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Time-dependent descriptors (mean squared displacement)

This module is relevant ot time-dependent descriptors of a simulation. At the current status, the only present function computes the Mean Squared Displacement (MSD) of atoms in the system along a simulation.

snow.descriptors.time_dependent

compute_MSD(movie, masks=None, step_by_step=False)

Computes the mean squared displacement (MSD) along a trajectory.

A mask can be used to select specific (groups of) atoms to contribute to the MSD. The calculation can be done relative to the initial positions or to the preceding timestep by appropriately setting the step_by_step flag.

Parameters:

Name Type Description Default
movie list[ndarray]

list of coordinates of sequential frames of the system. Each list item should be a (n,3) np.ndarray coordinates array

 required
masks list[list[bool]]

list of lists of bools for whether to count for an atom or not in the calculation of the MSD. Default to all True.

 None
step_by_step bool

If True, the MSD at each timestep is computed relative to the timestep before. If False, it is computed relative to the initial position. Default to False

 False

Returns:

Name Type Description
MSD ndarray

mean squared displacement along the trajectory
Source code in snow/descriptors/time_dependent.py 
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def compute_MSD(movie, masks=None, step_by_step=False):
    """
    Computes the mean squared displacement (MSD) along a trajectory. 

    A mask can be used to select specific (groups of) atoms to contribute to the MSD.
    The calculation can be done relative to the initial positions or to
    the preceding timestep by appropriately setting the step_by_step flag.

    Parameters
    ----------
    movie : list[np.ndarray]
        list of coordinates of sequential frames of the system. 
        Each list item should be a (n,3) np.ndarray coordinates array
    masks : list[list[bool]], optional
        list of lists of bools for whether to count for an atom or not in the calculation of the MSD.
        Default to all True.
    step_by_step : bool, default False
        If True, the MSD at each timestep is computed relative to the timestep before. If False, it is 
        computed relative to the initial position. Default to False

    Returns
    -------
    MSD : np.ndarray
        mean squared displacement along the trajectory

    """

    if masks is None: #set default mask
        masks = [[True]*len(movie[0])]*len(movie)

    ref_pos = movie[0]
    MSD = np.zeros(len(movie))

    for i, pos in enumerate(movie):

        if i==0:
            continue

        if(step_by_step):
            ref_pos = movie[i-1]

        #compute MSD
        diff2  = np.sum( (pos - ref_pos)**2, axis=1)
        mask   = np.array(masks[i])
        MSD[i] = diff2[ mask ].mean()

    return MSD