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Smoothed trajectories

smooth_trajectory averages the positions of each frame over a window of frames about it, the atoms followed through the periodic boundaries, as OVITO's smooth trajectory. The thermal vibrations average out and the slow motion stays; velocities, forces and other columns of real numbers are averaged too.

import numpy as np
import mdapy as mp
from mdapy.transform import smooth_trajectory

# an atom that drifts slowly along x through a periodic box of 10 Å,
# vibrating by 0.3 Å in each of 100 frames
box = mp.Box(10.0)
rng = np.random.default_rng(6)
t = np.arange(100)
x = 0.12 * t + rng.normal(0, 0.3, 100)
frames = [
    mp.System(box.wrap([[x[k], 5.0, 5.0]])[0], box, elements="Ar").with_columns(id=[1])
    for k in t
]

smoothed = smooth_trajectory(frames, 9)  # the frames, each computed when used
smoothed[50]["positions"]  # the mean of frames 46 to 54 about the atom

The path of the atom unwrapped, frame by frame and smoothed:

from mdapy.analysis import trajectory_lines
from mdapy.visualization import plot

with plot.style():
    fig, ax = plot.figure("single")
    ax.plot(
        t, trajectory_lines(frames)[0, :, 0], ".", color="#bbbbbb", label="each frame"
    )
    ax.plot(t, trajectory_lines(smoothed)[0, :, 0], label="smoothed over 9 frames")
    ax.set_xlabel("Frame")
    ax.set_ylabel("x (Å), unwrapped")
    ax.legend(frameon=False)
    plot.save(fig, "images/smooth-trajectory", formats=("png",))

A path smoothed over nine frames

The atom crosses the box about once every 80 frames; the smoothed path follows the drift through the boundary without the jumps.

Parameters

smooth_trajectory(frames, window)

Name Type Meaning
frames sequence of System the same atoms in every frame, such as a Trajectory, matched by the id column where the frames have one, else in the same order; without an image column, atoms must move less than half the box between frames
window int32 the number of frames averaged: the frame, (window - 1) // 2 frames before it and window // 2 after it, the first and last frames repeated beyond the ends; 1 leaves the positions as they are

Results

A sequence of systems, one per frame, each computed when it is used: the mean positions placed about the atoms where they are in that frame, the mean of every other column of real numbers matched by atom, and the columns of integers or text, such as ids and elements, as they are.

Errors

InvalidParameter for a window that is not a positive integer, no frames, or frames that do not hold the same atoms; IndexError for a frame beyond the end.

See also