def _regenerate_model(self):
"""Regenerate model fit from parameters."""
self._ap_fit = gen_aperiodic(self.freqs, self.aperiodic_params_)
self._peak_fit = gen_peaks(self.freqs,
np.ndarray.flatten(self.gaussian_params_))
self.fooofed_spectrum_ = self._peak_fit + self._ap_fit
def refit_aperiodic(freqs, powers, peak_fit):
"""Refit the aperiodic component following the periodic refit.
Parameters
----------
freqs : 1d array
Frequency values for the power spectrum, in linear scale.
powers : 1d array
Power values, in log10 scale.
peak_fit : 1d array
Perodic refit, in log10 scale.
Returns
-------
ap_params : 1d array
Exponent and offset values.
ap_fit : 1d array
Regenerated aperiodic fit.
"""
# Access simple ap fit method
_fm = FOOOF()
_fm.power_spectrum = powers
_fm.freqs = freqs
# Remove peaks
spectrum_peak_rm = powers - peak_fit
# Refit
ap_params = _fm._simple_ap_fit(freqs, spectrum_peak_rm)
ap_fit = gen_aperiodic(freqs, ap_params)
return ap_params, ap_fit
def _robust_ap_fit(self, freqs, power_spectrum):
"""Fit the aperiodic component of the power spectrum robustly, ignoring outliers.
Parameters
----------
freqs : 1d array
Frequency values for the power spectrum, in linear scale.
power_spectrum : 1d array
Power values, in log10 scale.
Returns
-------
aperiodic_params : 1d array
Parameter estimates for aperiodic fit.
"""
# Do a quick, initial aperiodic fit
popt = self._simple_ap_fit(freqs, power_spectrum)
initial_fit = gen_aperiodic(freqs, popt)
# Flatten power_spectrum based on initial aperiodic fit
flatspec = power_spectrum - initial_fit
# Flatten outliers - any points that drop below 0
flatspec[flatspec < 0] = 0
# Use percential threshold, in terms of # of points, to extract and re-fit
perc_thresh = np.percentile(flatspec, self._ap_percentile_thresh)
perc_mask = flatspec <= perc_thresh
freqs_ignore = freqs[perc_mask]
spectrum_ignore = power_spectrum[perc_mask]
# Second aperiodic fit - using results of first fit as guess parameters
# See note in _simple_ap_fit about warnings
with warnings.catch_warnings():
warnings.simplefilter("ignore")
aperiodic_params, _ = curve_fit(get_ap_func(self.aperiodic_mode),
freqs_ignore,
spectrum_ignore,
p0=popt,
maxfev=5000,
bounds=self._ap_bounds)
return aperiodic_params
def plot_aperiodic_fits(aps,
freq_range,
control_offset=False,
log_freqs=False,
colors=None,
labels=None,
ax=None,
**plot_kwargs):
"""Plot reconstructions of model aperiodic fits.
Parameters
----------
aps : 2d array
Aperiodic parameters. Each row is a parameter set, as [Off, Exp] or [Off, Knee, Exp].
freq_range : list of [float, float]
The frequency range to plot the peak fits across, as [f_min, f_max].
control_offset : boolean, optional, default: False
Whether to control for the offset, by setting it to zero.
log_freqs : boolean, optional, default: False
Whether to plot the x-axis in log space.
colors : str or list of str, optional
Color(s) to plot data.
labels : list of str, optional
Label(s) for plotted data, to be added in a legend.
ax : matplotlib.Axes, optional
Figure axes upon which to plot.
**plot_kwargs
Keyword arguments to pass into the ``style_plot``.
