def plot_spectral_error(freqs,
error,
shade=None,
log_freqs=False,
ax=None,
**plot_kwargs):
"""Plot frequency by frequency error values.
Parameters
----------
freqs : 1d array
Frequency values, to be plotted on the x-axis.
error : 1d array
Calculated error values or mean error values across frequencies, to plot on the y-axis.
shade : 1d array, optional
Values to shade in around the plotted error.
This could be, for example, the standard deviation of the errors.
log_freqs : bool, optional, default: False
Whether to plot the frequency axis in log spacing.
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['spectral']))
plt_freqs = np.log10(freqs) if log_freqs else freqs
plot_spectra(plt_freqs, error, ax=ax, linewidth=3)
if np.any(shade):
ax.fill_between(plt_freqs, error - shade, error + shade, alpha=0.25)
ymin, ymax = ax.get_ylim()
if ymin < 0:
ax.set_ylim([0, ymax])
ax.set_xlim(plt_freqs.min(), plt_freqs.max())
style_spectrum_plot(ax, log_freqs, True)
ax.set_ylabel('Absolute Error')
# Aperiodic params: define values for each spectrum, with length equal to n_spectra
aperiodic_params = [[0.5, 1], [1, 1.5]]
# Periodic parameters: define a single definition, to be applied to all spectra
periodic_params = [10, 0.4, 1]
###################################################################################################
# Simulate a group of power spectra
freqs, powers = gen_group_power_spectra(n_spectra, freq_range,
aperiodic_params, periodic_params, nlv)
###################################################################################################
# Plot the power spectra that were just generated
plot_spectra(freqs, powers, log_freqs=True, log_powers=True)
###################################################################################################
# Tracking Simulation Parameters
# ------------------------------
#
# When you start simulating multiple power spectra across different parameters,
# you may want to keep track of these parameters, so that you can compare any measure
# taken on these power spectra to ground truth values.
#
# When simulating power spectra, you also have the option of returning SimParams objects
# that keep track of the simulation parameters.
#
###################################################################################################
# Imports from fooof.synth.gen import gen_power_spectrum from fooof.synth.transform import rotate_spectrum from fooof.plts.spectra import plot_spectra ################################################################################################### # Generate a synthetic power spectrum fs, ps = gen_power_spectrum([3, 40], [1, 1], [10, 0.5, 1]) ################################################################################################### # rotate_spectrum # --------------- # # The :func:`rotate_spectrum` function takes in a power spectrum, and rotates the # power spectrum a specified amount, around a specified frequency point, changing # the aperiodic exponent of the spectrum. # ################################################################################################### # Rotate the power spectrum nps = rotate_spectrum(fs, ps, 0.25, 20) ################################################################################################### # Plot the two power spectra plot_spectra(fs, [ps, nps], log_freqs=True, log_powers=True)
# --------------------------------- # # First we will start with the core plotting function that plots an individual power spectrum. # # The :func:`~.plot_spectra` function takes in an array of frequency values and a 1d array of # of power values, and plots the corresponding power spectrum. # # This function, as all the functions in the plotting module, takes in optional inputs # `log_freqs` and `log_powers` that control whether the frequency and power axes # are plotted in log space. # ################################################################################################### # Create a spectrum plot with a single power spectrum plot_spectra(freqs, powers1, log_powers=True) ################################################################################################### # Plotting Multiple Power Spectra # ------------------------------- # # The :func:`~.plot_spectra` function takes in one or more frequency arrays and one or more # array of associated power values and plots multiple power spectra. # # Note that the inputs for either can be either 2d arrays, or lists of 1d arrays. You can also # pass in additional optional inputs including `labels`, to specify labels to use in a plot # legend, and `colors` to specify which colors to plot each spectrum in. # ###################################################################################################
def plot_fm(fm,
plot_peaks=None,
plot_aperiodic=True,
plt_log=False,
add_legend=True,
save_fig=False,
file_name=None,
file_path=None,
ax=None,
data_kwargs=None,
model_kwargs=None,
aperiodic_kwargs=None,
peak_kwargs=None,
**plot_kwargs):
"""Plot the power spectrum and model fit results from a FOOOF object.
Parameters
----------
fm : FOOOF
Object containing a power spectrum and (optionally) results from fitting.
plot_peaks : None or {'shade', 'dot', 'outline', 'line'}, optional
What kind of approach to take to plot peaks. If None, peaks are not specifically plotted.
