# Authors: Alexandre Gramfort # Matti Hämäläinen # Denis A. Engemann # # License: BSD-3-Clause from copy import deepcopy import itertools as itt from math import log import numpy as np from .defaults import (_INTERPOLATION_DEFAULT, _EXTRAPOLATE_DEFAULT, _BORDER_DEFAULT, DEFAULTS) from .io.write import start_and_end_file from .io.proj import (make_projector, _proj_equal, activate_proj, _check_projs, _needs_eeg_average_ref_proj, _has_eeg_average_ref_proj, _read_proj, _write_proj) from .io import fiff_open, RawArray from .io.pick import (pick_types, pick_channels_cov, pick_channels, pick_info, _picks_by_type, _pick_data_channels, _picks_to_idx, _DATA_CH_TYPES_SPLIT) from .io.constants import FIFF from .io.meas_info import _read_bad_channels, create_info from .io.tag import find_tag from .io.tree import dir_tree_find from .io.write import (start_block, end_block, write_int, write_name_list, write_double, write_float_matrix, write_string) from .defaults import _handle_default from .epochs import Epochs from .event import make_fixed_length_events from .evoked import EvokedArray from .rank import compute_rank from .utils import (check_fname, logger, verbose, check_version, _time_mask, warn, copy_function_doc_to_method_doc, _pl, _undo_scaling_cov, _scaled_array, _validate_type, _check_option, eigh, fill_doc, _on_missing, _check_on_missing, _check_fname, _verbose_safe_false) from . import viz from .fixes import (BaseEstimator, EmpiricalCovariance, _logdet, empirical_covariance, log_likelihood) def _check_covs_algebra(cov1, cov2): if cov1.ch_names != cov2.ch_names: raise ValueError('Both Covariance do not have the same list of ' 'channels.') projs1 = [str(c) for c in cov1['projs']] projs2 = [str(c) for c in cov1['projs']] if projs1 != projs2: raise ValueError('Both Covariance do not have the same list of ' 'SSP projections.') def _get_tslice(epochs, tmin, tmax): """Get the slice.""" mask = _time_mask(epochs.times, tmin, tmax, sfreq=epochs.info['sfreq']) tstart = np.where(mask)[0][0] if tmin is not None else None tend = np.where(mask)[0][-1] + 1 if tmax is not None else None tslice = slice(tstart, tend, None) return tslice @fill_doc class Covariance(dict): """Noise covariance matrix. .. note:: This class should not be instantiated directly via ``mne.Covariance(...)``. Instead, use one of the functions listed in the See Also section below. Parameters ---------- data : array-like The data. names : list of str Channel names. bads : list of str Bad channels. projs : list Projection vectors. nfree : int Degrees of freedom. eig : array-like | None Eigenvalues. eigvec : array-like | None Eigenvectors. method : str | None The method used to compute the covariance. loglik : float The log likelihood. %(verbose)s Attributes ---------- data : array of shape (n_channels, n_channels) The covariance. ch_names : list of str List of channels' names. nfree : int Number of degrees of freedom i.e. number of time points used. dim : int The number of channels ``n_channels``. See Also -------- compute_covariance compute_raw_covariance make_ad_hoc_cov read_cov """ @verbose def __init__(self, data, names, bads, projs, nfree, eig=None, eigvec=None, method=None, loglik=None, *, verbose=None): """Init of covariance.""" diag = (data.ndim == 1) projs = _check_projs(projs) self.update(data=data, dim=len(data), names=names, bads=bads, nfree=nfree, eig=eig, eigvec=eigvec, diag=diag, projs=projs, kind=FIFF.FIFFV_MNE_NOISE_COV) if method is not None: self['method'] = method if loglik is not None: self['loglik'] = loglik @property def data(self): """Numpy array of Noise covariance matrix.""" return self['data'] @property def ch_names(self): """Channel names.""" return self['names'] @property def nfree(self): """Number of degrees of freedom.""" return self['nfree'] @verbose def save(self, fname, *, overwrite=False, verbose=None): """Save covariance matrix in a FIF file. Parameters ---------- fname : str Output filename. %(overwrite)s .. versionadded:: 1.0 %(verbose)s """ check_fname(fname, 'covariance', ('-cov.fif', '-cov.fif.gz', '_cov.fif', '_cov.fif.gz')) fname = _check_fname(fname=fname, overwrite=overwrite) with start_and_end_file(fname) as fid: _write_cov(fid, self) def copy(self): """Copy the Covariance object. Returns ------- cov : instance of Covariance The copied object. """ return deepcopy(self) def as_diag(self): """Set covariance to be processed as being diagonal. Returns ------- cov : dict The covariance. Notes ----- This function allows creation of inverse operators equivalent to using the old "--diagnoise" mne option. This function operates in place. """ if self['diag']: return self self['diag'] = True self['data'] = np.diag(self['data']) self['eig'] = None