"""
ax = check_ax(ax, plot_kwargs.pop('figsize', PLT_FIGSIZES['params']))
if isinstance(aps, list):
if not colors:
colors = cycle(plt.rcParams['axes.prop_cycle'].by_key()['color'])
recursive_plot(aps,
plot_aperiodic_fits,
ax=ax,
freq_range=tuple(freq_range),
control_offset=control_offset,
log_freqs=log_freqs,
colors=colors,
labels=labels,
**plot_kwargs)
else:
freqs = gen_freqs(freq_range, 0.1)
plt_freqs = np.log10(freqs) if log_freqs else freqs
colors = colors[0] if isinstance(colors, list) else colors
avg_vals = np.zeros(shape=[len(freqs)])
for ap_params in aps:
if control_offset:
# Copy the object to not overwrite any data
ap_params = ap_params.copy()
ap_params[0] = 0
# Recreate & plot the aperiodic component from parameters
ap_vals = gen_aperiodic(freqs, ap_params)
ax.plot(plt_freqs,
ap_vals,
color=colors,
alpha=0.35,
linewidth=1.25)
# Collect a running average across components
avg_vals = np.nansum(np.vstack([avg_vals, ap_vals]), axis=0)
# Plot the average component
avg = avg_vals / aps.shape[0]
avg_color = 'black' if not colors else colors
ax.plot(plt_freqs, avg, linewidth=3.75, color=avg_color, label=labels)
# Add axis labels
ax.set_xlabel('log(Frequency)' if log_freqs else 'Frequency')
ax.set_ylabel('log(Power)')
# Set plot limit
ax.set_xlim(np.log10(freq_range) if log_freqs else freq_range)
style_param_plot(ax)
###################################################################################################
#
# The FOOOF object stores most of the intermediate steps internally.
#
# For this notebook, we will first fit the full model, as normal, but then step through,
# and visualize each step the algorithm takes to come to that final fit.
#
# Fit the FOOOF model
fm.fit(freqs, spectrum, [3, 40])
###################################################################################################
# Do an initial aperiodic signal fit - a robust fit, that excludes outliers
# This recreates an initial fit that isn't ultimately stored in the FOOOF object)
init_ap_fit = gen_aperiodic(fm.freqs,
fm._robust_ap_fit(fm.freqs, fm.power_spectrum))
# Plot the initial aperiodic fit
_, ax = plt.subplots(figsize=(12, 10))
plot_spectrum(fm.freqs,
fm.power_spectrum,
plt_log,
label='Original Power Spectrum',
ax=ax)
plot_spectrum(fm.freqs,
init_ap_fit,
plt_log,
label='Initial Aperiodic Fit',
ax=ax)
###################################################################################################
def plot_annotated_peak_search(fm, plot_style=style_spectrum_plot):
"""Plot a series of plots illustrating the peak search from a flattened spectrum.
Parameters
----------
fm : FOOOF
FOOOF object, with model fit, data and settings available.
plot_style : callable, optional, default: style_spectrum_plot
A function to call to apply styling & aesthetics to the plots.
"""
# Recalculate the initial aperiodic fit and flattened spectrum that
# is the same as the one that is used in the peak fitting procedure
flatspec = fm.power_spectrum - \
gen_aperiodic(fm.freqs, fm._robust_ap_fit(fm.freqs, fm.power_spectrum))
# Calculate ylims of the plot that are scaled to the range of the data
ylims = [
min(flatspec) - 0.1 * np.abs(min(flatspec)),
max(flatspec) + 0.1 * max(flatspec)
]
# Loop through the iterative search for each peak
for ind in range(fm.n_peaks_ + 1):
# This forces the creation of a new plotting axes per iteration
ax = check_ax(None, PLT_FIGSIZES['spectral'])
plot_spectrum(fm.freqs,
flatspec,
ax=ax,
plot_style=None,
label='Flattened Spectrum',
color=PLT_COLORS['data'],
linewidth=2.5)
plot_spectrum(fm.freqs,
[fm.peak_threshold * np.std(flatspec)] * len(fm.freqs),
ax=ax,
plot_style=None,
label='Relative Threshold',
color='orange',
linewidth=2.5,
linestyle='dashed')
plot_spectrum(fm.freqs, [fm.min_peak_height] * len(fm.freqs),
ax=ax,
plot_style=None,
label='Absolute Threshold',
color='red',
linewidth=2.5,
linestyle='dashed')
maxi = np.argmax(flatspec)
ax.plot(fm.freqs[maxi],
flatspec[maxi],
'.',
color=PLT_COLORS['periodic'],
alpha=0.75,
markersize=30)
ax.set_ylim(ylims)
ax.set_title('Iteration #' + str(ind + 1), fontsize=16)
if ind < fm.n_peaks_:
gauss = gaussian_function(fm.freqs, *fm.gaussian_params_[ind, :])
plot_spectrum(fm.freqs,
gauss,
ax=ax,
plot_style=None,
label='Gaussian Fit',
color=PLT_COLORS['periodic'],
linestyle=':',
linewidth=3.0)
flatspec = flatspec - gauss
check_n_style(plot_style, ax, False, True)
def fit(self, freqs=None, power_spectrum=None, freq_range=None):
"""Fit the full power spectrum as a combination of periodic and aperiodic components.
