# Source code for MDAnalysis.lib.distances

# -*- Mode: python; tab-width: 4; indent-tabs-mode:nil; -*-
# vim: tabstop=4 expandtab shiftwidth=4 softtabstop=4
#
# MDAnalysis --- https://www.mdanalysis.org
# Copyright (c) 2006-2017 The MDAnalysis Development Team and contributors
# (see the file AUTHORS for the full list of names)
#
# Released under the GNU Public Licence, v2 or any higher version
#
#
# R. J. Gowers, M. Linke, J. Barnoud, T. J. E. Reddy, M. N. Melo, S. L. Seyler,
# D. L. Dotson, J. Domanski, S. Buchoux, I. M. Kenney, and O. Beckstein.
# MDAnalysis: A Python package for the rapid analysis of molecular dynamics
# simulations. In S. Benthall and S. Rostrup editors, Proceedings of the 15th
# Python in Science Conference, pages 102-109, Austin, TX, 2016. SciPy.
# doi: 10.25080/majora-629e541a-00e
#
# N. Michaud-Agrawal, E. J. Denning, T. B. Woolf, and O. Beckstein.
# MDAnalysis: A Toolkit for the Analysis of Molecular Dynamics Simulations.
# J. Comput. Chem. 32 (2011), 2319--2327, doi:10.1002/jcc.21787
#
#

"""Fast distance array computation --- :mod:MDAnalysis.lib.distances
===================================================================

Fast C-routines to calculate arrays of distances or angles from coordinate
arrays. Many of the functions also exist in parallel versions, which typically
provide higher performance than the serial code.
The boolean attribute MDAnalysis.lib.distances.USED_OPENMP can be checked to
see if OpenMP was used in the compilation of MDAnalysis.

Selection of acceleration ("backend")
-------------------------------------

All functions take the optional keyword backend, which determines the type of
acceleration. Currently, the following choices are implemented (backend is
case-insensitive):

.. Table:: Available *backends* for accelerated distance functions.

========== ========================= ======================================
*backend*  module                    description
========== ========================= ======================================
"serial"   :mod:c_distances        serial implementation in C/Cython

"OpenMP"   :mod:c_distances_openmp parallel implementation in C/Cython
with OpenMP
========== ========================= ======================================

Functions
---------
.. autofunction:: distance_array
.. autofunction:: self_distance_array
.. autofunction:: capped_distance
.. autofunction:: self_capped_distance
.. autofunction:: calc_bonds
.. autofunction:: calc_angles
.. autofunction:: calc_dihedrals
.. autofunction:: apply_PBC
.. autofunction:: transform_RtoS
.. autofunction:: transform_StoR
.. autofunction:: augment_coordinates(coordinates, box, r)
.. autofunction:: undo_augment(results, translation, nreal)
.. autofunction:: minimize_vectors(vectors, box)
"""
import numpy as np
from numpy.lib.utils import deprecate

from .util import check_coords, check_box
from .mdamath import triclinic_vectors
from ._augment import augment_coordinates, undo_augment
from .nsgrid import FastNS
from .c_distances import _minimize_vectors_ortho, _minimize_vectors_triclinic

# hack to select backend with backend=<backend> kwarg. Note that
# the cython parallel code (prange) in parallel.distances is
# independent from the OpenMP code
import importlib
_distances = {}
_distances['serial'] = importlib.import_module(".c_distances",
package="MDAnalysis.lib")
try:
_distances['openmp'] = importlib.import_module(".c_distances_openmp",
package="MDAnalysis.lib")
except ImportError:
pass
del importlib

def _run(funcname, args=None, kwargs=None, backend="serial"):
"""Helper function to select a backend function funcname."""
args = args if args is not None else tuple()
kwargs = kwargs if kwargs is not None else dict()
backend = backend.lower()
try:
func = getattr(_distances[backend], funcname)
except KeyError:
errmsg = (f"Function {funcname} not available with backend {backend} "
f"try one of: {_distances.keys()}")
raise ValueError(errmsg) from None
return func(*args, **kwargs)

# serial versions are always available (and are typically used within
# the core and topology modules)
from .c_distances import (_UINT64_MAX,
calc_distance_array,
calc_distance_array_ortho,
calc_distance_array_triclinic,
calc_self_distance_array,
calc_self_distance_array_ortho,
calc_self_distance_array_triclinic,
coord_transform,
calc_bond_distance,
calc_bond_distance_ortho,
calc_bond_distance_triclinic,
calc_angle,
calc_angle_ortho,
calc_angle_triclinic,
calc_dihedral,
calc_dihedral_ortho,
calc_dihedral_triclinic,
ortho_pbc,
triclinic_pbc)

from .c_distances_openmp import OPENMP_ENABLED as USED_OPENMP

def _check_result_array(result, shape):
"""Check if the result array is ok to use.

The result array must meet the following requirements:
* Must have a shape equal to shape.
* Its dtype must be numpy.float64.

Paramaters
----------
result : numpy.ndarray or None
The result array to check. If result is None, a newly created
array of correct shape and dtype numpy.float64 will be returned.
shape : tuple
The shape expected for the result array.

Returns
-------
result : numpy.ndarray (dtype=numpy.float64, shape=shape)
The input array or a newly created array if the input was None.

Raises
------
ValueError
If result is of incorrect shape.
TypeError
If the dtype of result is not numpy.float64.
"""
if result is None:
return np.zeros(shape, dtype=np.float64)
if result.shape != shape:
raise ValueError("Result array has incorrect shape, should be {0}, got "
"{1}.".format(shape, result.shape))
if result.dtype != np.float64:
raise TypeError("Result array must be of type numpy.float64, got {}."
"".format(result.dtype))
# The following two lines would break a lot of tests. WHY?!
#    if not coords.flags['C_CONTIGUOUS']:
#        raise ValueError("{0} is not C-contiguous.".format(desc))
return result