self['eigvec'] = None return self def _as_square(self): # This is a hack but it works because np.diag() behaves nicely if self['diag']: self['diag'] = False self.as_diag() self['diag'] = False return self def _get_square(self): if self['diag'] != (self.data.ndim == 1): raise RuntimeError( 'Covariance attributes inconsistent, got data with ' 'dimensionality %d but diag=%s' % (self.data.ndim, self['diag'])) return np.diag(self.data) if self['diag'] else self.data.copy() def __repr__(self): # noqa: D105 if self.data.ndim == 2: s = 'size : %s x %s' % self.data.shape else: # ndim == 1 s = 'diagonal : %s' % self.data.size s += ", n_samples : %s" % self.nfree s += ", data : %s" % self.data return "" % s def __add__(self, cov): """Add Covariance taking into account number of degrees of freedom.""" _check_covs_algebra(self, cov) this_cov = cov.copy() this_cov['data'] = (((this_cov['data'] * this_cov['nfree']) + (self['data'] * self['nfree'])) / (self['nfree'] + this_cov['nfree'])) this_cov['nfree'] += self['nfree'] this_cov['bads'] = list(set(this_cov['bads']).union(self['bads'])) return this_cov def __iadd__(self, cov): """Add Covariance taking into account number of degrees of freedom.""" _check_covs_algebra(self, cov) self['data'][:] = (((self['data'] * self['nfree']) + (cov['data'] * cov['nfree'])) / (self['nfree'] + cov['nfree'])) self['nfree'] += cov['nfree'] self['bads'] = list(set(self['bads']).union(cov['bads'])) return self @verbose @copy_function_doc_to_method_doc(viz.misc.plot_cov) def plot(self, info, exclude=[], colorbar=True, proj=False, show_svd=True, show=True, verbose=None): return viz.misc.plot_cov(self, info, exclude, colorbar, proj, show_svd, show, verbose) @verbose def plot_topomap( self, info, ch_type=None, *, scalings=None, proj=False, noise_cov=None, sensors=True, show_names=False, mask=None, mask_params=None, contours=6, outlines='head', sphere=None, image_interp=_INTERPOLATION_DEFAULT, extrapolate=_EXTRAPOLATE_DEFAULT, border=_BORDER_DEFAULT, res=64, size=1, cmap=None, vlim=(None, None), cnorm=None, colorbar=True, cbar_fmt='%3.1f', units=None, axes=None, show=True, verbose=None): """Plot a topomap of the covariance diagonal. Parameters ---------- %(info_not_none)s %(ch_type_topomap)s .. versionadded:: 0.21 %(scalings_topomap)s %(proj_plot)s noise_cov : instance of Covariance | None If not None, whiten the instance with ``noise_cov`` before plotting. %(sensors_topomap)s %(show_names_topomap)s %(mask_topomap)s %(mask_params_topomap)s %(contours_topomap)s %(outlines_topomap)s %(sphere_topomap_auto)s %(image_interp_topomap)s %(extrapolate_topomap)s %(border_topomap)s %(res_topomap)s %(size_topomap)s %(cmap_topomap)s %(vlim_plot_topomap)s .. versionadded:: 1.2 %(cnorm)s .. versionadded:: 1.2 %(colorbar_topomap)s %(cbar_fmt_topomap)s %(units_topomap_evoked)s %(axes_cov_plot_topomap)s %(show)s %(verbose)s Returns ------- fig : instance of Figure The matplotlib figure. Notes ----- .. versionadded:: 0.21 """ from .viz.misc import _index_info_cov info, C, _, _ = _index_info_cov(info, self, exclude=()) evoked = EvokedArray(np.diag(C)[:, np.newaxis], info) if noise_cov is not None: # need to left and right multiply whitener, which for the diagonal # entries is the same as multiplying twice evoked = whiten_evoked(whiten_evoked(evoked, noise_cov), noise_cov) if units is None: units = 'AU' if scalings is None: scalings = 1. if units is None: units = {k: f'({v})²' for k, v in DEFAULTS['units'].items()} if scalings is None: scalings = {k: v * v for k, v in DEFAULTS['scalings'].items()} return evoked.plot_topomap( times=[0], ch_type=ch_type, vlim=vlim, cmap=cmap, sensors=sensors, cnorm=cnorm, colorbar=colorbar, scalings=scalings, units=units, res=res, size=size, cbar_fmt=cbar_fmt, proj=proj, show=show, show_names=show_names, mask=mask, mask_params=mask_params, outlines=outlines, contours=contours, image_interp=image_interp, axes=axes, extrapolate=extrapolate, sphere=sphere, border=border, time_format='') def pick_channels(self, ch_names, ordered=False): """Pick channels from this covariance matrix. Parameters ---------- ch_names : list of str List of channels to keep. All other channels are dropped. ordered : bool If True (default False), ensure that the order of the channels matches the order of ``ch_names``. Returns ------- cov : instance of Covariance. The modified covariance matrix. Notes ----- Operates in-place. .. versionadded:: 0.20.0 """ return pick_channels_cov(self, ch_names, exclude=[], ordered=ordered, copy=False) ############################################################################### # IO @verbose def read_cov(fname, verbose=None): """Read a noise covariance from a FIF file. Parameters ---------- fname : str