Fitfunctions

The builtin fitfunctions all follow this form:

mre.f_fitfunction(k, arg1, arg2, ...)

Parameters:

• k (array_like) – Independent variable as first argument. If an array is provided, an array of same length will be returned where the function is evaluated elementwise
• args (float) – Function arguments

Return type:

float or array

Example

import numpy as np
import matplotlib.pyplot as plt
import mrestimator as mre

# evaluate exp(-1) via A e^(-k/tau)
print(mre.f_exponential(1, 1, 1))

# test data
rk = mre.coefficients(mre.simulate_branching(m=0.9, h=10, numtrials=10))

# pass builtin function to fit
f = mre.f_exponential_offset
m = mre.fit(rk, f)

# provide an array as function argument to evaluate elementwise
# this is useful for plotting
xargs = np.array([0, 1, 2, 3])

print(m.popt)

# unpack m.popt to provide all contained arguments at once
print(f(xargs, *m.popt))

# get a TeX string compatible with matplotlib's legends
print(mre.math_from_doc(f))

mrestimator.f_exponential(k, tau, A)

\(|A| e^{-k/\tau}\)

mrestimator.f_exponential_offset(k, tau, A, O)

\(|A| e^{-k/\tau} + O\)

mrestimator.f_complex(k, tau, A, O, tauosc, B, gamma, nu, taugs, C)

\(|A| e^{-k/\tau} + B e^{-(k/\tau_{osc})^\gamma} \cos(2 \pi \nu k) + C e^{-(k/\tau_{gs})^2} + O\)

mrestimator.default_fitpars(fitfunc)

Called to get the default starting parameters for the built-in fitfunctions that are used to initialise the fitting routine. Timelike values specified here were derived assuming a timescale of miliseconds.

Parameters:fitfunc (callable) – The builtin fitfunction Returns:pars (~numpy.ndarray) – The default parameters of the given function, 2d array for multiple sets of initial conditions.