:step]`` [``None``] *neighbors* boolean; if ``True``, then stores dictionary of nearest neighbor frames/distances in :attr:`PSAnalysis.NN` [``False``] *hausdorff_pairs* boolean; 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 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() self._psa_pairs.append(pp) if neighbors: self._NN.append(pp.get_nearest_neighbors()) if hausdorff_pairs: self._HP.append(pp.get_hausdorff_pair())
[docs] def save_result(self, filename=None): """Save distance matrix :attr:`PSAnalysis.D` to a numpy compressed npz file and text file. :Arguments: *filename* string, specifies filename [``None``] The data are saved with :func:`numpy.savez_compressed` and :func:`numpy.savetxt` in the directory specified by :attr:`PSAnalysis.targetdir`. """ filename = filename or 'psa_distances' head = self.targetdir + self.datadirs['distance_matrices'] outfile = os.path.join(head, filename) if self.D is None: raise NoDataError("Distance matrix has not been calculated yet") np.save(outfile + '.npy', self.D) np.savetxt(outfile + '.dat', self.D) logger.info("Wrote distance matrix to file %r.npz", outfile) logger.info("Wrote distance matrix to file %r.dat", outfile) return filename
[docs] def save_paths(self, filename=None): """Save fitted :attr:`PSAnalysis.paths` to numpy compressed npz files. :Arguments: *filename* string, specifies filename [``None``] The data are saved with :func:`numpy.savez_compressed` in the directory specified by :attr:`PSAnalysis.targetdir`. """ filename = filename or 'path_psa' head = 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: cPickle.dump(self.path_names, output) return filename
[docs] def load(self): """Load fitted paths specified by 'psa_path-names.pkl' in :attr:`PSAnalysis.targetdir`. """ 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) 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) print("Loaded paths from " + 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 using method *linkage* along with the corresponding dendrogram. Rows (and columns) are identified using the list of strings specified by :attr:`PSAnalysis.labels`. :Arguments: *filename* string, save figure to *filename* [``None``] *linkage* string, name of linkage criterion for clustering [``'ward'``] *count_sort* boolean, see scipy.cluster.hierarchy.dendrogram [``False``] *distance_sort* boolean, see scipy.cluster.hierarchy.dendrogram [``False``] *figsize* set the vertical size of plot in inches [``4.5``] *labelsize* set the font size for colorbar labels; font size for path labels on dendrogram default to 3 points smaller [``12``] 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:`pylab.imshow`. """ from matplotlib.pyplot import figure, colorbar, cm, savefig, clf if self.D is None: err_str = "No distance data; do 'PSAnalysis.run(store=True)' first." raise ValueError(err_str) 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(dist_matrix, \ 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 from both heat map axes for tic in ax_hmap.xaxis.get_major_ticks(): tic.tick1On = tic.tick2On = False tic.label1On = tic.label2On = False for tic in ax_hmap.yaxis.get_major_ticks(): tic.tick1On = tic.tick2On = False tic.label1On = tic.label2On = False # Remove minor ticks from both heat map axes for tic in ax_hmap.xaxis.get_minor_ticks(): tic.tick1On = tic.tick2On = False for tic in ax_hmap.yaxis.get_minor_ticks(): tic.tick1On = tic.tick2On = False # Remove tickmarks from colorbar for tic in ax_color.yaxis.get_major_ticks(): tic.tick1On = tic.tick2On = False if filename is not None: head = 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 using method *linkage* with annotated distances in the matrix. Rows (and columns) are identified using the list of strings specified by :attr:`PSAnalysis.labels`. :Arguments: *filename* string, save figure to *filename* [``None``] *count_sort* boolean, see scipy.cluster.hierarchy.dendrogram [``False``] *distance_sort* boolean, see scipy.cluster.hierarchy.dendrogram [``False``] *linkage* string, name of linkage criterion for clustering [``'ward'``] *figsize* set the vertical size of plot in inches [``8``] *annot_size* float, font size of annotation labels on heat map [``6.5``] 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:`pylab.imshow`. """ from matplotlib.pylab import figure, colorbar, cm, savefig, clf try: import seaborn.apionly 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. """ ) if self.D is None: err_str = "No distance data; do 'PSAnalysis.run(store=True)' first." raise ValueError(err_str) dist_matrix = self.D Z, dgram = self.cluster(dist_matrix, \ 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.tick1On = tic.tick2On = False tic.label1On = tic.label2On = False for tic in ax_hmap.yaxis.get_major_ticks(): tic.tick1On = tic.tick2On = False tic.label1On = tic.label2On = False # Remove minor ticks from both heat map axes for tic in ax_hmap.xaxis.get_minor_ticks(): tic.tick1On = tic.tick2On = False for tic in ax_hmap.yaxis.get_minor_ticks(): tic.tick1On = tic.tick2On = False if filename is not None: head = 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 (mapped to the interval *[0,1]*). :Arguments: *filename* string, save figure to *filename* [``None``] *idx* integer, index of path (pair) comparison to plot [``0``] *labels* (string, string), 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* boolean, 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* set the font size for colorbar labels; font size for path labels on dendrogram default to 3 points smaller [``12``] 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:`pylab.imshow`. """ from matplotlib.pyplot import figure, savefig, tight_layout, clf, show try: import seaborn.apionly 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. """ ) colors = sns.xkcd_palette(["cherry", "windows blue"]) if self._NN is None: err_str = ("No nearest neighbor data; run " "'PSAnalysis.run_nearest_neighbors()' first.") raise ValueError(err_str) 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 = self.targetdir + self.datadirs['plots'] outfile = os.path.join(head, filename) savefig(outfile, dpi=300, bbox_inches='tight') show()
