def gen_background(xs, background_params, background_mode=None):
"""Generate background values, from parameter definition.
Parameters
----------
xs : 1d array
Frequency vector to create background from.
background_params : list of float
Paramters that define the background process.
background_mode : {'fixed', 'knee'}, optional
Which kind of background to generate power spectra with.
If not provided, is infered from the parameters.
Returns
-------
1d array
Generated background values
"""
if not background_mode:
background_mode = infer_bg_func(background_params)
bg_func = get_bg_func(background_mode)
return bg_func(xs, *background_params)
def _simple_bg_fit(self, freqs, power_spectrum):
"""Fit the 1/f background of power spectrum.
Parameters
----------
freqs : 1d array
Frequency values for the power_spectrum, in linear scale.
power_spectrum : 1d array
Power spectrum values, in log10 scale.
Returns
-------
background_params : 1d array
Parameter estimates for background fit.
"""
# Set guess params for lorentzian background fit, guess params set at init
guess = np.array(([power_spectrum[0]] if not self._bg_guess[0] else [self._bg_guess[0]]) +
([self._bg_guess[1]] if self.background_mode == 'knee' else []) +
[self._bg_guess[2]])
# Ignore warnings that are raised in curve_fit
# A runtime warning can occur while exploring parameters in curve fitting
# This doesn't effect outcome - it won't settle on an answer that does this
# It happens if / when b < 0 & |b| > x**2, as it leads to log of a negative number
with warnings.catch_warnings():
warnings.simplefilter("ignore")
background_params, _ = curve_fit(get_bg_func(self.background_mode),
freqs, power_spectrum, p0=guess,
maxfev=5000, bounds=self._bg_bounds)
return background_params
def _robust_bg_fit(self, freqs, power_spectrum):
"""Fit the 1/f background of power spectrum robustly, ignoring outliers.
Parameters
----------
freqs : 1d array
Frequency values for the power spectrum, in linear scale.
power_spectrum : 1d array
Power spectrum values, in log10 scale.
Returns
-------
background_params : 1d array
Parameter estimates for background fit.
"""
# Do a quick, initial background fit.
popt = self._simple_bg_fit(freqs, power_spectrum)
initial_fit = gen_background(freqs, popt)
# Flatten power_spectrum based on initial background fit.
flatspec = power_spectrum - initial_fit
# Flatten outliers - any points that drop below 0.
flatspec[flatspec < 0] = 0
# Amplitude threshold - in terms of # of points.
perc_thresh = np.percentile(flatspec, self._bg_amp_thresh)
amp_mask = flatspec <= perc_thresh
freqs_ignore = freqs[amp_mask]
spectrum_ignore = power_spectrum[amp_mask]
# Second background fit - using results of first fit as guess parameters.
# See note in _simple_bg_fit about warnings
with warnings.catch_warnings():
warnings.simplefilter("ignore")
background_params, _ = curve_fit(get_bg_func(self.background_mode),
freqs_ignore,
spectrum_ignore,
p0=popt,
maxfev=5000,
bounds=self._bg_bounds)
return background_params