13.2.1. Fast distance array computation — `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.

13.2.1.1. 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):

Available *backends* for accelerated distance functions.¶
backend	module	description
“serial”	`c_distances`	serial implementation in C/Cython
“OpenMP”	`c_distances_openmp`	parallel implementation in C/Cython with OpenMP

New in version 0.13.0.

13.2.1.2. Functions¶

MDAnalysis.lib.distances.distance_array(reference, configuration, box=None, result=None, backend='serial')[source]¶

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 `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 – Array containing the distances `d[i,j]` between reference coordinates `i` and configuration coordinates `j`.
Return type:	numpy.ndarray (`dtype=numpy.float64`, `shape=(n, m)`)

Changed in version 0.13.0: Added backend keyword.

Changed in version 0.19.0: Internal dtype conversion of input coordinates to numpy.float32. Now also accepts single coordinates as input.

MDAnalysis.lib.distances.self_distance_array(reference, box=None, result=None, backend='serial')[source]¶

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 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 – Array containing the distances dist[i,j] between reference coordinates i and j at position d[k]. Loop through d:

for i in range(n):
    for j in range(i + 1, n):
        k += 1
        dist[i, j] = d[k]

Return type:

numpy.ndarray (dtype=numpy.float64, shape=(n*(n-1)/2,))

Changed in version 0.13.0: Added backend keyword.

Changed in version 0.19.0: Internal dtype conversion of input coordinates to numpy.float32.

MDAnalysis.lib.distances.capped_distance(reference, configuration, max_cutoff, min_cutoff=None, box=None, method=None, return_distances=True)[source]¶

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 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 MDAnalysis.coordinates.base.Timestep.dimensions:

[lx, ly, lz, alpha, beta, gamma].
method ({'bruteforce', '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]].

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]

Note

Currently supports brute force, and periodic KDtree search methods.

Changed in version 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)

MDAnalysis.lib.distances.self_capped_distance(reference, max_cutoff, min_cutoff=None, box=None, method=None, return_distances=True)[source]¶

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, 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 MDAnalysis.coordinates.base.Timestep.dimensions:

[lx, ly, lz, alpha, beta, gamma].
method ({'bruteforce', '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]].

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, and periodic KDtree search methods.

Changed in version 0.20.0: Added return_distances keyword.

Changed in version 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)

MDAnalysis.lib.distances.calc_bonds(coords1, coords2, box=None, result=None, backend='serial')[source]¶

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 distance_array() and self_distance_array(), which calculate distances between all possible combinations of coordinates, 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 `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 – 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.
Return type:	numpy.ndarray (`dtype=numpy.float64`, `shape=(n,)`) or numpy.float64

New in version 0.8.

Changed in version 0.13.0: Added backend keyword.

Changed in version 0.19.0: Internal dtype conversion of input coordinates to numpy.float32. Now also accepts single coordinates as input.

MDAnalysis.lib.distances.calc_angles(coords1, coords2, coords3, box=None, result=None, backend='serial')[source]¶

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 `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 – 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.
Return type:	numpy.ndarray (`dtype=numpy.float64`, `shape=(n,)`) or numpy.float64

New in version 0.8.

Changed in version 0.9.0: Added optional box argument to account for periodic boundaries in calculation

Changed in version 0.13.0: Added backend keyword.

Changed in version 0.19.0: Internal dtype conversion of input coordinates to numpy.float32. Now also accepts single coordinates as input.

MDAnalysis.lib.distances.calc_dihedrals(coords1, coords2, coords3, coords4, box=None, result=None, backend='serial')[source]¶

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 \(\pi\) 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 `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 – 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.
Return type:	numpy.ndarray (`dtype=numpy.float64`, `shape=(n,)`) or numpy.float64

New in version 0.8.

Changed in version 0.9.0: Added optional box argument to account for periodic boundaries in calculation

Changed in version 0.11.0: Renamed from calc_torsions to calc_dihedrals

Changed in version 0.13.0: Added backend keyword.

Changed in version 0.19.0: Internal dtype conversion of input coordinates to numpy.float32. Now also accepts single coordinates as input.

MDAnalysis.lib.distances.apply_PBC(coords, box, backend='serial')[source]¶

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 `MDAnalysis.coordinates.base.Timestep.dimensions`: `[lx, ly, lz, alpha, beta, gamma]`. backend ({'serial', 'OpenMP'}, optional) – Keyword selecting the type of acceleration.
Returns:	newcoords – Array containing coordinates that all lie within the primary unit cell as defined by box.
Return type:	numpy.ndarray (`dtype=numpy.float32`, `shape=coords.shape`)

New in version 0.8.

Changed in version 0.13.0: Added backend keyword.

Changed in version 0.19.0: Internal dtype conversion of input coordinates to numpy.float32. Now also accepts (and, likewise, returns) single coordinates.

MDAnalysis.lib.distances.transform_RtoS(coords, box, backend='serial')[source]¶

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 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 `MDAnalysis.coordinates.base.Timestep.dimensions`: `[lx, ly, lz, alpha, beta, gamma]`. backend ({'serial', 'OpenMP'}, optional) – Keyword selecting the type of acceleration.
Returns:	newcoords – An array containing fractional coordiantes.
Return type:	numpy.ndarray (`dtype=numpy.float32`, `shape=coords.shape`)

Changed in version 0.13.0: Added backend keyword.

