"""Functions for generating model components and simulated power spectra."""

import numpy as np

from fooof.core.utils import check_iter, check_flat

from fooof.core.funcs import get_ap_func, get_pe_func, infer_ap_func

from fooof.sim.params import collect_sim_params

from fooof.sim.transform import rotate_spectrum, compute_rotation_offset

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def gen_freqs(freq_range, freq_res):

"""Generate a frequency vector.

Parameters

----------

freq_range : list of [float, float]

Frequency range to create frequencies across, as [f_low, f_high], inclusive.

freq_res : float

Frequency resolution of desired frequency vector.

Returns

-------

freqs : 1d array

Frequency values, in linear spacing.

Examples

--------

Generate a vector of frequency values from 1 to 50:

>>> freqs = gen_freqs([1, 50], freq_res=0.5)

"""

# The end value has something added to it, to make sure the last value is included

# It adds a fraction to not accidentally include points beyond range

# due to rounding / or uneven division of the freq_res into range to simulate

freqs = np.arange(freq_range[0], freq_range[1] + (0.5 * freq_res), freq_res)

return freqs

def gen_power_spectrum(freq_range, aperiodic_params, periodic_params, nlv=0.005,

freq_res=0.5, f_rotation=None, return_params=False):

"""Generate a simulated power spectrum.

Parameters

----------

freq_range : list of [float, float]

Frequency range to simulate power spectrum across, as [f_low, f_high], inclusive.

aperiodic_params : list of float

Parameters to create the aperiodic component of a power spectrum.

Length should be 2 or 3 (see note).

periodic_params : list of float or list of list of float

Parameters to create the periodic component of a power spectrum.

Total length of n_peaks * 3 (see note).

nlv : float, optional, default: 0.005

Noise level to add to generated power spectrum.

freq_res : float, optional, default: 0.5

Frequency resolution for the simulated power spectrum.

f_rotation : float, optional

Frequency value, in Hz, to rotate around.

Should only be set if spectrum is to be rotated.

return_params : bool, optional, default: False

Whether to return the parameters for the simulated spectrum.

Returns

-------

freqs : 1d array

Frequency values, in linear spacing.

powers : 1d array

Power values, in linear spacing.

sim_params : SimParams

Definition of parameters used to create the spectrum.

Only returned if `return_params` is True.

Notes

-----

Aperiodic Parameters:

- The function for the aperiodic process to use is inferred from the provided parameters.

- If length of 2, the 'fixed' aperiodic mode is used, if length of 3, 'knee' is used.

Periodic Parameters:

- The periodic component is comprised of a set of 'peaks', each of which is described as:

* Mean (Center Frequency), height (Power), and standard deviation (Bandwidth).

* Make sure any center frequencies you request are within the simulated frequency range.

- The total number of parameters that need to be specified is number of peaks * 3

* These can be specified in as all together in a flat list (ex: [10, 1, 1, 20, 0.5, 1])

* They can also be grouped into a list of lists (ex: [[10, 1, 1], [20, 0.5, 1]])

Rotating Power Spectra:

- You can optionally specify a rotation frequency, such that power spectra will be

simulated and rotated around that point to the specified aperiodic exponent.

* This can be used so that any power spectra simulated with the same 'f_rotation'

will relate to each other by having the specified rotation point.

- Note that rotating power spectra changes the offset.

* If you specify an offset value to simulate as well as 'f_rotation', the returned

spectrum will NOT have the requested offset. It instead will have the offset

value required to create the requested aperiodic exponent with the requested

rotation point.

* If you return SimParams, the recorded offset will be the calculated offset

of the data post rotation, and not the entered value.

- You cannot rotate power spectra simulated with a knee.

* The procedure we use to rotate does not support spectra with a knee, and so

setting 'f_rotation' with a knee will lead to an error.

Examples

--------

Generate a power spectrum with a single peak, at 10 Hz:

>>> freqs, powers = gen_power_spectrum([1, 50], [0, 2], [10, 0.5, 1])

Generate a power spectrum with alpha and beta peaks:

>>> freqs, powers = gen_power_spectrum([1, 50], [0, 2], [[10, 0.5, 1], [20, 0.5, 1]])

Generate a power spectrum, that was rotated around a particular frequency point:

>>> freqs, powers = gen_power_spectrum([1, 50], [None, 2], [10, 0.5, 1], f_rotation=15)

"""

freqs = gen_freqs(freq_range, freq_res)

if f_rotation:

powers = gen_rotated_power_vals(freqs, aperiodic_params,

check_flat(periodic_params), nlv, f_rotation)

# The rotation changes the offset, so recalculate it's value & update params

new_offset = compute_rotation_offset(aperiodic_params[1], f_rotation)

aperiodic_params = [new_offset, aperiodic_params[1]]

else:

powers = gen_power_vals(freqs, aperiodic_params, check_flat(periodic_params), nlv)

if return_params:

sim_params = collect_sim_params(aperiodic_params, periodic_params, nlv)

return freqs, powers, sim_params

else:

return freqs, powers

def gen_group_power_spectra(n_spectra, freq_range, aperiodic_params, periodic_params, nlvs=0.005,

freq_res=0.5, f_rotation=None, return_params=False):

"""Generate a group of simulated power spectra.

