tidfit

pip install tidfit

Overview

This package provides a tiny routine to fit a curve to pairs of points and draw it with some error bands. Only depends on numpy, scipy, and matplotlib. It's essentially a wrapper around scipy.optimize.curve_fit.

import numpy as np
import matplotlib.pyplot as plt

x = np.array([0.05, 0.15, 0.25, 0.35, 0.45, 0.55, 0.65, 0.75, 0.85, 0.95])
y = np.array([184., 193., 199., 208., 200., 225., 216., 190., 212., 173.])

fig, ax = plt.subplots()
ax.errorbar(x, y, yerr=y**0.5, fmt="o", label="data")

To specify the function to fit, one can use an eval-able string expression, which needs one x to serve as the independent variable. The remaining variables are considered as fittable function parameters. Of course, fit takes a regular callable function (lambda x,a,b: a*x+b) as well, but who has the time to type out 10 more characters?

from tidfit import fit
fit("a*x+b", x, y)

A boolean mask specifies which points to consider in each fit.

bins = np.linspace(-5, 5, 41)
y  = np.histogram(np.random.normal(-2, 1, 500), bins=bins)[0]
y += np.histogram(np.random.normal(+2, 1, 500), bins=bins)[0]
x = bins[:-1] + 0.25

fig, ax = plt.subplots()
ax.errorbar(x, y, yerr=y**0.5, fmt="o", ms=5)

gaussian = "const + peak * np.exp(-((x - mu) ** 2) / (2 * sigma ** 2))"

fit(gaussian, x, y, sigma=y**0.5, mask=(x < -1), color="C1")
fit(gaussian, x, y, sigma=y**0.5, mask=(x > +1), color="C2")

An array of initial parameter values, p0, is also accepted as a keyword argument to fit and passed through to curve_fit, but keeping track of an array while modifying the fitting function is cumbersome. If an explicit function is specified, any default arguments are extracted and used as the initial p0 to curve_fit.

def f(x, const=None, peak=None, mu1=+2, sigma1=1, mu2=-2, sigma2=1):
    return (
        const
        + peak * np.exp(-((x - mu1) ** 2) / (2 * sigma1 ** 2))
        + peak * np.exp(-((x - mu2) ** 2) / (2 * sigma2 ** 2))
    )

fit(f, x, y, sigma=y**0.5)

The object returned by fit has a nice representation in notebooks

out = fit("a+b*x", [0,1,2], [1,3,3], draw=False)
out

parameter	value
a	1.333 ± 0.7454
b	1 ± 0.5774

but out is just a dict, and provides two ways of getting the parameter names, values, and errors:

print(out)

{'func': <function fit.<locals>.<lambda> at 0x12e049f28>,
 'params': {'a': {'error': 0.75, 'value': 1.3333},
            'b': {'error': 0.5774, 'value': 1.0}},
 'parerrors': array([0.745, 0.577]),
 'parnames': ('a', 'b'),
 'parvalues': array([1.333, 1.   ])}

And for convenience, out contains the fitted function ready to be called with an array of x-values

func = out["func"]

residuals = ydata - func(xdata)