[docs]@check_coords('reference', 'configuration', reduce_result_if_single=False, check_lengths_match=False) def distance_array(reference, configuration, box=None, result=None, backend="serial"): """Calculate all possible distances between a reference set and another configuration. If there are n positions in reference and m positions in configuration, a distance array of shape (n, m) will be computed. If the optional argument box is supplied, the minimum image convention is applied when calculating distances. Either orthogonal or triclinic boxes are supported. If a 2D numpy array of dtype numpy.float64 with the shape (n, m) is provided in result, then this preallocated array is filled. This can speed up calculations. Parameters ---------- reference : numpy.ndarray Reference coordinate array of shape (3,) or (n, 3) (dtype is arbitrary, will be converted to numpy.float32 internally). configuration : numpy.ndarray Configuration coordinate array of shape (3,) or (m, 3) (dtype is arbitrary, will be converted to numpy.float32 internally). box : array_like, optional The unitcell dimensions of the system, which can be orthogonal or triclinic and must be provided in the same format as returned by :attr:MDAnalysis.coordinates.base.Timestep.dimensions: [lx, ly, lz, alpha, beta, gamma]. result : numpy.ndarray, optional Preallocated result array which must have the shape (n, m) and dtype numpy.float64. Avoids creating the array which saves time when the function is called repeatedly. backend : {'serial', 'OpenMP'}, optional Keyword selecting the type of acceleration. Returns ------- d : numpy.ndarray (dtype=numpy.float64, shape=(n, m)) Array containing the distances d[i,j] between reference coordinates i and configuration coordinates j. .. versionchanged:: 0.13.0 Added *backend* keyword. .. versionchanged:: 0.19.0 Internal dtype conversion of input coordinates to numpy.float32. Now also accepts single coordinates as input. """ confnum = configuration.shape[0] refnum = reference.shape[0] # check resulting array will not overflow UINT64_MAX if refnum * confnum > _UINT64_MAX: raise ValueError(f"Size of resulting array {refnum * confnum} elements" " larger than size of maximum integer") distances = _check_result_array(result, (refnum, confnum)) if len(distances) == 0: return distances if box is not None: boxtype, box = check_box(box) if boxtype == 'ortho': _run("calc_distance_array_ortho", args=(reference, configuration, box, distances), backend=backend) else: _run("calc_distance_array_triclinic", args=(reference, configuration, box, distances), backend=backend) else: _run("calc_distance_array", args=(reference, configuration, distances), backend=backend) return distances
[docs]@check_coords('reference', reduce_result_if_single=False) def self_distance_array(reference, box=None, result=None, backend="serial"): """Calculate all possible distances within a configuration reference. If the optional argument box is supplied, the minimum image convention is applied when calculating distances. Either orthogonal or triclinic boxes are supported. If a 1D numpy array of dtype numpy.float64 with the shape (n*(n-1)/2,) is provided in result, then this preallocated array is filled. This can speed up calculations. Parameters ---------- reference : numpy.ndarray Reference coordinate array of shape (3,) or (n, 3) (dtype is arbitrary, will be converted to numpy.float32 internally). box : array_like, optional The unitcell dimensions of the system, which can be orthogonal or triclinic and must be provided in the same format as returned by :attr:MDAnalysis.coordinates.base.Timestep.dimensions: [lx, ly, lz, alpha, beta, gamma]. result : numpy.ndarray, optional Preallocated result array which must have the shape (n*(n-1)/2,) and dtype numpy.float64. Avoids creating the array which saves time when the function is called repeatedly. backend : {'serial', 'OpenMP'}, optional Keyword selecting the type of acceleration. Returns ------- d : numpy.ndarray (dtype=numpy.float64, shape=(n*(n-1)/2,)) Array containing the distances dist[i,j] between reference coordinates i and j at position d[k]. Loop through d: .. code-block:: python for i in range(n): for j in range(i + 1, n): k += 1 dist[i, j] = d[k] .. versionchanged:: 0.13.0 Added *backend* keyword. .. versionchanged:: 0.19.0 Internal dtype conversion of input coordinates to numpy.float32. """ refnum = reference.shape[0] distnum = refnum * (refnum - 1) // 2 # check resulting array will not overflow UINT64_MAX if distnum > _UINT64_MAX: raise ValueError(f"Size of resulting array {distnum} elements larger" " than size of maximum integer") distances = _check_result_array(result, (distnum,)) if len(distances) == 0: return distances if box is not None: boxtype, box = check_box(box) if boxtype == 'ortho': _run("calc_self_distance_array_ortho", args=(reference, box, distances), backend=backend) else: _run("calc_self_distance_array_triclinic", args=(reference, box, distances), backend=backend) else: _run("calc_self_distance_array", args=(reference, distances), backend=backend) return distances
[docs]def capped_distance(reference, configuration, max_cutoff, min_cutoff=None, box=None, method=None, return_distances=True): """Calculates pairs of indices corresponding to entries in the reference and configuration arrays which are separated by a distance lying within the specified cutoff(s). Optionally, these distances can be returned as well. If the optional argument box is supplied, the minimum image convention is applied when calculating distances. Either orthogonal or triclinic boxes are supported. An automatic guessing of the optimal method to calculate the distances is included in the function. An optional keyword for the method is also provided. Users can enforce a particular method with this functionality. Currently brute force, grid search, and periodic KDtree methods are implemented. Parameters ----------- reference : numpy.ndarray Reference coordinate array with shape (3,) or (n, 3). configuration : numpy.ndarray Configuration coordinate array with shape (3,) or (m, 3). max_cutoff : float Maximum cutoff distance between the reference and configuration. min_cutoff : float, optional Minimum cutoff distance between reference and configuration. box : array_like, optional The unitcell dimensions of the system, which can be orthogonal or triclinic and must be provided in the same format as returned by :attr:MDAnalysis.coordinates.base.Timestep.dimensions: [lx, ly, lz, alpha, beta, gamma]. method : {'bruteforce', 'nsgrid', 'pkdtree'}, optional Keyword to override the automatic guessing of the employed search method. return_distances : bool, optional If set to True, distances will also be returned. Returns ------- pairs : numpy.ndarray (dtype=numpy.int64, shape=(n_pairs, 2)) Pairs of indices, corresponding to coordinates in the reference and configuration arrays such that the distance between them lies within the interval (min_cutoff, max_cutoff]. Each row in pairs is an index pair [i, j] corresponding to the i-th coordinate in reference and the j-th coordinate in configuration. distances : numpy.ndarray (dtype=numpy.float64, shape=(n_pairs,)), optional Distances corresponding to each pair of indices. Only returned if return_distances is True. distances[k] corresponds to the k-th pair returned in pairs and gives the distance between the coordinates reference[pairs[k, 0]] and configuration[pairs[k, 1]]. .. code-block:: python pairs, distances = capped_distances(reference, configuration, max_cutoff, return_distances=True) for k, [i, j] in enumerate(pairs): coord1 = reference[i] coord2 = configuration[j] distance = distances[k] See Also -------- distance_array MDAnalysis.lib.pkdtree.PeriodicKDTree.search MDAnalysis.lib.nsgrid.FastNS.search .. versionchanged:: 1.0.1 nsgrid was temporarily removed and replaced with pkdtree due to issues relating to its reliability and accuracy (Issues #2919, #2229, #2345, #2670, #2930) .. versionchanged:: 1.0.2 nsgrid enabled again """ if box is not None: box = np.asarray(box, dtype=np.float32) if box.shape[0] != 6: raise ValueError("Box Argument is of incompatible type. The " "dimension should be either None or of the form " "[lx, ly, lz, alpha, beta, gamma]") method = _determine_method(reference, configuration, max_cutoff, min_cutoff=min_cutoff, box=box, method=method) return method(reference, configuration, max_cutoff, min_cutoff=min_cutoff, box=box, return_distances=return_distances)
def _determine_method(reference, configuration, max_cutoff, min_cutoff=None, box=None, method=None): """Guesses the fastest method for capped distance calculations based on the size of the coordinate sets and the relative size of the target volume. Parameters ---------- reference : numpy.ndarray Reference coordinate array with shape (3,) or (n, 3). configuration : numpy.ndarray Configuration coordinate array with shape (3,) or (m, 3). max_cutoff : float Maximum cutoff distance between reference and configuration coordinates. min_cutoff : float, optional Minimum cutoff distance between reference and configuration coordinates. box : numpy.ndarray The unitcell dimensions of the system, which can be orthogonal or triclinic and must be provided in the same format as returned by :attr:MDAnalysis.coordinates.base.Timestep.dimensions: [lx, ly, lz, alpha, beta, gamma]. method : {'bruteforce', 'nsgrid', 'pkdtree'}, optional Keyword to override the automatic guessing of the employed search method. Returns ------- function : callable The function implementing the guessed (or deliberatly chosen) method. .. versionchanged:: 1.0.1 nsgrid was temporarily removed and replaced with pkdtree due to issues relating to its reliability and accuracy (Issues #2919, #2229, #2345, #2670, #2930) .. versionchanged:: 1.1.0 enabled nsgrid again """ methods = {'bruteforce': _bruteforce_capped, 'pkdtree': _pkdtree_capped, 'nsgrid': _nsgrid_capped, } if method is not None: return methods[method.lower()] if len(reference) < 10 or len(configuration) < 10: return methods['bruteforce'] elif len(reference) * len(configuration) >= 1e8: # CAUTION : for large datasets, shouldnt go into 'bruteforce' # in any case. Arbitrary number, but can be characterized return methods['nsgrid'] else: if box is None: min_dim = np.array([reference.min(axis=0), configuration.min(axis=0)]) max_dim = np.array([reference.max(axis=0), configuration.max(axis=0)]) size = max_dim.max(axis=0) - min_dim.min(axis=0) elif np.all(box[3:] == 90.0): size = box[:3] else: tribox = triclinic_vectors(box) size = tribox.max(axis=0) - tribox.min(axis=0) if np.any(max_cutoff > 0.3*size): return methods['bruteforce'] else: return methods['nsgrid'] @check_coords('reference', 'configuration', enforce_copy=False, reduce_result_if_single=False, check_lengths_match=False) def _bruteforce_capped(reference, configuration, max_cutoff, min_cutoff=None, box=None, return_distances=True): """Capped distance evaluations using a brute force method. Computes and returns an array containing pairs of indices corresponding to entries in the reference and configuration arrays which are separated by a distance lying within the specified cutoff(s). Employs naive distance computations (brute force) to find relevant distances. Optionally, these distances can be returned as well. If the optional argument box is supplied, the minimum image convention is applied when calculating distances. Either orthogonal or triclinic boxes are supported. Parameters ---------- reference : numpy.ndarray Reference coordinate array with shape (3,) or (n, 3) (dtype will be converted to numpy.float32 internally). configuration : array Configuration coordinate array with shape (3,) or (m, 3) (dtype will be converted to numpy.float32 internally). max_cutoff : float Maximum cutoff distance between reference and configuration coordinates. min_cutoff : float, optional Minimum cutoff distance between reference and configuration coordinates. box : numpy.ndarray, optional The unitcell dimensions of the system, which can be orthogonal or triclinic and must be provided in the same format as returned by :attr:MDAnalysis.coordinates.base.Timestep.dimensions: [lx, ly, lz, alpha, beta, gamma]. return_distances : bool, optional If set to True, distances will also be returned. Returns ------- pairs : numpy.ndarray (dtype=numpy.int64, shape=(n_pairs, 2)) Pairs of indices, corresponding to coordinates in the reference and configuration arrays such that the distance between them lies within the interval (min_cutoff, max_cutoff]. Each row in pairs is an index pair [i, j] corresponding to the i-th coordinate in reference and the j-th coordinate in configuration. distances : numpy.ndarray (dtype=numpy.float64, shape=(n_pairs,)), optional Distances corresponding to each pair of indices. Only returned if return_distances is True. distances[k] corresponds to the k-th pair returned in pairs and gives the distance between the coordinates reference[pairs[k, 0]] and configuration[pairs[k, 1]]. """ # Default return values (will be overwritten only if pairs are found): pairs = np.empty((0, 2), dtype=np.intp) distances = np.empty((0,), dtype=np.float64) if len(reference) > 0 and len(configuration) > 0: _distances = distance_array(reference, configuration, box=box) if min_cutoff is not None: mask = np.where((_distances <= max_cutoff) & \ (_distances > min_cutoff)) else: mask = np.where((_distances <= max_cutoff)) if mask[0].size > 0: pairs = np.c_[mask[0], mask[1]] if return_distances: distances = _distances[mask] if return_distances: return pairs, distances else: return pairs @check_coords('reference', 'configuration', enforce_copy=False, reduce_result_if_single=False, check_lengths_match=False) def _pkdtree_capped(reference, configuration, max_cutoff, min_cutoff=None, box=None, return_distances=True): """Capped distance evaluations using a KDtree method. Computes and returns an array containing pairs of indices corresponding to entries in the reference and configuration arrays which are separated by a distance lying within the specified cutoff(s). Employs a (periodic) KDtree algorithm to find relevant distances. Optionally, these distances can be returned as well. If the optional argument box is supplied, the minimum image convention is applied when