[docs] def cluster(self, distArray, method='ward', count_sort=False, \ distance_sort=False, no_plot=False, no_labels=True, \ color_threshold=4): """Cluster trajectories and optionally plot the dendrogram. :Arguments: *method* string, name of linkage criterion for clustering [``'ward'``] *no_plot* boolean, if ``True``, do not render the dendrogram [``False``] *no_labels* boolean, if ``True`` then do not label dendrogram [``True``] *color_threshold* 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: list of indices representing the row-wise order of the objects after clustering """ import matplotlib from scipy.cluster.hierarchy import linkage, dendrogram from brewer2mpl import get_map color_list = get_map('Set1', 'qualitative', 9).mpl_colors matplotlib.rcParams['lines.linewidth'] = 0.5 Z = linkage(distArray, method=method) dgram = dendrogram(Z, no_labels=no_labels, orientation='right', \ count_sort=count_sort, distance_sort=distance_sort, \ no_plot=no_plot, color_threshold=color_threshold, \ color_list=color_list) return Z, dgram
def _get_plot_obj_locs(self): """Find and return coordinates for dendrogram, heat map, and colorbar. :Returns: 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`s in :class:`PSA`. .. note:: Must run :method:`PSAnalysis.generate_paths()` prior to calling this method. :Returns: int, the number of atoms in :class:`PSA`'s :class:`Path`s' """ if self.natoms is None: err_str = "No path data; do 'PSAnalysis.generate_paths()' first." raise ValueError(err_str) return self.natoms
[docs] def get_num_paths(self): """Return the number of paths in :class:`PSA`. .. note:: Must run :method:`PSAnalysis.generate_paths()` prior to calling this method. :Returns: int, the number of paths in :class:`PSA` """ if self.npaths is None: err_str = "No path data; do 'PSAnalysis.generate_paths()' first." raise ValueError(err_str) return self.npaths
[docs] def get_paths(self): """Return the paths in :class:`PSA`. .. note:: Must run :method:`PSAnalysis.generate_paths()` prior to calling this method. :Returns: list of :class:`numpy.ndarray` representations of paths in :class:`PSA` """ if self.paths is None: err_str = "No path data; do 'PSAnalysis.generate_paths()' first." raise ValueError(err_str) return self.paths
[docs] def get_pairwise_distances(self, vectorform=False): """Return the distance matrix (or vector) of pairwise path distances. .. note:: Must run :method:`PSAnalysis.run(store=True)` prior to calling this method. :Arguments: *vectorform* boolean, if ``True``, return the distance vector instead [``False``] :Returns: :class:`numpy.ndarray` representation of the distance matrix (or vector) """ if self.D is None: err_str = "No distance data; do 'PSAnalysis.run(store=True)' first." raise ValueError(err_str) if vectorform: from scipy.spatial.distance import squareform return squareform(self.D) else: return self.D
@property def psa_pairs(self): """Get the list of :class:`PSAPair`s for each pair of paths. :method:`psa_pairs` is a list of :class:`PSAPair` whose elements are pairs of paths that have been compared using :method:`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 :method:`PSAnalysis.run_pairs_analysis()` prior to calling this method. :Returns: list of all :class:`PSAPair` objects (in distance vector order) """ if self._psa_pairs is None: err_str = "No nearest neighbors data; do" \ + " 'PSAnalysis.run_pairs_analysis()' first." raise ValueError(err_str) return self._psa_pairs @property def hausdorff_pairs(self): """Get the Hausdorff pair for each (unique) pairs of paths. This method returns a list of Hausdorff pair information, where each element is a dictionary containing the pair of frames and the (Hausdorff) distance between a pair of paths. See :method:`PSAnalysis.psa_pairs` and :attr:`PSAPair.hausdorff_pair` for more information about accessing Hausdorff pair data. .. note:: Must run :method:`PSAnalysis.run_pairs_analysis(hausdorff_pairs=True)` prior to calling this method. :Returns: list of all Hausdorff pairs (in distance vector order) """ if self._HP is None: err_str = "No Hausdorff pairs data; do " \ + "'PSAnalysis.run_pairs_analysis(hausdorff_pairs=True)' " \ + "first." raise ValueError(err_str) return self._HP @property def nearest_neighbors(self): """Get the nearest neighbors for each (unique) pair of paths. This method returns a list of nearest neighbor information, where each element is a dictionary containing the nearest neighbor frames and distances between a pair of paths. See :method:`PSAnalysis.psa_pairs` and :attr:`PSAPair.nearest_neighbors` for more information about accessing nearest neighbor data. .. note:: Must run :method:`PSAnalysis.run_pairs_analysis(neighbors=True)` prior to calling this method. :Returns: list of all nearest neighbors (in distance vector order) """ if self._NN is None: err_str = "No nearest neighbors data; do" \ + " 'PSAnalysis.run_pairs_analysis(neighbors=True)' first." raise ValueError(err_str) return self._NN