3.1.5. Calculating path similarity — MDAnalysis.analysis.psa

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

New in version 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.

See also

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.

References

[Seyler2015]Sean L. Seyler, Avishek Kumar, Michael F. Thorpe, Oliver Beckstein. Path Similarity Analysis: a Method for Quantifying Macromolecular Pathways. arXiv:1505.04807 (2015).

3.1.5.1. Helper functions and variables

The following convenience functions are used by other functions in this module.

MDAnalysis.analysis.psa.sqnorm(v, axis=None)[source]

Compute the sum of squares of elements along specified axes.

Parameters:
  • *v*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

MDAnalysis.analysis.psa.get_msd_matrix(P, Q, axis=None)[source]

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 numpy.ndarray of \(N_p\) (\(N_q\)) time steps, \(N\) atoms, and \(3N\) coordinates (e.g., MDAnalysis.core.AtomGroup.AtomGroup.coordinates()). The pairwise MSD matrix has dimensions \(N_p\) by \(N_q\).

Parameters:
Returns:

numpy.ndarray of pairwise MSDs between points in P and points in Q

Return type:

:class

MDAnalysis.analysis.psa.get_coord_axes(path)[source]

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 numpy.ndarray where the 0th axis corresponds to a frame (a snapshot of coordinates). The \(3N\) (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

3.1.5.2. Classes, methods, and functions

MDAnalysis.analysis.psa.get_path_metric_func(name)[source]

Selects a path metric function by name.

Parameters:*name* – string, name of path metric
Returns:The path metric function specified by name (if found).
MDAnalysis.analysis.psa.hausdorff(P, Q)[source]

Calculate the Hausdorff distance between two paths.

P (Q) is a numpy.ndarray of \(N_p\) (\(N_q\)) time steps, \(N\) atoms, and \(3N\) coordinates (e.g., MDAnalysis.core.AtomGroup.AtomGroup.coordinates()). P (Q) has either shape \(N_p \times N \times 3\) (\(N_q \times N \times 3\)), or \(N_p \times (3N)\) (\(N_q \times (3N)\)) in flattened form.

Parameters:
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
MDAnalysis.analysis.psa.hausdorff_wavg(P, Q)[source]

Calculate the weighted average Hausdorff distance between two paths.

P (Q) is a numpy.ndarray of \(N_p\) (\(N_q\)) time steps, \(N\) atoms, and \(3N\) coordinates (e.g., MDAnalysis.core.AtomGroup.AtomGroup.coordinates()). P (Q) has either shape \(N_p \times N \times 3\) (\(N_q \times N \times 3\)), or \(N_p \times (3N)\) (\(N_q \times (3N)\)) 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:
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
MDAnalysis.analysis.psa.hausdorff_avg(P, Q)[source]

Calculate the average Hausdorff distance between two paths.

P (Q) is a numpy.ndarray of \(N_p\) (\(N_q\)) time steps, \(N\) atoms, and \(3N\) coordinates (e.g., MDAnalysis.core.AtomGroup.AtomGroup.coordinates()). P (Q) has either shape \(N_p \times N \times 3\) (\(N_q \times N \times 3\)), or \(N_p \times (3N)\) (\(N_q \times (3N)\)) 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:
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
MDAnalysis.analysis.psa.hausdorff_neighbors(P, Q)[source]

Calculate the Hausdorff distance between two paths.

P (Q) is a numpy.ndarray of \(N_p\) (\(N_q\)) time steps, \(N\) atoms, and \(3N\) coordinates (e.g., MDAnalysis.core.AtomGroup.AtomGroup.coordinates()). P (Q) has either shape \(N_p \times N \times 3\) (\(N_q \times N \times 3\)), or \(N_p \times (3N)\) (\(N_q \times (3N)\)) in flattened form.

Parameters:
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

MDAnalysis.analysis.psa.discrete_frechet(P, Q)[source]

Calculate the discrete Frechet distance between two paths.

P (Q) is a numpy.ndarray of \(N_p\) (\(N_q\)) time steps, \(N\) atoms, and \(3N\) coordinates (e.g., MDAnalysis.core.AtomGroup.AtomGroup.coordinates()). P (Q) has either shape \(N_p \times N \times 3\) (\(N_q \times N \times 3\)), or :\(N_p \times (3N)\) (\(N_q \times (3N)\)) in flattened form.