calculating distances. Either orthogonal or triclinic boxes are supported. Parameters ---------- reference : numpy.ndarray Reference coordinate array with shape (3,) or (n, 3) (dtype will be converted to numpy.float32 internally). configuration : array Configuration coordinate array with shape (3,) or (m, 3) (dtype will be converted to numpy.float32 internally). max_cutoff : float Maximum cutoff distance between reference and configuration coordinates. min_cutoff : float, optional Minimum cutoff distance between reference and configuration coordinates. box : numpy.ndarray, optional The unitcell dimensions of the system, which can be orthogonal or triclinic and must be provided in the same format as returned by :attr:MDAnalysis.coordinates.base.Timestep.dimensions: [lx, ly, lz, alpha, beta, gamma]. return_distances : bool, optional If set to True, distances will also be returned. Returns ------- pairs : numpy.ndarray (dtype=numpy.int64, shape=(n_pairs, 2)) Pairs of indices, corresponding to coordinates in the reference and configuration arrays such that the distance between them lies within the interval (min_cutoff, max_cutoff]. Each row in pairs is an index pair [i, j] corresponding to the i-th coordinate in reference and the j-th coordinate in configuration. distances : numpy.ndarray (dtype=numpy.float64, shape=(n_pairs,)), optional Distances corresponding to each pair of indices. Only returned if return_distances is True. distances[k] corresponds to the k-th pair returned in pairs and gives the distance between the coordinates reference[pairs[k, 0]] and configuration[pairs[k, 1]]. """ from .pkdtree import PeriodicKDTree # must be here to avoid circular import # Default return values (will be overwritten only if pairs are found): pairs = np.empty((0, 2), dtype=np.intp) distances = np.empty((0,), dtype=np.float64) if len(reference) > 0 and len(configuration) > 0: kdtree = PeriodicKDTree(box=box) cut = max_cutoff if box is not None else None kdtree.set_coords(configuration, cutoff=cut) _pairs = kdtree.search_tree(reference, max_cutoff) if _pairs.size > 0: pairs = _pairs if (return_distances or (min_cutoff is not None)): refA, refB = pairs[:, 0], pairs[:, 1] distances = calc_bonds(reference[refA], configuration[refB], box=box) if min_cutoff is not None: mask = np.where(distances > min_cutoff) pairs, distances = pairs[mask], distances[mask] if return_distances: return pairs, distances else: return pairs @check_coords('reference', 'configuration', enforce_copy=False, reduce_result_if_single=False, check_lengths_match=False) def _nsgrid_capped(reference, configuration, max_cutoff, min_cutoff=None, box=None, return_distances=True): """Capped distance evaluations using a grid-based search method. Computes and returns an array containing pairs of indices corresponding to entries in the reference and configuration arrays which are separated by a distance lying within the specified cutoff(s). Employs a grid-based search algorithm to find relevant distances. Optionally, these distances can be returned as well. If the optional argument box is supplied, the minimum image convention is applied when calculating distances. Either orthogonal or triclinic boxes are supported. Parameters ---------- reference : numpy.ndarray Reference coordinate array with shape (3,) or (n, 3) (dtype will be converted to numpy.float32 internally). configuration : array Configuration coordinate array with shape (3,) or (m, 3) (dtype will be converted to numpy.float32 internally). max_cutoff : float Maximum cutoff distance between reference and configuration coordinates. min_cutoff : float, optional Minimum cutoff distance between reference and configuration coordinates. box : numpy.ndarray (dtype=numpy.float64, shape=(n_pairs,)), optional The unitcell dimensions of the system, which can be orthogonal or triclinic and must be provided in the same format as returned by :attr:MDAnalysis.coordinates.base.Timestep.dimensions: [lx, ly, lz, alpha, beta, gamma]. return_distances : bool, optional If set to True, distances will also be returned. Returns ------- pairs : numpy.ndarray (dtype=numpy.int64, shape=(n_pairs, 2)) Pairs of indices, corresponding to coordinates in the reference and configuration arrays such that the distance between them lies within the interval (min_cutoff, max_cutoff]. Each row in pairs is an index pair [i, j] corresponding to the i-th coordinate in reference and the j-th coordinate in configuration. distances : numpy.ndarray, optional Distances corresponding to each pair of indices. Only returned if return_distances is True. distances[k] corresponds to the k-th pair returned in pairs and gives the distance between the coordinates reference[pairs[k, 0]] and configuration[pairs[k, 1]]. """ # Default return values (will be overwritten only if pairs are found): pairs = np.empty((0, 2), dtype=np.intp) distances = np.empty((0,), dtype=np.float64) if len(reference) > 0 and len(configuration) > 0: if box is None: # create a pseudobox # define the max range # and supply the pseudobox # along with only one set of coordinates pseudobox = np.zeros(6, dtype=np.float32) all_coords = np.concatenate([reference, configuration]) lmax = all_coords.max(axis=0) lmin = all_coords.min(axis=0) # Using maximum dimension as the box size boxsize = (lmax-lmin).max() # to avoid failures for very close particles but with # larger cutoff boxsize = np.maximum(boxsize, 2 * max_cutoff) pseudobox[:3] = boxsize + 2.2*max_cutoff pseudobox[3:] = 90. shiftref, shiftconf = reference.copy(), configuration.copy() # Extra padding near the origin shiftref -= lmin - 0.1*max_cutoff shiftconf -= lmin - 0.1*max_cutoff gridsearch = FastNS(max_cutoff, shiftconf, box=pseudobox, pbc=False) results = gridsearch.search(shiftref) else: gridsearch = FastNS(max_cutoff, configuration, box=box) results = gridsearch.search(reference) pairs = results.get_pairs() if return_distances or (min_cutoff is not None): distances = results.get_pair_distances() if min_cutoff is not None: idx = distances > min_cutoff pairs, distances = pairs[idx], distances[idx] if return_distances: return pairs, distances else: return pairs
