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