MSDFunctions module

Created on Tue Apr 23 14:30:10 2024

@author: jbeckwith

class MSDFunctions.MSD

Bases: object

DSigma2_OLSF(coordinates, dT, R=0.16666666666666666, n_d=1, maxiter=100, min_points=10, supress_warning=False)

Compute diffusion coefficient estimate, and estimate of the dynamic localisation error, using the OLSF MSD approach.

Parameters:

  • coordinates (numpy.ndarray) – Input trajectory.

  • dT (float) – Time interval.

  • R (float) – Motion blur coefficient.

  • n_d (int) – number of dimensions. If above 1, coordinates second dimension should be same shape as this number

  • maxiter (int) – Maximum number of iterations. Defaults to 100.

  • min_points (int) – minimum number of points for a diffusion estimate. Default is 10.

Returns:

  • D (float) – Diffusion coefficient estimate.

  • var (float) – var estimate.

DSigma2_OLSF_BootStrap(coordinates, dT, R=0.16666666666666666, n_d=1, maxiter=100, min_points=10, n_samples=1000)

Compute diffusion coefficient error estimate, and estimate of the dynamic localisation variance, using bootstrapping of the OLSF MSD approach.

Parameters:

  • coordinates (numpy.ndarray) – Input trajectory.

  • dT (float) – Time interval.

  • R (float) – Motion blur coefficient.

  • n_d (int) – number of dimensions. If above 1, coordinates second dimension should be same shape as this number

  • maxiter (int) – Maximum number of iterations. Defaults to 100.

  • min_points (int) – minimum number of points for a diffusion estimate. Default is 10.

  • n_samples (int) – number of bootstrapped samples. Default 1000.

Returns:

  • D_error (float) – Diffusion coefficient error estimate.

  • var_error (float) – var error estimate.

static PMin_XM(x, N)

Calculate optimal fit point from formulae in Michalet, X. Mean Square Displacement Analysis of Single-Particle Trajectories with Localization Error: Brownian Motion in an Isotropic Medium. Phys. Rev. E 2010, 82 (4), 041914. https://doi.org/10.1103/PhysRevE.82.041914.

Parameters:

  • x (float) – Input value.

  • N (int) – Number of trajectory points.

Returns:

  • pa (int) – Optimal fit point for parameter ‘a’.

  • pb (int) – Optimal fit point for parameter ‘b’.

autocorrFFT(x)

Compute the autocorrelation of a 1D signal using the Fast Fourier Transform (FFT) method.

Parameters:

x (numpy.ndarray) – Input signal.

Returns:

res (numpy.ndarray) – Autocorrelation of the input signal.

msd_fft(r)

Compute the mean squared displacement (MSD) using the Fast Fourier Transform (FFT) method.

Parameters:

  • r (numpy.ndarray) – Trajectory data, where each row represents the

  • steps. (coordinates of a particle at different time)

Returns:

S (numpy.ndarray) – MSD computed for each time step.