[docs]def self_capped_distance(reference, max_cutoff, min_cutoff=None, box=None, method=None, return_distances=True): """Calculates pairs of indices corresponding to entries in the reference array which are separated by a distance lying within the specified cutoff(s). Optionally, these distances can be returned as well. If the optional argument box is supplied, the minimum image convention is applied when calculating distances. Either orthogonal or triclinic boxes are supported. An automatic guessing of the optimal method to calculate the distances is included in the function. An optional keyword for the method is also provided. Users can enforce a particular method with this functionality. Currently brute force, grid search, and periodic KDtree methods are implemented. Parameters ----------- reference : numpy.ndarray Reference coordinate array with shape (3,) or (n, 3). max_cutoff : float Maximum cutoff distance between reference coordinates. min_cutoff : float, optional Minimum cutoff distance between reference coordinates. box : array_like, optional The unitcell dimensions of the system, which can be orthogonal or triclinic and must be provided in the same format as returned by :attr:MDAnalysis.coordinates.base.Timestep.dimensions: [lx, ly, lz, alpha, beta, gamma]. method : {'bruteforce', 'nsgrid', 'pkdtree'}, optional Keyword to override the automatic guessing of the employed search method. return_distances : bool, optional If set to True, distances will also be returned. Returns ------- pairs : numpy.ndarray (dtype=numpy.int64, shape=(n_pairs, 2)) Pairs of indices, corresponding to coordinates in the reference array such that the distance between them lies within the interval (min_cutoff, max_cutoff]. Each row in pairs is an index pair [i, j] corresponding to the i-th and the j-th coordinate in reference. distances : numpy.ndarray (dtype=numpy.float64, shape=(n_pairs,)) Distances corresponding to each pair of indices. Only returned if return_distances is True. distances[k] corresponds to the k-th pair returned in pairs and gives the distance between the coordinates reference[pairs[k, 0]] and reference[pairs[k, 1]]. .. code-block:: python pairs, distances = self_capped_distances(reference, max_cutoff, return_distances=True) for k, [i, j] in enumerate(pairs): coord1 = reference[i] coord2 = reference[j] distance = distances[k] Note ----- Currently supports brute force, grid-based, and periodic KDtree search methods. See Also -------- self_distance_array MDAnalysis.lib.pkdtree.PeriodicKDTree.search MDAnalysis.lib.nsgrid.FastNS.self_search .. versionchanged:: 0.20.0 Added return_distances keyword. .. versionchanged:: 1.0.1 nsgrid was temporarily removed and replaced with pkdtree due to issues relating to its reliability and accuracy (Issues #2919, #2229, #2345, #2670, #2930) .. versionchanged:: 1.0.2 enabled nsgrid again """ if box is not None: box = np.asarray(box, dtype=np.float32) if box.shape[0] != 6: raise ValueError("Box Argument is of incompatible type. The " "dimension should be either None or of the form " "[lx, ly, lz, alpha, beta, gamma]") method = _determine_method_self(reference, max_cutoff, min_cutoff=min_cutoff, box=box, method=method) return method(reference, max_cutoff, min_cutoff=min_cutoff, box=box, return_distances=return_distances)
def _determine_method_self(reference, max_cutoff, min_cutoff=None, box=None, method=None): """Guesses the fastest method for capped distance calculations based on the size of the reference coordinate set and the relative size of the target volume. Parameters ---------- reference : numpy.ndarray Reference coordinate array with shape (3,) or (n, 3). max_cutoff : float Maximum cutoff distance between reference coordinates. min_cutoff : float, optional Minimum cutoff distance between reference coordinates. box : numpy.ndarray The unitcell dimensions of the system, which can be orthogonal or triclinic and must be provided in the same format as returned by :attr:MDAnalysis.coordinates.base.Timestep.dimensions: [lx, ly, lz, alpha, beta, gamma]. method : {'bruteforce', 'nsgrid', 'pkdtree'}, optional Keyword to override the automatic guessing of the employed search method. Returns ------- function : callable The function implementing the guessed (or deliberatly chosen) method. .. versionchanged:: 1.0.1 nsgrid was temporarily removed and replaced with pkdtree due to issues relating to its reliability and accuracy (Issues #2919, #2229, #2345, #2670, #2930) .. versionchanged:: 1.0.2 enabled nsgrid again """ methods = {'bruteforce': _bruteforce_capped_self, 'pkdtree': _pkdtree_capped_self, 'nsgrid': _nsgrid_capped_self, } if method is not None: return methods[method.lower()] if len(reference) < 100: return methods['bruteforce'] if box is None: min_dim = np.array([reference.min(axis=0)]) max_dim = np.array([reference.max(axis=0)]) size = max_dim.max(axis=0) - min_dim.min(axis=0) elif np.all(box[3:] == 90.0): size = box[:3] else: tribox = triclinic_vectors(box) size = tribox.max(axis=0) - tribox.min(axis=0) if max_cutoff < 0.03*size.min(): return methods['pkdtree'] else: return methods['nsgrid'] @check_coords('reference', enforce_copy=False, reduce_result_if_single=False) def _bruteforce_capped_self(reference, max_cutoff, min_cutoff=None, box=None, return_distances=True): """Capped distance evaluations using a brute force method. Computes and returns an array containing pairs of indices corresponding to entries in the reference array which are separated by a distance lying within the specified cutoff(s). Employs naive distance computations (brute force) to find relevant distances. Optionally, these distances can be returned as well. If the optional argument box is supplied, the minimum image convention is applied when calculating distances. Either orthogonal or triclinic boxes are supported. Parameters ---------- reference : numpy.ndarray Reference coordinate array with shape (3,) or (n, 3) (dtype will be converted to numpy.float32 internally). max_cutoff : float Maximum cutoff distance between reference coordinates. min_cutoff : float, optional Minimum cutoff distance between reference coordinates. box : numpy.ndarray, optional The unitcell dimensions of the system, which can be orthogonal or triclinic and must be provided in the same format as returned by :attr:MDAnalysis.coordinates.base.Timestep.dimensions: [lx, ly, lz, alpha, beta, gamma]. return_distances : bool, optional If set to True, distances will also be returned. Returns ------- pairs : numpy.ndarray (dtype=numpy.int64, shape=(n_pairs, 2)) Pairs of indices, corresponding to coordinates in the reference array such that the distance between them lies within the interval (min_cutoff, max_cutoff]. Each row in pairs is an index pair [i, j] corresponding to the i-th and the j-th coordinate in reference. distances : numpy.ndarray (dtype=numpy.float64, shape=(n_pairs,)), optional Distances corresponding to each pair of indices. Only returned if return_distances is True. distances[k] corresponds to the k-th pair returned in pairs and gives the distance between the coordinates reference[pairs[k, 0]] and configuration[pairs[k, 1]]. .. versionchanged:: 0.20.0 Added return_distances keyword. """ # Default return values (will be overwritten only if pairs are found): pairs = np.empty((0, 2), dtype=np.intp) distances = np.empty((0,), dtype=np.float64) N = len(reference) # We're searching within a single coordinate set, so we need at least two # coordinates to find distances between them. if N > 1: distvec = self_distance_array(reference, box=box) dist = np.full((N, N), np.finfo(np.float64).max, dtype=np.float64) dist[np.triu_indices(N, 1)] = distvec if min_cutoff is not None: mask = np.where((dist <= max_cutoff) & (dist > min_cutoff)) else: mask = np.where((dist <= max_cutoff)) if mask[0].size > 0: pairs = np.c_[mask[0], mask[1]] distances = dist[mask] if return_distances: return pairs, distances return pairs @check_coords('reference', enforce_copy=False, reduce_result_if_single=False) def _pkdtree_capped_self(reference, max_cutoff, min_cutoff=None, box=None, return_distances=True): """Capped