Parameters:
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
MDAnalysis.analysis.psa.dist_mat_to_vec(N, i, j)[source]

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

class MDAnalysis.analysis.psa.PDBToBinaryTraj(universe, output_type='.dcd', infix='')[source]
universe

MDAnalysis.Universe object with a trajectory

frames

MDAnalysis.Universe.trajectory

newname

string, filename for converted trajectory, including file extension

class MDAnalysis.analysis.psa.Path(universe, reference, ref_select='name CA', path_select='all', ref_frame=0)[source]

Pre-process a MDAnalysis.Universe object: (1) fit the trajectory to a reference structure, (2) convert fitted time series to a numpy.ndarray representation of Path.path.

The analysis is performed with PSAnalysis.run() and stores the result in the numpy.ndarray distance matrix PSAnalysis.D. PSAnalysis.run() also generates a fitted trajectory and path from alignment of the original trajectories to a reference structure.

New in version 0.9.1.

Setting up trajectory alignment and fitted path generation.

Parameters:
  • *universe*MDAnalysis.Universe object containing a trajectory
  • *reference* – reference structure; 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 select_atoms() that produces identical selections in mobile and reference; or
    2. a dictionary {'mobile':sel1, 'reference':sel2} (the 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 Ordered selections).

  • *path_select* – atom selection composing coordinates of (fitted) path; if None then path_select is set to ref_select [None]
u_original

MDAnalysis.Universe object with a trajectory

u_reference

MDAnalysis.Universe object containing a reference structure

ref_select

string, selection for select_atoms() to select frame from Path.u_reference

path_select

string, selection for select_atoms() to select atoms to compose Path.path

ref_frame

int, frame index to select frame from Path.u_reference

u_fitted

MDAnalysis.Universe object with the fitted trajectory

path

numpy.ndarray object representation of the fitted trajectory

fit_to_reference(filename=None, prefix='', postfix='_fit', rmsdfile=None, targetdir='.', mass_weighted=False, tol_mass=0.1)[source]

Align each trajectory frame to the reference structure with MDAnalysis.analysis.align.rms_fit_trj().

Parameters:
  • *filename* – file name for the RMS-fitted trajectory or pdb; defaults to the original trajectory filename (from 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:

MDAnalysis.Universe object containing a fitted trajectory

Return type:

:class

get_num_atoms()[source]

Return the number of atoms used to construct the Path.

Must run :method:`Path.to_path()` prior to calling this method.

Returns:class:Path
Return type:int, the number of atoms in the
run(align=False, filename=None, postfix='_fit', rmsdfile=None, targetdir='.', mass_weighted=False, tol_mass=0.1, flat=False)[source]

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 (Path.u_original) and reference structure (Path.u_reference). Path.fit_to_reference() and Path.to_path() are used consecutively to generate a new universe (Path.u_fitted) containing the fitted trajectory along with the corresponding Path.path represented as an numpy.ndarray. The method returns a tuple of the topology name and new trajectory name, which can be fed directly into an MDAnalysis.Universe object after unpacking the tuple using the * operator, as in MDAnalysis.Universe(*(top_name, newtraj_name)).

Parameters:
  • *align* – Align trajectory to atom selection Path.ref_select of Path.u_reference. If True, a universe containing an aligned trajectory is produced with Path.fit_to_reference() [False]
  • *filename* – filename for the RMS-fitted trajectory or pdb; defaults to the original trajectory filename (from 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 Path.path with 2D (\(N_p\times 3N\)) numpy.ndarray; if False then Path.path is a 3D (\(N_p\times N\times 3\)) numpy.ndarray [False]
Returns:

A tuple of the topology name and new trajectory name.

to_path(fitted=False, select=None, flat=False)[source]

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 (Path.u_fitted) trajectory (with \(N_p\) total frames) are appended sequentially to form a 3D or 2D (if flat is True) numpy.ndarray representation of the fitted trajectory (with dimensions \(N_p\times N\times 3\) or \(N_p\times 3N\), respectively).

Parameters:
Returns:

numpy.ndarray representing a time series of atomic positions of an MDAnalysis.core.AtomGroup.AtomGroup selection from Path.u_fitted.trajectory

Return type:

:class

class MDAnalysis.analysis.psa.PSAPair(npaths, i, j)[source]

Generate nearest neighbor and Hausdorff pair information between a pair of paths from an all-pairs comparison generated by PSA.

