# -*- coding: utf-8 -*-
"""
Python Module for (Weighted) Linear Regression.
:authors:
Thomas Lecocq (thomas.lecocq@seismology.be)
:copyright:
The ObsPy Development Team (devs@obspy.org)
:license:
GNU Lesser General Public License, Version 3
(https://www.gnu.org/copyleft/lesser.html)
"""
import numpy as np
import scipy.optimize
[docs]def linear_regression(xdata, ydata, weights=None, p0=None,
intercept_origin=True, **kwargs):
"""
Use linear least squares to fit a function, f, to data.
This method is a generalized version of
:func:`scipy.optimize.curve_fit`; allowing for Ordinary Least
Square and Weighted Least Square regressions:
* OLS through origin: ``linear_regression(xdata, ydata)``
* OLS with any intercept: ``linear_regression(xdata, ydata,
intercept_origin=False)``
* WLS through origin: ``linear_regression(xdata, ydata, weights)``
* WLS with any intercept: ``linear_regression(xdata, ydata, weights,
intercept_origin=False)``
If the expected values of slope (and intercept) are different from 0.0,
provide the p0 value(s).
:param xdata: The independent variable where the data is measured.
:param ydata: The dependent data - nominally f(xdata, ...)
:param weights: If not None, the uncertainties in the ydata array. These
are used as weights in the least-squares problem. If ``None``, the
uncertainties are assumed to be 1. In SciPy vocabulary, our weights are
1/sigma.
:param p0: Initial guess for the parameters. If ``None``, then the initial
values will all be 0 (Different from SciPy where all are 1)
:param intercept_origin: If ``True``: solves ``y=a*x`` (default);
if ``False``: solves ``y=a*x+b``.
Extra keword arguments will be passed to
:func:`scipy.optimize.curve_fit`.
:rtype: tuple
:returns: (slope, std_slope) if ``intercept_origin`` is ``True``;
(slope, intercept, std_slope, std_intercept) if ``False``.
"""
if weights is not None:
sigma = 1. / weights
else:
sigma = None
if p0 is None:
if intercept_origin:
p0 = 0.0
else:
p0 = [0.0, 0.0]
if intercept_origin:
p, cov = scipy.optimize.curve_fit(lambda x, a: a * x,
xdata, ydata, p0, sigma=sigma,
**kwargs)
slope = p[0]
std_slope = np.sqrt(cov[0, 0])
return slope, std_slope
else:
p, cov = scipy.optimize.curve_fit(lambda x, a, b: a * x + b,
xdata, ydata, p0, sigma=sigma,
**kwargs)
slope, intercept = p
std_slope = np.sqrt(cov[0, 0])
std_intercept = np.sqrt(cov[1, 1])
return slope, intercept, std_slope, std_intercept
if __name__ == '__main__':
import doctest
doctest.testmod(exclude_empty=True)