Parameters

----------

n_spectra : int

The number of power spectra to generate.

freq_range : list of [float, float]

Frequency range to simulate power spectra across, as [f_low, f_high], inclusive.

aperiodic_params : list of float or generator

Parameters for the aperiodic component of the power spectra.

periodic_params : list of float or generator

Parameters for the periodic component of the power spectra.

Length of n_peaks * 3.

nlvs : float or list of float or generator, optional, default: 0.005

Noise level to add to generated power spectrum.

freq_res : float, optional, default: 0.5

Frequency resolution for the simulated power spectra.

f_rotation : float, optional

Frequency value, in Hz, to rotate around.

Should only be set if spectra are to be rotated.

return_params : bool, optional, default: False

Whether to return the parameters for the simulated spectra.

Returns

-------

freqs : 1d array

Frequency values, in linear spacing.

powers : 2d array

Matrix of power values, in linear spacing, as [n_power_spectra, n_freqs].

sim_params : list of SimParams

Definitions of parameters used for each spectrum. Has length of n_spectra.

Only returned if `return_params` is True.

Notes

-----

Parameters options can be:

- A single set of parameters.

If so, these same parameters are used for all spectra.

- A list of parameters whose length is n_spectra.

If so, each successive parameter set is such for each successive spectrum.

- A generator object that returns parameters for a power spectrum.

If so, each spectrum has parameters sampled from the generator.

Aperiodic Parameters:

- The function for the aperiodic process to use is inferred from the provided parameters.

- If length of 2, the 'fixed' aperiodic mode is used, if length of 3, 'knee' is used.

Periodic Parameters:

- The periodic component is comprised of a set of 'peaks', each of which is described as:

* Mean (Center Frequency), height (Power), and standard deviation (Bandwidth).

* Make sure any center frequencies you request are within the simulated frequency range.

Rotating Power Spectra:

- You can optionally specify a rotation frequency, such that power spectra will be

simulated and rotated around that point to the specified aperiodic exponent.

* This can be used so that any power spectra simulated with the same 'f_rotation'

will relate to each other by having the specified rotation point.

- Note that rotating power spectra changes the offset.

* If you specify an offset value to simulate as well as 'f_rotation', the returned

spectrum will NOT have the requested offset. It instead will have the offset

value required to create the requested aperiodic exponent with the requested

rotation point.

* If you return SimParams, the recorded offset will be the calculated offset

of the data post rotation, and not the entered value.

- You cannot rotate power spectra simulated with a knee.

* The procedure we use to rotate does not support spectra with a knee, and so

setting 'f_rotation' with a knee will lead to an error.

Examples

--------

Generate 2 power spectra using the same parameters:

>>> freqs, powers = gen_group_power_spectra(2, [1, 50], [0, 2], [10, 0.5, 1])

Generate 10 power spectra, randomly sampling possible parameters:

>>> from fooof.sim.params import param_sampler

>>> ap_opts = param_sampler([[0, 1.0], [0, 1.5], [0, 2]])

>>> pe_opts = param_sampler([[], [10, 0.5, 1], [10, 0.5, 1, 20, 0.25, 1]])

>>> freqs, powers = gen_group_power_spectra(10, [1, 50], ap_opts, pe_opts)

Generate 5 power spectra, rotated around 20 Hz:

>>> ap_params = [[None, 1], [None, 1.25], [None, 1.5], [None, 1.75], [None, 2]]

>>> pe_params = [10, 0.5, 1]

>>> freqs, powers = gen_group_power_spectra(5, [1, 50], ap_params, pe_params, f_rotation=20)

Generate power spectra stepping across exponent values, and return parameter values:

>>> from fooof.sim.params import Stepper, param_iter

>>> ap_params = param_iter([0, Stepper(1, 2, 0.25)])

>>> pe_params = [10, 0.5, 1]

>>> freqs, powers, sps = gen_group_power_spectra(5, [1, 50], ap_params, pe_params,

... return_params=True)

"""

# Initialize things

freqs = gen_freqs(freq_range, freq_res)

powers = np.zeros([n_spectra, len(freqs)])

sim_params = [None] * n_spectra

# Check if inputs are generators, if not, make them into repeat generators

ap_params = check_iter(aperiodic_params, n_spectra)

pe_params = check_iter(periodic_params, n_spectra)

nlvs = check_iter(nlvs, n_spectra)

f_rots = check_iter(f_rotation, n_spectra)

# Simulate power spectra

for ind, ap, pe, nlv, f_rot in zip(range(n_spectra), ap_params, pe_params, nlvs, f_rots):

if f_rotation:

powers[ind, :] = gen_rotated_power_vals(freqs, ap, check_flat(pe), nlv, f_rot)

aperiodic_params = [compute_rotation_offset(ap[1], f_rot), ap[1]]

else:

powers[ind, :] = gen_power_vals(freqs, ap, check_flat(pe), nlv)

sim_params[ind] = collect_sim_params(ap, pe, nlv)

if return_params:

return freqs, powers, sim_params

else:

return freqs, powers

def gen_aperiodic(freqs, aperiodic_params, aperiodic_mode=None):

"""Generate aperiodic values.