Can also be a combination of approaches, separated by '-', for example: 'shade-line'.
plot_aperiodic : boolean, optional, default: True
Whether to plot the aperiodic component of the model fit.
plt_log : boolean, optional, default: False
Whether to plot the frequency values in log10 spacing.
add_legend : boolean, optional, default: False
Whether to add a legend describing the plot components.
save_fig : bool, optional, default: False
Whether to save out a copy of the plot.
file_name : str, optional
Name to give the saved out file.
file_path : str, optional
Path to directory to save to. If None, saves to current directory.
ax : matplotlib.Axes, optional
Figure axes upon which to plot.
data_kwargs, model_kwargs, aperiodic_kwargs, peak_kwargs : None or dict, optional
Keyword arguments to pass into the plot call for each plot element.
**plot_kwargs
Keyword arguments to pass into the ``style_plot``.
Notes
-----
Since FOOOF objects store power values in log spacing,
the y-axis (power) is plotted in log spacing by default.
"""
ax = check_ax(ax, PLT_FIGSIZES['spectral'])
# Log settings - note that power values in FOOOF objects are already logged
log_freqs = plt_log
log_powers = False
# Plot the data, if available
if fm.has_data:
data_defaults = {
'color': PLT_COLORS['data'],
'linewidth': 2.0,
'label': 'Original Spectrum' if add_legend else None
}
data_kwargs = check_plot_kwargs(data_kwargs, data_defaults)
plot_spectra(fm.freqs,
fm.power_spectrum,
log_freqs,
log_powers,
ax=ax,
**data_kwargs)
# Add the full model fit, and components (if requested)
if fm.has_model:
model_defaults = {
'color': PLT_COLORS['model'],
'linewidth': 3.0,
'alpha': 0.5,
'label': 'Full Model Fit' if add_legend else None
}
model_kwargs = check_plot_kwargs(model_kwargs, model_defaults)
plot_spectra(fm.freqs,
fm.fooofed_spectrum_,
log_freqs,
log_powers,
ax=ax,
**model_kwargs)
# Plot the aperiodic component of the model fit
if plot_aperiodic:
aperiodic_defaults = {
'color': PLT_COLORS['aperiodic'],
'linewidth': 3.0,
'alpha': 0.5,
'linestyle': 'dashed',
'label': 'Aperiodic Fit' if add_legend else None
}
aperiodic_kwargs = check_plot_kwargs(aperiodic_kwargs,
aperiodic_defaults)
plot_spectra(fm.freqs,
fm._ap_fit,
log_freqs,
log_powers,
ax=ax,
**aperiodic_kwargs)
# Plot the periodic components of the model fit
if plot_peaks:
_add_peaks(fm, plot_peaks, plt_log, ax, peak_kwargs)
# Apply default style to plot
style_spectrum_plot(ax, log_freqs, True)
# Step 1: Initial Aperiodic Fit
# ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
#
# We start by taking an initial aperiodic fit. This goal of this fit is to get an initial
# fit that is good enough to get started with the fitting process.
#
###################################################################################################
# Do an initial aperiodic 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_spectra(fm.freqs, fm.power_spectrum, plt_log,
label='Original Power Spectrum', color='black', ax=ax)
plot_spectra(fm.freqs, init_ap_fit, plt_log, label='Initial Aperiodic Fit',
color='blue', alpha=0.5, linestyle='dashed', ax=ax)
###################################################################################################
# Step 2: Flatten the Spectrum
# ^^^^^^^^^^^^^^^^^^^^^^^^^^^^
#
# The initial fit is then used to create a flattened spectrum.
#
# The initial aperiodic fit is subtracted out from the original data, leaving a flattened
# version of the data which no longer contains the aperiodic component.
#
###################################################################################################
# -------------------------------
#
# The :func:`~.plot_spectra` function takes in one or more frequency arrays and one or more
# array of associated power values and plots multiple power spectra.
#
# Note that the inputs for either can be either 2d arrays, or lists of 1d arrays. You can also
# pass in additional optional inputs including `labels`, to specify labels to use in a plot
# legend, and `colors` to specify which colors to plot each spectrum in.
#
###################################################################################################
# Plot multiple spectra on the same plot, in log-log space, specifying some labels
labels = ['PSD-1', 'PSD-2']
plot_spectra(freqs, [powers1, powers2],
log_freqs=True,
log_powers=True,
labels=labels)
###################################################################################################