The nearest neighbors for each path of a pair of paths is generated by PSAPair.compute_nearest_neighbors() and stores the result in a dictionary (nearest_neighbors): each path has a numpy.ndarray of the frames of its nearest neighbors, and a numpy.ndarray of its nearest neighbor distances PSAnalysis.D. For example, nearest_neighbors[‘frames’] is a pair of 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 find_hausdorff_pair() (locates the nearest neighbor pair having the largest overall distance separating them), which stores the result in a dictionary (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.

New in version 0.11.

Set up a PSAPair for a pair of paths that are part of a PSA comparison of npaths total paths.

Each unique pair of paths compared using PSA is related by their nearest neighbors (and corresponding distances) and the Hausdorff pair and distance. PSAPair is a convenience class for calculating and encapsulating nearest neighbor and Hausdorff pair information for one pair of paths.

Given npaths, PSA performs and all-pairs comparison among all paths for a total of :math:` ext{npaths}*( ext{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 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 PSA used to generate this PSAPair
  • *i* – int, row index (starting at 0) of the distance matrix
  • *j* – int, column index (starting at 0) of the distance matrix
npaths

int, total number of paths in the comparison in which this PSAPair was generated

matrix_id

(int, int), (row, column) indices of the location of this PSAPair in the corresponding pairwise distance matrix

pair_id

int, ID of this PSAPair (the pair_id:math:^text{th} comparison) in the distance vector corresponding to the pairwise distance matrix

nearest_neighbors

dict, contains the nearest neighbors by frame index and the nearest neighbor distances for each path in this PSAPair

hausdorff_pair

dict, contains the frame indices of the Hausdorff pair for each path in this PSAPair and the corresponding (Hausdorff) distance

class MDAnalysis.analysis.psa.PSAnalysis(universes, reference=None, ref_select='name CA', ref_frame=0, path_select=None, labels=None, targetdir=None)[source]

Perform Path Similarity Analysis (PSA) on a set of trajectories.

The analysis is performed with PSAnalysis.run() and stores the result in the numpy.ndarray distance matrix PSAnalysis.D. PSAnalysis.run() also generates a fitted trajectory and path from alignment of the original trajectories to a reference structure.

New in version 0.8.

Setting up Path Similarity Analysis.

The mutual similarity between all unique pairs of trajectories are computed using a selected path metric.

Parameters:
  • *universes* – a list of universes (MDAnalysis.Universe object), each containing a trajectory
  • *reference* – reference coordinates; 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 select_atoms() that produces identical selections in mobile and reference; or
    2. a dictionary {'mobile':sel1, 'reference':sel2} (the 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 Ordered selections).

  • *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 (MDAnalysis.Universe); if None, defaults to trajectory names [None]
universes

list of MDAnalysis.Universe objects containing trajectories

u_reference

MDAnalysis.Universe object containing a reference structure

ref_select

string, selection for select_atoms() to select frame from PSAnalysis.u_reference

path_select

string, selection for select_atoms() to select atoms to compose Path.path

ref_frame

int, frame index to select frame from Path.u_reference

filename

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

paths

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

D

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

cluster(distArray, method='ward', count_sort=False, distance_sort=False, no_plot=False, no_labels=True, color_threshold=4)[source]

Cluster trajectories and optionally plot the dendrogram.

Parameters:
  • *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

generate_paths(**kwargs)[source]

Generate paths, aligning each to reference structure if necessary.

Keywords:
align

Align trajectories to atom selection PSAnalysis.ref_select of 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 Path.path as a 2D (\(N_p\times 3N\)) numpy.ndarray; if False then Path.path is a 3D (\(N_p\times N\times 3\)) numpy.ndarray [False]

save

boolean; if True, pickle list of names for fitted trajectories [True]

store

boolean; if True then writes each path (numpy.ndarray) in PSAnalysis.paths to compressed npz (numpy) files [False]

The fitted trajectories are written to new files in the “/trj_fit” subdirectory in 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 PSAnalysis.targetdir for persistence and can be accessed as the attribute PSAnalysis.paths.

get_num_atoms()[source]

Return the number of atoms used to construct the Path`s in :class:`PSA.

Must run :method:`PSAnalysis.generate_paths()` prior to calling this method.

