def compute_inertia_tensor(traj):
"""Compute the inertia tensor of a trajectory.
For each frame,
I_{ab} = sum_{i_atoms} [m_i * (r_i^2 * d_{ab} - r_{ia} * r_{ib})]
Parameters
----------
traj : Trajectory
Trajectory to compute inertia tensor of.
Returns
-------
I_ab: np.ndarray, shape=(traj.n_frames, 3, 3), dtype=float64
Inertia tensors for each frame.
"""
center_of_mass = np.expand_dims(compute_center_of_mass(traj), axis=1)
xyz = traj.xyz - center_of_mass
masses = np.array([atom.element.mass for atom in traj.top.atoms])
eyes = np.empty(shape=(traj.n_frames, 3, 3), dtype=np.float64)
eyes[:] = np.eye(3)
A = np.einsum("i, kij->k", masses, xyz ** 2).reshape(traj.n_frames, 1, 1)
B = np.einsum("ij..., ...jk->...ki", masses[:, np.newaxis] * xyz.T, xyz)
return A * eyes - B
def compute_inertia_tensor(traj):
"""Compute the inertia tensor of a trajectory.
For each frame,
I_{ab} = sum_{i_atoms} [m_i * (r_i^2 * d_{ab} - r_{ia} * r_{ib})]
Parameters
----------
traj : Trajectory
Trajectory to compute inertia tensor of.
Returns
-------
I_ab: np.ndarray, shape=(traj.n_frames, 3, 3), dtype=float64
Inertia tensors for each frame.
"""
center_of_mass = np.expand_dims(compute_center_of_mass(traj), axis=1)
xyz = traj.xyz - center_of_mass
masses = np.array([atom.element.mass for atom in traj.top.atoms])
eyes = np.empty(shape=(traj.n_frames, 3, 3), dtype=np.float64)
eyes[:] = np.eye(3)
A = np.einsum("i, kij->k", masses, xyz**2).reshape(traj.n_frames, 1, 1)
B = np.einsum("ij..., ...jk->...ki", masses[:, np.newaxis] * xyz.T, xyz)
return A * eyes - B
def _compute_inertia_tensor_slow(traj):
"""Compute the inertia tensor of a trajectory. """
center_of_mass = np.expand_dims(compute_center_of_mass(traj), axis=1)
centered_xyz = traj.xyz - center_of_mass
masses = np.array([atom.element.mass for atom in traj.top.atoms])
I_ab = np.zeros(shape=(traj.n_frames, 3, 3), dtype=np.float64)
for n, xyz in enumerate(centered_xyz):
for i, r in enumerate(xyz):
mass = masses[i]
I_ab[n, 0, 0] += mass * (r[1] * r[1] + r[2] * r[2])
I_ab[n, 1, 1] += mass * (r[0] * r[0] + r[2] * r[2])
I_ab[n, 2, 2] += mass * (r[0] * r[0] + r[1] * r[1])
I_ab[n, 0, 1] -= mass * r[0] * r[1]
I_ab[n, 0, 2] -= mass * r[0] * r[2]
I_ab[n, 1, 2] -= mass * r[1] * r[2]
I_ab[n, 1, 0] = I_ab[n, 0, 1]
I_ab[n, 2, 0] = I_ab[n, 0, 2]
I_ab[n, 2, 1] = I_ab[n, 1, 2]
return I_ab
def _compute_inertia_tensor_slow(traj):
"""Compute the inertia tensor of a trajectory. """
center_of_mass = np.expand_dims(compute_center_of_mass(traj), axis=1)
centered_xyz = traj.xyz - center_of_mass
masses = np.array([atom.element.mass for atom in traj.top.atoms])
I_ab = np.zeros(shape=(traj.n_frames, 3, 3), dtype=np.float64)
for n, xyz in enumerate(centered_xyz):
for i, r in enumerate(xyz):
mass = masses[i]
I_ab[n, 0, 0] += mass * (r[1] * r[1] + r[2] * r[2])
I_ab[n, 1, 1] += mass * (r[0] * r[0] + r[2] * r[2])
I_ab[n, 2, 2] += mass * (r[0] * r[0] + r[1] * r[1])
I_ab[n, 0, 1] -= mass * r[0] * r[1]
I_ab[n, 0, 2] -= mass * r[0] * r[2]
I_ab[n, 1, 2] -= mass * r[1] * r[2]
I_ab[n, 1, 0] = I_ab[n, 0, 1]
I_ab[n, 2, 0] = I_ab[n, 0, 2]
I_ab[n, 2, 1] = I_ab[n, 1, 2]
return I_ab