# Plots With Shaded Regions
# -------------------------
#
# In some cases it may be useful to highlight or shade in particular frequency regions,
# for example, when examining power in particular frequency regions.
#
# The :func:`~.plot_spectrum_shading` function takes in a power spectrum and one or more
# shaded regions, and plot the power spectrum with the indicated region shaded.
#
# The same can be done for multiple power spectra with :func:`~.plot_spectra_shading`.
#
# These functions take in an input designating one or more shade regions, each specified
# Create a sampler to choose from two options for aperiodic parameters
ap_opts = param_sampler([[1, 1.25], [1, 1]])
# Create sampler to choose from two options for periodic parameters, and specify probabilities
gauss_opts = param_sampler([[10, 0.5, 1], [[10, 0.5, 1], [20, 0.25, 2]]],
[0.75, 0.25])
###################################################################################################
# Generate some power spectra, using the param samplers
fs, ps, syn_params = gen_group_power_spectra(10, [3, 40], ap_opts, gauss_opts)
###################################################################################################
# Plot some of the spectra that were generated
plot_spectra(fs, ps[0:4, :], log_powers=True)
###################################################################################################
# param_iter
# ~~~~~~~~~~
#
# The :func:`param_iter` function can be used to create iterators that can 'step' across
# a range of parameter values to be simulated.
#
# The :class:`Stepper` object needs to be used in conjuction with :func:`param_iter`,
# as it specifies the values to be iterated across.
#
###################################################################################################
# Set the aperiodic parameters to be stable
#
# Plotted below is an example power spectrum, plotted in semi-log space (log10 power values
# and linear frequencies). This is our data, that we will be trying to model.
#
# In the plot, we see a power spectrum in which there is decreasing power across increasing
# frequencies. In some frequency regions, there is a 'peak' of power, over and above the general
# trend across frequencies. These properties - a pattern of decreasing power across frequencies,
# with overlying peaks - are considered to be hallmarks of neural field data.
#
###################################################################################################
# Plot one of the example power spectra
plot_spectra(freqs1,
powers1,
log_powers=True,
color='black',
label='Original Spectrum')
###################################################################################################
# Conceptual Overview
# -------------------
#
# The goal of this module is to fit models to parameterize neural power spectra.
#
# One reason to do so is the idea that there are multiple distinct 'components' within
# neural field data. The model is therefore designed to measure these different
# 'components' of the data.
#
# By components, we mean that we are going to conceptualize neural field data as consisting
# of a combination of periodic (oscillatory) and aperiodic activity. Restated, we could say
def plot_annotated_peak_search(fm):
"""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.
"""
# 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_spectra(fm.freqs,
flatspec,
ax=ax,
linewidth=2.5,
label='Flattened Spectrum',
color=PLT_COLORS['data'])
plot_spectra(fm.freqs,
[fm.peak_threshold * np.std(flatspec)] * len(fm.freqs),
ax=ax,
label='Relative Threshold',
color='orange',
linewidth=2.5,
linestyle='dashed')
plot_spectra(fm.freqs, [fm.min_peak_height] * len(fm.freqs),
ax=ax,
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_spectra(fm.freqs,
gauss,
ax=ax,
label='Gaussian Fit',
color=PLT_COLORS['periodic'],
linestyle=':',
linewidth=3.0)
flatspec = flatspec - gauss
style_spectrum_plot(ax, False, True)
# changing the aperiodic exponent of the spectrum. # ################################################################################################### # Rotation settings delta_exp = 0.25 # How much to change the exponent by f_rotation = 20 # The frequency at which to rotate the spectrum # Rotate the power spectrum r_powers = rotate_spectrum(freqs, powers, delta_exp, f_rotation) ################################################################################################### # Plot the two power spectra, with the rotation applied plot_spectra(freqs, [powers, r_powers], log_freqs=True, log_powers=True) ################################################################################################### # # Next, we can fit power spectrum models to check if our change in exponent worked as expected. # ################################################################################################### # Initialize FOOOF objects fm1 = FOOOF(verbose=False) fm2 = FOOOF(verbose=False) # Fit power spectrum models to the original, and rotated, spectrum fm1.fit(freqs, powers) fm2.fit(freqs, r_powers)
#
# To visualize how much the exponent values vary, we can again plot some example power
# spectra, in this case extracting those with the highest and lower exponent values.
#
###################################################################################################
# Compare the power spectra between low and high exponent channels
fig, ax = plt.subplots(figsize=(8, 6))
spectra = [
fg.get_fooof(np.argmin(exps)).power_spectrum,
fg.get_fooof(np.argmax(exps)).power_spectrum
]
plot_spectra(fg.freqs,
spectra,
ax=ax,
labels=['Low Exponent', 'High Exponent'])
###################################################################################################
# Conclusion
# ----------
#
# In this example, we have seen how to apply power spectrum models to data that is
# managed and processed with MNE.
#
###################################################################################################
#