def log_linear_fitting(x, y, method='lsq'):
"""Function to perform log linear regression.
Parameters
----------
x : ndarray, shape (n_samples)
Corresponds to the x. In our case, it should be the time.
y : ndarray, shape (n_samples)
Corresponds to the y. In our case, it should be the rpp.
method : string, optional (default='lsq')
The method to use to perform the regression. The choices are:
- If 'lsq', an ordinary least-square approach is used.
- If 'lm', the Levenberg-Marquardt is used.
Returns
-------
slope : float
slope of the regression line.
intercept : float
intercept of the regression line.
std_err : float
Standard error of the estimate.
coeff_det : float
Coefficient of determination.
"""
# Check that the array x and y have the same size
if x.shape != y.shape:
raise ValueError('The size of x and y should be the same.')
if method == 'lsq':
# Perform the fitting using least-square
slope, intercept, _, _, _ = linregress(np.log(x), y)
std_err = res_std_dev(y, log_linear_model(x, slope, intercept))
coeff_det = r_squared(y, log_linear_model(x, slope, intercept))
elif method == 'lm':
# Perform the fitting using non-linear least-square
# Levenberg-Marquardt
popt, _ = curve_fit(linear_model, np.log(x), y)
slope = popt[0]
intercept = popt[1]
std_err = res_std_dev(y, log_linear_model(x, slope, intercept))
coeff_det = r_squared(y, log_linear_model(x, slope, intercept))
else:
raise NotImplementedError
return slope, intercept, std_err, coeff_det
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