distance evaluations using a KDtree method. Computes and returns an array containing pairs of indices corresponding to entries in the reference array which are separated by a distance lying within the specified cutoff(s). Employs a (periodic) KDtree algorithm to find relevant distances. Optionally, these distances can be returned as well. If the optional argument box is supplied, the minimum image convention is applied when calculating distances. Either orthogonal or triclinic boxes are supported. Parameters ---------- reference : numpy.ndarray Reference coordinate array with shape (3,) or (n, 3) (dtype will be converted to numpy.float32 internally). max_cutoff : float Maximum cutoff distance between reference coordinates. min_cutoff : float, optional Minimum cutoff distance between reference coordinates. box : numpy.ndarray, optional The unitcell dimensions of the system, which can be orthogonal or triclinic and must be provided in the same format as returned by :attr:MDAnalysis.coordinates.base.Timestep.dimensions: [lx, ly, lz, alpha, beta, gamma]. return_distances : bool, optional If set to True, distances will also be returned. Returns ------- pairs : numpy.ndarray (dtype=numpy.int64, shape=(n_pairs, 2)) Pairs of indices, corresponding to coordinates in the reference array such that the distance between them lies within the interval (min_cutoff, max_cutoff]. Each row in pairs is an index pair [i, j] corresponding to the i-th and the j-th coordinate in reference. distances : numpy.ndarray (dtype=numpy.float64, shape=(n_pairs,)) Distances corresponding to each pair of indices. Only returned if return_distances is True. distances[k] corresponds to the k-th pair returned in pairs and gives the distance between the coordinates reference[pairs[k, 0]] and reference[pairs[k, 1]]. .. versionchanged:: 0.20.0 Added return_distances keyword. """ from .pkdtree import PeriodicKDTree # must be here to avoid circular import # Default return values (will be overwritten only if pairs are found): pairs = np.empty((0, 2), dtype=np.intp) distances = np.empty((0,), dtype=np.float64) # We're searching within a single coordinate set, so we need at least two # coordinates to find distances between them. if len(reference) > 1: kdtree = PeriodicKDTree(box=box) cut = max_cutoff if box is not None else None kdtree.set_coords(reference, cutoff=cut) _pairs = kdtree.search_pairs(max_cutoff) if _pairs.size > 0: pairs = _pairs if (return_distances or (min_cutoff is not None)): refA, refB = pairs[:, 0], pairs[:, 1] distances = calc_bonds(reference[refA], reference[refB], box=box) if min_cutoff is not None: idx = distances > min_cutoff pairs, distances = pairs[idx], distances[idx] if return_distances: return pairs, distances return pairs @check_coords('reference', enforce_copy=False, reduce_result_if_single=False) def _nsgrid_capped_self(reference, max_cutoff, min_cutoff=None, box=None, return_distances=True): """Capped distance evaluations using a grid-based search method. Computes and returns an array containing pairs of indices corresponding to entries in the reference array which are separated by a distance lying within the specified cutoff(s). Employs a grid-based search algorithm to find relevant distances. Optionally, these distances can be returned as well. If the optional argument box is supplied, the minimum image convention is applied when calculating distances. Either orthogonal or triclinic boxes are supported. Parameters ---------- reference : numpy.ndarray Reference coordinate array with shape (3,) or (n, 3) (dtype will be converted to numpy.float32 internally). max_cutoff : float Maximum cutoff distance between reference coordinates. min_cutoff : float, optional Minimum cutoff distance between reference coordinates. box : numpy.ndarray, optional The unitcell dimensions of the system, which can be orthogonal or triclinic and must be provided in the same format as returned by :attr:MDAnalysis.coordinates.base.Timestep.dimensions: [lx, ly, lz, alpha, beta, gamma]. Returns ------- pairs : numpy.ndarray (dtype=numpy.int64, shape=(n_pairs, 2)) Pairs of indices, corresponding to coordinates in the reference array such that the distance between them lies within the interval (min_cutoff, max_cutoff]. Each row in pairs is an index pair [i, j] corresponding to the i-th and the j-th coordinate in reference. distances : numpy.ndarray, optional Distances corresponding to each pair of indices. Only returned if return_distances is True. distances[k] corresponds to the k-th pair returned in pairs and gives the distance between the coordinates reference[pairs[k, 0]] and configuration[pairs[k, 1]]. .. versionchanged:: 0.20.0 Added return_distances keyword. """ # Default return values (will be overwritten only if pairs are found): pairs = np.empty((0, 2), dtype=np.intp) distances = np.empty((0,), dtype=np.float64) # We're searching within a single coordinate set, so we need at least two # coordinates to find distances between them. if len(reference) > 1: if box is None: # create a pseudobox # define the max range # and supply the pseudobox # along with only one set of coordinates pseudobox = np.zeros(6, dtype=np.float32) lmax = reference.max(axis=0) lmin = reference.min(axis=0) # Using maximum dimension as the box size boxsize = (lmax-lmin).max() # to avoid failures of very close particles # but with larger cutoff if boxsize < 2*max_cutoff: # just enough box size so that NSGrid doesnot fails sizefactor = 2.2*max_cutoff/boxsize else: sizefactor = 1.2 pseudobox[:3] = sizefactor*boxsize pseudobox[3:] = 90. shiftref = reference.copy() # Extra padding near the origin shiftref -= lmin - 0.1*boxsize gridsearch = FastNS(max_cutoff, shiftref, box=pseudobox, pbc=False) results = gridsearch.self_search() else: gridsearch = FastNS(max_cutoff, reference, box=box) results = gridsearch.self_search() pairs = results.get_pairs() if return_distances or (min_cutoff is not None): distances = results.get_pair_distances() if min_cutoff is not None: idx = distances > min_cutoff pairs, distances = pairs[idx], distances[idx] if return_distances: return pairs, distances return pairs
[docs]@check_coords('coords') def transform_RtoS(coords, box, backend="serial"): """Transform an array of coordinates from real space to S space (a.k.a. lambda space) S space represents fractional space within the unit cell for this system. Reciprocal operation to :meth:transform_StoR. Parameters ---------- coords : numpy.ndarray A (3,) or (n, 3) array of coordinates (dtype is arbitrary, will be converted to numpy.float32 internally). box : numpy.ndarray The unitcell dimensions of the system, which can be orthogonal or triclinic and must be provided in the same format as returned by :attr:MDAnalysis.coordinates.base.Timestep.dimensions: [lx, ly, lz, alpha, beta, gamma]. backend : {'serial', 'OpenMP'}, optional Keyword selecting the type of acceleration. Returns ------- newcoords : numpy.ndarray (dtype=numpy.float32, shape=coords.shape) An array containing fractional coordiantes. .. versionchanged:: 0.13.0 Added *backend* keyword. .. versionchanged:: 0.19.0 Internal dtype conversion of input coordinates to numpy.float32. Now also accepts (and, likewise, returns) a single coordinate. """ if len(coords) == 0: return coords boxtype, box = check_box(box) if boxtype == 'ortho': box = np.diag(box) box = box.astype(np.float64) # Create inverse matrix of box # need order C here inv = np.array(np.linalg.inv(box), order='C') _run("coord_transform", args=(coords, inv), backend=backend) return coords