Parameters
----------
freqs : 1d array, optional
Frequency values for the power spectrum, in linear space.
power_spectrum : 1d array, optional
Power values, which must be input in linear space.
freq_range : list of [float, float], optional
Frequency range to restrict power spectrum to. If not provided, keeps the entire range.
Notes
-----
Data is optional if data has been already been added to FOOOF object.
"""
# If freqs & power_spectrum provided together, add data to object.
if freqs is not None and power_spectrum is not None:
self.add_data(freqs, power_spectrum, freq_range)
# If power spectrum provided alone, add to object, and use existing frequency data
# Note: be careful passing in power_spectrum data like this:
# It assumes the power_spectrum is already logged, with correct freq_range.
elif isinstance(power_spectrum, np.ndarray):
self.power_spectrum = power_spectrum
# Check that data is available
if self.freqs is None or self.power_spectrum is None:
raise ValueError('No data available to fit - can not proceed.')
# Check and warn about width limits (if in verbose mode)
if self.verbose:
self._check_width_limits()
# In rare cases, the model fails to fit. Therefore it's in a try/except
# Cause of failure: RuntimeError, failure to find parameters in curve_fit
try:
# Fit the aperiodic component
self.aperiodic_params_ = self._robust_ap_fit(
self.freqs, self.power_spectrum)
self._ap_fit = gen_aperiodic(self.freqs, self.aperiodic_params_)
# Flatten the power_spectrum using fit aperiodic fit
self._spectrum_flat = self.power_spectrum - self._ap_fit
# Find peaks, and fit them with gaussians
self.gaussian_params_ = self._fit_peaks(
np.copy(self._spectrum_flat))
# Calculate the peak fit
# Note: if no peaks are found, this creates a flat (all zero) peak fit.
self._peak_fit = gen_peaks(
self.freqs, np.ndarray.flatten(self.gaussian_params_))
# Create peak-removed (but not flattened) power spectrum.
self._spectrum_peak_rm = self.power_spectrum - self._peak_fit
# Run final aperiodic fit on peak-removed power spectrum
# Note: This overwrites previous aperiodic fit
self.aperiodic_params_ = self._simple_ap_fit(
self.freqs, self._spectrum_peak_rm)
self._ap_fit = gen_aperiodic(self.freqs, self.aperiodic_params_)
# Create full power_spectrum model fit
self.fooofed_spectrum_ = self._peak_fit + self._ap_fit
# Convert gaussian definitions to peak parameters
self.peak_params_ = self._create_peak_params(self.gaussian_params_)
# Calculate R^2 and error of the model fit.
self._calc_r_squared()
self._calc_rmse_error()
# Catch failure, stemming from curve_fit process
except RuntimeError:
# Clear any interim model results that may have run
# Partial model results shouldn't be interpreted in light of overall failure
self._reset_data_results(clear_freqs=False,
clear_spectrum=False,
clear_results=True)
# Print out status
if self.verbose:
print('Model fitting was unsuccessful.')