Diffusion_MLE module

Created on Sun Feb 23 08:54:52 2020

@author: jbeckwith

class Diffusion_MLE.D_MLE

Bases: object

DSigma_MLE(coordinates, dT, R=0.16666666666666666, n_d=1, maxiter=100000, maxfun=100000, min_points=10)

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

Parameters:

  • coordinates (np.ndarray) – coordinates over time.

  • dT (float) – Time step.

  • 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 optimisation iterations to make

  • maxfun (int) – maximum number of function evaluations to make

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

Returns:

  • D (float) – estimate of D value.

  • sigma (float) – estimate of dynamic localisation std.

DSigma_MLE_BootStrap(coordinates, dT, R=0.16666666666666666, n_d=1, maxiter=100000, maxfun=100000, n_samples=1000, min_points=10)

Compute diffusion coefficient error estimate, and estimate of the error on the dynamic localisation error, using bootstrapping.

Parameters:

  • coordinates (np.ndarray) – coordinates over time.

  • dT (float) – Time step.

  • 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 optimisation iterations to make

  • maxfun (int) – maximum number of function evaluations to make

  • n_samples (int) – number of boostrapped samples. default 1000.

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

Returns:

  • D_err (float) – estimate of D value error

  • sigma_err (float) – estimate of dynamic localisation std error

static likelihood_subfunction(d_xx, D, sig2, dT, R, n_d=1)

Compute log-likelihood for trajectories of particle tracking.

Parameters:

  • d_xx (numpy.ndarray) – Square distance of the difference of trajectory. Second axis should be n_d

  • D (float) – Diffusion coefficient.

  • sig2 (float) – Variance.

  • dT (float) – Time step.

  • R (float) – Motion blur coefficient.

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

Returns:

L (float) – Likelihood value.