[docs]@check_coords('coords') def transform_StoR(coords, box, backend="serial"): """Transform an array of coordinates from S space into real space. S space represents fractional space within the unit cell for this system. Reciprocal operation to :meth:transform_RtoS Parameters ---------- coords : numpy.ndarray A (3,) or (n, 3) array of coordinates (dtype is arbitrary, will be converted to numpy.float32 internally). box : numpy.ndarray The unitcell dimensions of the system, which can be orthogonal or triclinic and must be provided in the same format as returned by :attr:MDAnalysis.coordinates.base.Timestep.dimensions: [lx, ly, lz, alpha, beta, gamma]. backend : {'serial', 'OpenMP'}, optional Keyword selecting the type of acceleration. Returns ------- newcoords : numpy.ndarray (dtype=numpy.float32, shape=coords.shape) An array containing real space coordiantes. .. versionchanged:: 0.13.0 Added *backend* keyword. .. versionchanged:: 0.19.0 Internal dtype conversion of input coordinates to numpy.float32. Now also accepts (and, likewise, returns) a single coordinate. """ if len(coords) == 0: return coords boxtype, box = check_box(box) if boxtype == 'ortho': box = np.diag(box) box = box.astype(np.float64) _run("coord_transform", args=(coords, box), backend=backend) return coords
[docs]@check_coords('coords1', 'coords2') def calc_bonds(coords1, coords2, box=None, result=None, backend="serial"): """Calculates the bond lengths between pairs of atom positions from the two coordinate arrays coords1 and coords2, which must contain the same number of coordinates. coords1[i] and coords2[i] represent the positions of atoms connected by the i-th bond. If single coordinates are supplied, a single distance will be returned. In comparison to :meth:distance_array and :meth:self_distance_array, which calculate distances between all possible combinations of coordinates, :meth:calc_bonds only calculates distances between pairs of coordinates, similar to:: numpy.linalg.norm(a - b) for a, b in zip(coords1, coords2) If the optional argument box is supplied, the minimum image convention is applied when calculating distances. Either orthogonal or triclinic boxes are supported. If a numpy array of dtype numpy.float64 with shape (n,) (for n coordinate pairs) is provided in result, then this preallocated array is filled. This can speed up calculations. Parameters ---------- coords1 : numpy.ndarray Coordinate array of shape (3,) or (n, 3) for one half of a single or n bonds, respectively (dtype is arbitrary, will be converted to numpy.float32 internally). coords2 : numpy.ndarray Coordinate array of shape (3,) or (n, 3) for the other half of a single or n bonds, respectively (dtype is arbitrary, will be converted to numpy.float32 internally). box : numpy.ndarray, optional The unitcell dimensions of the system, which can be orthogonal or triclinic and must be provided in the same format as returned by :attr:MDAnalysis.coordinates.base.Timestep.dimensions: [lx, ly, lz, alpha, beta, gamma]. result : numpy.ndarray, optional Preallocated result array of dtype numpy.float64 and shape (n,) (for n coordinate pairs). Avoids recreating the array in repeated function calls. backend : {'serial', 'OpenMP'}, optional Keyword selecting the type of acceleration. Returns ------- bondlengths : numpy.ndarray (dtype=numpy.float64, shape=(n,)) or numpy.float64 Array containing the bond lengths between each pair of coordinates. If two single coordinates were supplied, their distance is returned as a single number instead of an array. .. versionadded:: 0.8 .. versionchanged:: 0.13.0 Added *backend* keyword. .. versionchanged:: 0.19.0 Internal dtype conversion of input coordinates to numpy.float32. Now also accepts single coordinates as input. """ numatom = coords1.shape[0] bondlengths = _check_result_array(result, (numatom,)) if numatom > 0: if box is not None: boxtype, box = check_box(box) if boxtype == 'ortho': _run("calc_bond_distance_ortho", args=(coords1, coords2, box, bondlengths), backend=backend) else: _run("calc_bond_distance_triclinic", args=(coords1, coords2, box, bondlengths), backend=backend) else: _run("calc_bond_distance", args=(coords1, coords2, bondlengths), backend=backend) return bondlengths
[docs]@check_coords('coords1', 'coords2', 'coords3') def calc_angles(coords1, coords2, coords3, box=None, result=None, backend="serial"): """Calculates the angles formed between triplets of atom positions from the three coordinate arrays coords1, coords2, and coords3. All coordinate arrays must contain the same number of coordinates. The coordinates in coords2 represent the apices of the angles:: 2---3 / 1 Configurations where the angle is undefined (e.g., when coordinates 1 or 3 of a triplet coincide with coordinate 2) result in a value of **zero** for that angle. If the optional argument box is supplied, periodic boundaries are taken into account when constructing the connecting vectors between coordinates, i.e., the minimum image convention is applied for the vectors forming the angles. Either orthogonal or triclinic boxes are supported. If a numpy array of dtype numpy.float64 with shape (n,) (for n coordinate triplets) is provided in result, then this preallocated array is filled. This can speed up calculations. Parameters ---------- coords1 : numpy.ndarray Array of shape (3,) or (n, 3) containing the coordinates of one side of a single or n angles, respectively (dtype is arbitrary, will be converted to numpy.float32 internally) coords2 : numpy.ndarray Array of shape (3,) or (n, 3) containing the coordinates of the apices of a single or n angles, respectively (dtype is arbitrary, will be converted to numpy.float32 internally) coords3 : numpy.ndarray Array of shape (3,) or (n, 3) containing the coordinates of the other side of a single or n angles, respectively (dtype is arbitrary, will be converted to numpy.float32 internally) box : numpy.ndarray, optional The unitcell dimensions of the system, which can be orthogonal or triclinic and must be provided in the same format as returned by :attr:MDAnalysis.coordinates.base.Timestep.dimensions: [lx, ly, lz, alpha, beta, gamma]. result : numpy.ndarray, optional Preallocated result array of dtype numpy.float64 and shape (n,) (for n coordinate triplets). Avoids recreating the array in repeated function calls. backend : {'serial', 'OpenMP'}, optional Keyword selecting the type of acceleration. Returns ------- angles : numpy.ndarray (dtype=numpy.float64, shape=(n,)) or numpy.float64 Array containing the angles between each triplet of coordinates. Values are returned in radians (rad). If three single coordinates were supplied, the angle is returned as a single number instead of an array. .. versionadded:: 0.8 .. versionchanged:: 0.9.0 Added optional box argument to account for periodic boundaries in calculation .. versionchanged:: 0.13.0 Added *backend* keyword. .. versionchanged:: 0.19.0 Internal dtype conversion of input coordinates to numpy.float32. Now also accepts single coordinates as input. """ numatom = coords1.shape[0] angles = _check_result_array(result, (numatom,)) if numatom > 0: if box is not None: boxtype, box = check_box(box) if boxtype == 'ortho': _run("calc_angle_ortho", args=(coords1, coords2, coords3, box, angles), backend=backend) else: _run("calc_angle_triclinic", args=(coords1, coords2, coords3, box, angles), backend=backend) else: _run("calc_angle", args=(coords1, coords2, coords3, angles), backend=backend) return angles