Returns:class:PSA‘s :class:`Path`s’
Return type:int, the number of atoms in
get_num_paths()[source]

Return the number of paths in PSA.

Must run :method:`PSAnalysis.generate_paths()` prior to calling this method.

Returns:class:PSA
Return type:int, the number of paths in
get_pairwise_distances(vectorform=False)[source]

Return the distance matrix (or vector) of pairwise path distances.

Must run :method:`PSAnalysis.run(store=True)` prior to calling this method.

Parameters:*vectorform* – boolean, if True, return the distance vector instead [False]
Returns:numpy.ndarray representation of the distance matrix (or vector)
Return type::class
get_paths()[source]

Return the paths in PSA.

Must run :method:`PSAnalysis.generate_paths()` prior to calling this method.

Returns:class:numpy.ndarray representations of paths in PSA
Return type:list of
hausdorff_pairs

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 PSAPair.hausdorff_pair for more information about accessing Hausdorff pair data.

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)
load()[source]

Load fitted paths specified by ‘psa_path-names.pkl’ in PSAnalysis.targetdir.

nearest_neighbors

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 PSAPair.nearest_neighbors for more information about accessing nearest neighbor data.

Must run :method:`PSAnalysis.run_pairs_analysis(neighbors=True)` prior to calling this method.

Returns:list of all nearest neighbors (in distance vector order)
plot(filename=None, linkage='ward', count_sort=False, distance_sort=False, figsize=4.5, labelsize=12)[source]

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 PSAnalysis.labels.

Parameters:
  • *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 pylab.imshow().

plot_annotated_heatmap(filename=None, linkage='ward', count_sort=False, distance_sort=False, figsize=8, annot_size=6.5)[source]

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 PSAnalysis.labels.

Parameters:
  • *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 pylab.imshow().

plot_nearest_neighbors(filename=None, idx=0, labels=('Path 1', 'Path 2'), figsize=4.5, multiplot=False, aspect_ratio=1.75, labelsize=12)[source]

Plot nearest neighbor distances as a function of normalized frame number (mapped to the interval [0,1]).

Parameters:
  • *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 pylab.imshow().

psa_pairs

Get the list of :class:`PSAPair`s for each pair of paths.

:method:`psa_pairs` is a list of PSAPair whose elements are pairs of paths that have been compared using :method:`PSAnalysis.run_pairs_analysis()`. Each PSAPair contains nearest neighbor and Hausdorff pair information specific to a pair of paths. The nearest neighbor frames and distances for a PSAPair can be accessed in the nearest neighbor dictionary using the keys ‘frames’ and ‘distances’, respectively. E.g., PSAPair.nearest_neighbors['distances'] returns a pair of numpy.ndarray corresponding to the nearest neighbor distances for each path. Similarly, Hausdorff pair information can be accessed using PSAPair.hausdorff_pair with the keys ‘frames’ and ‘distance’.

Must run :method:`PSAnalysis.run_pairs_analysis()` prior to calling this method.

Returns:class:PSAPair objects (in distance vector order)
Return type:list of all
run(**kwargs)[source]

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 PSAnalysis.D.

Keywords:
metric

selection string specifying the path metric to measure pairwise distances among 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 PSAnalysis.D to text and compressed npz (numpy) files [True]

filename

string, filename to save PSAnalysis.D

run_pairs_analysis(**kwargs)[source]

Perform PSA Hausdorff (nearest neighbor) pairs analysis on all unique pairs of paths in 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 \(s=N*i+j-(i+1)*(i+2)\) in distance vector representation, which is the \(s^ ext{th}\) comparison). For each unique pair of paths, the nearest neighbors for that pair can be stored in NN and the Hausdorff pair in HP. 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 PSAnalysis.NN [False]

hausdorff_pairs

boolean; if True, then stores dictionary of Hausdorff pair frames/distances in PSAnalysis.HP [False]

save_paths(filename=None)[source]

Save fitted PSAnalysis.paths to numpy compressed npz files.

Parameters:*filename* – string, specifies filename [None]

The data are saved with numpy.savez_compressed() in the directory specified by PSAnalysis.targetdir.

save_result(filename=None)[source]

Save distance matrix PSAnalysis.D to a numpy compressed npz file and text file.

Parameters:*filename* – string, specifies filename [None]

The data are saved with numpy.savez_compressed() and numpy.savetxt() in the directory specified by PSAnalysis.targetdir.