def _displacement_mic(xyz, pairs, box_vectors, orthogonal):
"""Displacement vector between pairs of points in each frame under the
minimum image convention for periodic boundary conditions.
The computation follows scheme B.9 in Tukerman, M. "Statistical
Mechanics: Theory and Molecular Simulation", 2010.
This is a very slow pure python implementation, mostly for testing.
"""
out = np.empty((xyz.shape[0], pairs.shape[0], 3), dtype=np.float32)
for i in range(len(xyz)):
bv1, bv2, bv3 = _reduce_box_vectors(box_vectors[i].T)
hinv = np.linalg.inv(np.array([bv1, bv2, bv3]).T)
for j, (a,b) in enumerate(pairs):
r12 = xyz[i,b,:] - xyz[i,a,:]
r12 -= bv3*round(r12[2]/bv3[2]);
r12 -= bv2*round(r12[1]/bv2[1]);
r12 -= bv1*round(r12[0]/bv1[0]);
min_disp = r12
dist2 = (r12*r12).sum()
if not orthogonal:
for ii in range(-1, 2):
v1 = bv1*ii
for jj in range(-1, 2):
v12 = bv2*jj+v1
for kk in range(-1, 2):
tmp = r12 + v12 + bv3*kk
new_dist2 = (tmp*tmp).sum()
if new_dist2 < dist2:
dist2 = new_dist2
min_disp = tmp
out[i, j] = min_disp
return out
def _distance_mic(xyz, pairs, box_vectors, orthogonal):
"""Distance between pairs of points in each frame under the minimum image
convention for periodic boundary conditions.
The computation follows scheme B.9 in Tukerman, M. "Statistical
Mechanics: Theory and Molecular Simulation", 2010.
This is a slow pure python implementation, mostly for testing.
"""
out = np.empty((xyz.shape[0], pairs.shape[0]), dtype=np.float32)
for i in range(len(xyz)):
bv1, bv2, bv3 = _reduce_box_vectors(box_vectors[i].T)
for j, (a,b) in enumerate(pairs):
r12 = xyz[i,b,:] - xyz[i,a,:]
r12 -= bv3*round(r12[2]/bv3[2]);
r12 -= bv2*round(r12[1]/bv2[1]);
r12 -= bv1*round(r12[0]/bv1[0]);
dist = np.linalg.norm(r12)
if not orthogonal:
for ii in range(-1, 2):
v1 = bv1*ii
for jj in range(-1, 2):
v12 = bv2*jj + v1
for kk in range(-1, 2):
new_r12 = r12 + v12 + bv3*kk
dist = min(dist, np.linalg.norm(new_r12))
out[i, j] = dist
return out
def _displacement_mic(xyz, pairs, box_vectors, orthogonal):
"""Displacement vector between pairs of points in each frame under the
minimum image convention for periodic boundary conditions.
The computation follows scheme B.9 in Tukerman, M. "Statistical
Mechanics: Theory and Molecular Simulation", 2010.
This is a very slow pure python implementation, mostly for testing.
"""
out = np.empty((xyz.shape[0], pairs.shape[0], 3), dtype=np.float32)
for i in range(len(xyz)):
hinv = np.linalg.inv(box_vectors[i])
bv1, bv2, bv3 = box_vectors[i].T
for j, (a,b) in enumerate(pairs):
s1 = np.dot(hinv, xyz[i,a,:])
s2 = np.dot(hinv, xyz[i,b,:])
s12 = s2 - s1
s12 = s12 - np.round(s12)
disp = np.dot(box_vectors[i], s12)
min_disp = disp
dist2 = (disp*disp).sum()
if not orthogonal:
for ii in range(-1, 2):
v1 = bv1*ii
for jj in range(-1, 2):
v12 = bv2*jj+v1
for kk in range(-1, 2):
tmp = disp + v12 + bv3*kk
new_dist2 = (tmp*tmp).sum()
if new_dist2 < dist2:
dist2 = new_dist2
min_disp = tmp
out[i, j] = min_disp
return out
def _displacement_mic(xyz, pairs, box_vectors, orthogonal):
"""Displacement vector between pairs of points in each frame under the
minimum image convention for periodic boundary conditions.
The computation follows scheme B.9 in Tukerman, M. "Statistical
Mechanics: Theory and Molecular Simulation", 2010.
This is a very slow pure python implementation, mostly for testing.