[docs]@check_coords('coords1', 'coords2', 'coords3', 'coords4') def calc_dihedrals(coords1, coords2, coords3, coords4, box=None, result=None, backend="serial"): r"""Calculates the dihedral angles formed between quadruplets of positions from the four coordinate arrays coords1, coords2, coords3, and coords4, which must contain the same number of coordinates. The dihedral angle formed by a quadruplet of positions (1,2,3,4) is calculated around the axis connecting positions 2 and 3 (i.e., the angle between the planes spanned by positions (1,2,3) and (2,3,4)):: 4 | 2-----3 / 1 If all coordinates lie in the same plane, the cis configuration corresponds to a dihedral angle of zero, and the trans configuration to :math:\pi radians (180 degrees). Configurations where the dihedral angle is undefined (e.g., when all coordinates lie on the same straight line) result in a value of nan (not a number) for that dihedral. If the optional argument box is supplied, periodic boundaries are taken into account when constructing the connecting vectors between coordinates, i.e., the minimum image convention is applied for the vectors forming the dihedral angles. Either orthogonal or triclinic boxes are supported. If a numpy array of dtype numpy.float64 with shape (n,) (for n coordinate quadruplets) is provided in result then this preallocated array is filled. This can speed up calculations. Parameters ---------- coords1 : numpy.ndarray Coordinate array of shape (3,) or (n, 3) containing the 1st positions in dihedrals (dtype is arbitrary, will be converted to numpy.float32 internally) coords2 : numpy.ndarray Coordinate array of shape (3,) or (n, 3) containing the 2nd positions in dihedrals (dtype is arbitrary, will be converted to numpy.float32 internally) coords3 : numpy.ndarray Coordinate array of shape (3,) or (n, 3) containing the 3rd positions in dihedrals (dtype is arbitrary, will be converted to numpy.float32 internally) coords4 : numpy.ndarray Coordinate array of shape (3,) or (n, 3) containing the 4th positions in dihedrals (dtype is arbitrary, will be converted to numpy.float32 internally) box : numpy.ndarray, optional The unitcell dimensions of the system, which can be orthogonal or triclinic and must be provided in the same format as returned by :attr:MDAnalysis.coordinates.base.Timestep.dimensions: [lx, ly, lz, alpha, beta, gamma]. result : numpy.ndarray, optional Preallocated result array of dtype numpy.float64 and shape (n,) (for n coordinate quadruplets). Avoids recreating the array in repeated function calls. backend : {'serial', 'OpenMP'}, optional Keyword selecting the type of acceleration. Returns ------- dihedrals : numpy.ndarray (dtype=numpy.float64, shape=(n,)) or numpy.float64 Array containing the dihedral angles formed by each quadruplet of coordinates. Values are returned in radians (rad). If four single coordinates were supplied, the dihedral angle is returned as a single number instead of an array. .. versionadded:: 0.8 .. versionchanged:: 0.9.0 Added optional box argument to account for periodic boundaries in calculation .. versionchanged:: 0.11.0 Renamed from calc_torsions to calc_dihedrals .. versionchanged:: 0.13.0 Added *backend* keyword. .. versionchanged:: 0.19.0 Internal dtype conversion of input coordinates to numpy.float32. Now also accepts single coordinates as input. """ numatom = coords1.shape[0] dihedrals = _check_result_array(result, (numatom,)) if numatom > 0: if box is not None: boxtype, box = check_box(box) if boxtype == 'ortho': _run("calc_dihedral_ortho", args=(coords1, coords2, coords3, coords4, box, dihedrals), backend=backend) else: _run("calc_dihedral_triclinic", args=(coords1, coords2, coords3, coords4, box, dihedrals), backend=backend) else: _run("calc_dihedral", args=(coords1, coords2, coords3, coords4, dihedrals), backend=backend) return dihedrals
[docs]@check_coords('coords') def apply_PBC(coords, box, backend="serial"): """Moves coordinates into the primary unit cell. Parameters ---------- coords : numpy.ndarray Coordinate array of shape (3,) or (n, 3) (dtype is arbitrary, will be converted to numpy.float32 internally). box : numpy.ndarray The unitcell dimensions of the system, which can be orthogonal or triclinic and must be provided in the same format as returned by :attr:MDAnalysis.coordinates.base.Timestep.dimensions: [lx, ly, lz, alpha, beta, gamma]. backend : {'serial', 'OpenMP'}, optional Keyword selecting the type of acceleration. Returns ------- newcoords : numpy.ndarray (dtype=numpy.float32, shape=coords.shape) Array containing coordinates that all lie within the primary unit cell as defined by box. .. versionadded:: 0.8 .. versionchanged:: 0.13.0 Added *backend* keyword. .. versionchanged:: 0.19.0 Internal dtype conversion of input coordinates to numpy.float32. Now also accepts (and, likewise, returns) single coordinates. """ if len(coords) == 0: return coords boxtype, box = check_box(box) if boxtype == 'ortho': _run("ortho_pbc", args=(coords, box), backend=backend) else: _run("triclinic_pbc", args=(coords, box), backend=backend) return coords
[docs]@check_coords('vectors', enforce_copy=False, enforce_dtype=False) def minimize_vectors(vectors, box): """Apply minimum image convention to an array of vectors This function is required for calculating the correct vectors between two points. A naive approach of ag1.positions - ag2.positions will not provide the minimum vectors between particles, even if all particles are within the primary unit cell (box). Parameters ---------- vectors : numpy.ndarray Vector array of shape (n, 3), either float32 or float64. These represent many vectors (such as between two particles). box : numpy.ndarray The unitcell dimensions of the system, which can be orthogonal or triclinic and must be provided in the same format as returned by :attr:MDAnalysis.coordinates.base.Timestep.dimensions: [lx, ly, lz, alpha, beta, gamma]`. Returns ------- minimized_vectors : numpy.ndarray Same shape and dtype as input. The vectors from the input, but minimized according to the size of the box. .. versionadded:: 2.1.0 """ boxtype, box = check_box(box) output = np.empty_like(vectors) # use box which is same precision as input vectors box = box.astype(vectors.dtype) if boxtype == 'ortho': _minimize_vectors_ortho(vectors, box, output) else: _minimize_vectors_triclinic(vectors, box.ravel(), output) return output