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Relax

Summary:

A small tool for calculating non-linear relaxation fits from arbitrary time-resolved experiments

Authors:

Ben Barad

Available Relaxation Kinetics Functions:

  • Single Step Relaxation: y = A*(1-e-Bx)+C
  • Two Step Relaxation: y = A*(1-e-Bx)+C*(1-e-Dx)+E
  • Three Step Relaxation: y = A*(1-e-Bx) + C*(1-e-Dx) + E*(1-e-Fx) + G

Example Usage:

import numpy as np
from relax import relaxation_fit, single_step_relaxation

x = [1,2,5,10,15,25,35,60,90, 200, 500, 1000, 10000, 1000000, 10000000000]
y = [25*(1-np.exp(-5*i))+2 for i in x]

parameters, covariances, y_calc = relaxation_fit(x, y, relaxation_function = single_step_relaxation, initial_guess=[18, 11, 10])

print(parameters) 
# Ideally this should converge to 25., 5., 2. for this example - more data points will improve convergence.

Requirements:

  • Python >= 3.6
  • Numpy
  • Scipy