Parameters

----------

freqs : 1d array

Frequency vector to create aperiodic component for.

aperiodic_params : list of float

Parameters that define the aperiodic component.

aperiodic_mode : {'fixed', 'knee'}, optional

Which kind of aperiodic component to generate.

If not provided, is inferred from the parameters.

Returns

-------

ap_vals : 1d array

Aperiodic values, in log10 spacing.

"""

if not aperiodic_mode:

aperiodic_mode = infer_ap_func(aperiodic_params)

ap_func = get_ap_func(aperiodic_mode)

ap_vals = ap_func(freqs, *aperiodic_params)

return ap_vals

def gen_periodic(freqs, periodic_params, periodic_mode='gaussian'):

"""Generate periodic values.

Parameters

----------

freqs : 1d array

Frequency vector to create peak values for.

periodic_params : list of float

Parameters to create the periodic component.

periodic_mode : {'gaussian'}, optional

Which kind of periodic component to generate.

Returns

-------

peak_vals : 1d array

Peak values, in log10 spacing.

"""

pe_func = get_pe_func(periodic_mode)

pe_vals = pe_func(freqs, *periodic_params)

return pe_vals

def gen_noise(freqs, nlv):

"""Generate noise values for a simulated power spectrum.

Parameters

----------

freqs : 1d array

Frequency vector to create noise values for.

nlv : float

Noise level to generate.

Returns

-------

noise_vals : 1d vector

Noise values.

Notes

-----

This approach generates noise as randomly distributed white noise.

The 'level' of noise is controlled as the scale of the normal distribution.

"""

noise_vals = np.random.normal(0, nlv, len(freqs))

return noise_vals

def gen_power_vals(freqs, aperiodic_params, periodic_params, nlv):

"""Generate power values for a simulated power spectrum.

Parameters

----------

freqs : 1d array

Frequency vector to create power values for.

aperiodic_params : list of float

Parameters to create the aperiodic component of the power spectrum.

periodic_params : list of float

Parameters to create the periodic component of the power spectrum.

nlv : float

Noise level to add to generated power spectrum.

Returns

-------

powers : 1d vector

Power values, in linear spacing.

Notes

-----

This function should be used when simulating power spectra, as it:

- Takes in input parameter definitions as lists, as used for simulating power spectra.

- Returns the power spectrum in linear spacing, as is used for simulating power spectra.

"""

ap_vals = gen_aperiodic(freqs, aperiodic_params)

pe_vals = gen_periodic(freqs, periodic_params)

noise = gen_noise(freqs, nlv)

powers = np.power(10, ap_vals + pe_vals + noise)

return powers

def gen_rotated_power_vals(freqs, aperiodic_params, periodic_params, nlv, f_rotation):

"""Generate power values for a simulated power spectrum, rotated around a given frequency.

Parameters

----------

freqs : 1d array

Frequency vector to create power values for.

aperiodic_params : list of float

Parameters to create the aperiodic component of the power spectrum.

periodic_params : list of float

Parameters to create the periodic component of the power spectrum.

nlv : float

Noise level to add to generated power spectrum.

f_rotation : float

Frequency value, in Hz, about which rotation is applied, at which power is unchanged.

Returns

-------

powers : 1d vector

Power values, in linear spacing.

Raises

------

ValueError

If a rotation is requested on a power spectrum with a knee, as this is not supported.

"""

if len(aperiodic_params) == 3:

raise ValueError('Cannot rotate power spectra generated with a knee.')

powers = gen_power_vals(freqs, [0, 0], periodic_params, nlv)

powers = rotate_spectrum(freqs, powers, aperiodic_params[1], f_rotation)

return powers

def gen_model(freqs, aperiodic_params, periodic_params, return_components=False):

"""Generate a power spectrum model for a given parameter definition.

Parameters

----------

freqs : 1d array

Frequency vector to create the model for.

aperiodic_params : 1d array

Parameters to create the aperiodic component of the modeled power spectrum.

periodic_params : 2d array

Parameters to create the periodic component of the modeled power spectrum.

return_components : bool, optional, default: False

Whether to also return the components of the model.

Returns

-------

full_model : 1d array

The full power spectrum model, in log10 spacing.

pe_fit : 1d array

The periodic component of the model, containing the peaks.

Only returned if `return_components` is True.

ap_fit : 1d array

The aperiodic component of the model.

Only returned if `return_components` is True.

Notes

-----

This function should be used when computing model reconstructions, as it:

- Takes in input parameter definitions as arrays, as used in FOOOF objects.

- Returns the power spectrum in log10 spacing, as is used in FOOOF models.

"""

ap_fit = gen_aperiodic(freqs, aperiodic_params)

pe_fit = gen_periodic(freqs, np.ndarray.flatten(periodic_params))

full_model = pe_fit + ap_fit

if return_components:

return full_model, pe_fit, ap_fit

else:

return full_model