"""
out = np.empty((xyz.shape[0], pairs.shape[0], 3), dtype=np.float32)
for i in range(len(xyz)):
hinv = np.linalg.inv(box_vectors[i])
bv1, bv2, bv3 = box_vectors[i].T
for j, (a, b) in enumerate(pairs):
s1 = np.dot(hinv, xyz[i, a, :])
s2 = np.dot(hinv, xyz[i, b, :])
s12 = s2 - s1
s12 = s12 - np.round(s12)
disp = np.dot(box_vectors[i], s12)
min_disp = disp
dist2 = (disp * disp).sum()
if not orthogonal:
for ii in range(-1, 2):
v1 = bv1 * ii
for jj in range(-1, 2):
v12 = bv2 * jj + v1
for kk in range(-1, 2):
tmp = disp + v12 + bv3 * kk
new_dist2 = (tmp * tmp).sum()
if new_dist2 < dist2:
dist2 = new_dist2
min_disp = tmp
out[i, j] = min_disp
return out
def compute_distances(traj, atom_pairs, periodic=True, opt=True):
"""Compute the distances between pairs of atoms in each frame.
Parameters
----------
traj : Trajectory
An mtraj trajectory.
atom_pairs : np.ndarray, shape=(num_pairs, 2), dtype=int
Each row gives the indices of two atoms involved in the interaction.
periodic : bool, default=True
If `periodic` is True and the trajectory contains unitcell
information, we will compute distances under the minimum image
convention.
opt : bool, default=True
Use an optimized native library to calculate distances. Our optimized
SSE minimum image convention calculation implementation is over 1000x
faster than the naive numpy implementation.
Returns
-------
distances : np.ndarray, shape=(n_frames, num_pairs), dtype=float
The distance, in each frame, between each pair of atoms.
"""
xyz = ensure_type(traj.xyz,
dtype=np.float32,
ndim=3,
name='traj.xyz',
shape=(None, None, 3),
warn_on_cast=False)
pairs = ensure_type(atom_pairs,
dtype=np.int32,
ndim=2,
name='atom_pairs',
shape=(None, 2),
warn_on_cast=False)
if not np.all(np.logical_and(pairs < traj.n_atoms, pairs >= 0)):
raise ValueError('atom_pairs must be between 0 and %d' % traj.n_atoms)
if len(pairs) == 0:
return np.zeros((len(xyz), 0), dtype=np.float32)
if periodic and traj._have_unitcell:
out = np.empty((xyz.shape[0], pairs.shape[0]), dtype=np.float32)
a = traj.unitcell_lengths[0][0] * 10.0
b = traj.unitcell_lengths[0][1] * 10.0
c = traj.unitcell_lengths[0][2] * 10.0
cosalpha = math.cos(math.radians(traj.unitcell_angles[0][0]))
cosbeta = math.cos(math.radians(traj.unitcell_angles[0][1]))
cosgamma = math.cos(math.radians(traj.unitcell_angles[0][2]))
for i in range(len(xyz)):
for j, (ta, tb) in enumerate(pairs):
x1 = xyz[0, ta, 0] * 10.0
y1 = xyz[0, ta, 1] * 10.0
z1 = xyz[0, ta, 2] * 10.0
x2 = xyz[0, tb, 0] * 10.0
y2 = xyz[0, tb, 1] * 10.0
z2 = xyz[0, tb, 2] * 10.0
#get min dist from all images
dist = cal_dist(x1, y1, z1, x2, y2, z2, a, b, c, cosalpha,
cosbeta, cosgamma)
dist = min(
dist,
cal_dist(x1 + 1, y1, z1, x2, y2, z2, a, b, c, cosalpha,
cosbeta, cosgamma))
dist = min(
dist,
cal_dist(x1 - 1, y1, z1, x2, y2, z2, a, b, c, cosalpha,
cosbeta, cosgamma))
dist = min(
dist,
cal_dist(x1, y1 + 1, z1, x2, y2, z2, a, b, c, cosalpha,
cosbeta, cosgamma))
dist = min(
dist,
cal_dist(x1, y1 - 1, z1, x2, y2, z2, a, b, c, cosalpha,
cosbeta, cosgamma))
dist = min(
dist,
cal_dist(x1 + 1, y1 + 1, z1, x2, y2, z2, a, b, c, cosalpha,
cosbeta, cosgamma))
dist = min(
dist,
cal_dist(x1 + 1, y1 - 1, z1, x2, y2, z2, a, b, c, cosalpha,
cosbeta, cosgamma))
dist = min(
dist,
cal_dist(x1 - 1, y1 + 1, z1, x2, y2, z2, a, b, c, cosalpha,
cosbeta, cosgamma))
dist = min(
dist,
cal_dist(x1 - 1, y1 - 1, z1, x2, y2, z2, a, b, c, cosalpha,
cosbeta, cosgamma))
#print("pair:", ta, tb)
#print("final dist:",dist)
out[i, j] = dist
return out
else:
out = np.empty((xyz.shape[0], pairs.shape[0]), dtype=np.float32)
return out