Changed in version 0.19.0: Internal dtype conversion of input coordinates to numpy.float32. Now also accepts (and, likewise, returns) a single coordinate.

MDAnalysis.lib.distances.transform_StoR(coords, box, backend='serial')[source]¶

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 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 `MDAnalysis.coordinates.base.Timestep.dimensions`: `[lx, ly, lz, alpha, beta, gamma]`. backend ({'serial', 'OpenMP'}, optional) – Keyword selecting the type of acceleration.
Returns:	newcoords – An array containing real space coordiantes.
Return type:	numpy.ndarray (`dtype=numpy.float32`, `shape=coords.shape`)

Changed in version 0.13.0: Added backend keyword.

Changed in version 0.19.0: Internal dtype conversion of input coordinates to numpy.float32. Now also accepts (and, likewise, returns) a single coordinate.

MDAnalysis.lib.distances.augment_coordinates(coordinates, box, r)¶

Calculates the periodic images of particles which are within a distance r from the box walls.

The algorithm works by generating explicit periodic images of atoms residing close to any of the six box walls. The steps involved in generating images involves the evaluation of reciprocal box vectors followed by the calculation of distances of atoms from the walls by means of projection onto the reciprocal vectors. If the distance is less than a specified cutoff distance, relevant periodic images are generated using box translation vectors \(\vec{t}\) with

\[\vec{t}=l\cdot\vec{a}+m\cdot\vec{b}+n\cdot \vec{c}\,,\]

where \(l,\,m,\,n \in \{-1,\,0,\,1\}\) are the neighboring cell indices in \(x\)-, \(y\)-, and \(z\)-direction relative to the central cell with box vectors \(\vec{a},\,\vec{b},\,\vec{c}\).

For instance, an atom close to the \(xy\)-plane containing the origin will generate a periodic image outside the central cell and close to the opposite \(xy\)-plane of the box, i.e., shifted by \(\vec{t} = 0\cdot\vec{a}+0\cdot\vec{b}+1\cdot\vec{c}=\vec{c}\).

Likewise, if the particle is close to more than one box walls, images along the diagonals are also generated:

                            x            x
+------------+                +------------+
|            |   augment      |            |
|            |   ------->     |            |
|          o |              x |          o |
+------------+                +------------+

Parameters:

coordinates (numpy.ndarray) – Input coordinate array of shape (n, 3) and dtype numpy.float32 used to generate duplicate images in the vicinity of the central cell. All coordinates must be within the primary unit cell.
box (numpy.ndarray) – Box dimensions of shape (6,) and dtype numpy.float32. The dimensions must be provided in the same format as returned by MDAnalysis.coordinates.base.Timestep.dimensions: [lx, ly, lz, alpha, beta, gamma]
r (float) – Thickness of cutoff region for duplicate image generation.

Returns:

output (numpy.ndarray) – Coordinates of duplicate (augmented) particles (dtype numpy.float32).
indices (numpy.ndarray) – Original indices of the augmented coordinates (dtype numpy.int64). Maps the indices of augmented particles to their original particle index such that indices[augmented_index] = original_index.

Note

Output does not return coordinates from the initial array. To merge the particles with their respective images, the following operation is necessary when generating the images:

images, mapping = augment_coordinates(coordinates, box, max_cutoff)
all_coords = numpy.concatenate([coordinates, images])

See also

undo_augment()

New in version 0.19.0.

MDAnalysis.lib.distances.undo_augment(results, translation, nreal)¶

Translate augmented indices back to original indices.

Parameters:	results (numpy.ndarray) – Array of dtype `numpy.int64` containing coordinate indices, including “augmented” indices. translation (numpy.ndarray) – Index map of dtype `numpy.int64` linking the augmented indices to the original particle indices such that `translation[augmented_index] = original_index`. nreal (int) – Number of real coordinates, i.e., indices in results equal or larger than this need to be mapped to their real counterpart.
Returns:	results – Modified input results with all the augmented indices translated to their corresponding initial original indices.
Return type:	numpy.ndarray

Note

Modifies the results array in place.

See also

augment_coordinates()

New in version 0.19.0.

13.2.2. Low-level modules for `MDAnalysis.lib.distances`¶

MDAnalysis.lib._distances contains low level access to the serial MDAnalysis Cython functions in distances. These have little to no error checking done on inputs so should be used with caution. Similarly, MDAnalysis.lib._distances_openmp contains the OpenMP-enable functions.

13.2.1. Fast distance array computation — MDAnalysis.lib.distances¶

13.2.1.1. Selection of acceleration (“backend”)¶

13.2.1.2. Functions¶

13.2.2. Low-level modules for MDAnalysis.lib.distances¶

13.2.1. Fast distance array computation — `MDAnalysis.lib.distances`¶

13.2.2. Low-level modules for `MDAnalysis.lib.distances`¶