The name of file containing the covariance matrix. It should end with -cov.fif or -cov.fif.gz. %(verbose)s Returns ------- cov : Covariance The noise covariance matrix. See Also -------- write_cov, compute_covariance, compute_raw_covariance """ check_fname(fname, 'covariance', ('-cov.fif', '-cov.fif.gz', '_cov.fif', '_cov.fif.gz')) fname = _check_fname(fname=fname, must_exist=True, overwrite='read') f, tree = fiff_open(fname)[:2] with f as fid: return Covariance(**_read_cov(fid, tree, FIFF.FIFFV_MNE_NOISE_COV, limited=True)) ############################################################################### # Estimate from data @verbose def make_ad_hoc_cov(info, std=None, *, verbose=None): """Create an ad hoc noise covariance. Parameters ---------- %(info_not_none)s std : dict of float | None Standard_deviation of the diagonal elements. If dict, keys should be ``'grad'`` for gradiometers, ``'mag'`` for magnetometers and ``'eeg'`` for EEG channels. If None, default values will be used (see Notes). %(verbose)s Returns ------- cov : instance of Covariance The ad hoc diagonal noise covariance for the M/EEG data channels. Notes ----- The default noise values are 5 fT/cm, 20 fT, and 0.2 µV for gradiometers, magnetometers, and EEG channels respectively. .. versionadded:: 0.9.0 """ picks = pick_types(info, meg=True, eeg=True, exclude=()) std = _handle_default('noise_std', std) data = np.zeros(len(picks)) for meg, eeg, val in zip(('grad', 'mag', False), (False, False, True), (std['grad'], std['mag'], std['eeg'])): these_picks = pick_types(info, meg=meg, eeg=eeg) data[np.searchsorted(picks, these_picks)] = val * val ch_names = [info['ch_names'][pick] for pick in picks] return Covariance(data, ch_names, info['bads'], info['projs'], nfree=0) def _check_n_samples(n_samples, n_chan): """Check to see if there are enough samples for reliable cov calc.""" n_samples_min = 10 * (n_chan + 1) // 2 if n_samples <= 0: raise ValueError('No samples found to compute the covariance matrix') if n_samples < n_samples_min: warn('Too few samples (required : %d got : %d), covariance ' 'estimate may be unreliable' % (n_samples_min, n_samples)) @verbose def compute_raw_covariance(raw, tmin=0, tmax=None, tstep=0.2, reject=None, flat=None, picks=None, method='empirical', method_params=None, cv=3, scalings=None, n_jobs=None, return_estimators=False, reject_by_annotation=True, rank=None, verbose=None): """Estimate noise covariance matrix from a continuous segment of raw data. It is typically useful to estimate a noise covariance from empty room data or time intervals before starting the stimulation. .. note:: To estimate the noise covariance from epoched data, use :func:`mne.compute_covariance` instead. Parameters ---------- raw : instance of Raw Raw data. tmin : float Beginning of time interval in seconds. Defaults to 0. tmax : float | None (default None) End of time interval in seconds. If None (default), use the end of the recording. tstep : float (default 0.2) Length of data chunks for artifact rejection in seconds. Can also be None to use a single epoch of (tmax - tmin) duration. This can use a lot of memory for large ``Raw`` instances. reject : dict | None (default None) Rejection parameters based on peak-to-peak amplitude. Valid keys are 'grad' | 'mag' | 'eeg' | 'eog' | 'ecg'. If reject is None then no rejection is done. Example:: reject = dict(grad=4000e-13, # T / m (gradiometers) mag=4e-12, # T (magnetometers) eeg=40e-6, # V (EEG channels) eog=250e-6 # V (EOG channels) ) flat : dict | None (default None) Rejection parameters based on flatness of signal. Valid keys are 'grad' | 'mag' | 'eeg' | 'eog' | 'ecg', and values are floats that set the minimum acceptable peak-to-peak amplitude. If flat is None then no rejection is done. %(picks_good_data_noref)s method : str | list | None (default 'empirical') The method used for covariance estimation. See :func:`mne.compute_covariance`. .. versionadded:: 0.12 method_params : dict | None (default None) Additional parameters to the estimation procedure. See :func:`mne.compute_covariance`. .. versionadded:: 0.12 cv : int | sklearn.model_selection object (default 3) The cross validation method. Defaults to 3, which will internally trigger by default :class:`sklearn.model_selection.KFold` with 3 splits. .. versionadded:: 0.12 scalings : dict | None (default None) Defaults to ``dict(mag=1e15, grad=1e13, eeg=1e6)``. These defaults will scale magnetometers and gradiometers at the same unit. .. versionadded:: 0.12 %(n_jobs)s .. versionadded:: 0.12 return_estimators : bool (default False) Whether to return all estimators or the best. Only considered if method equals 'auto' or is a list of str. Defaults to False. .. versionadded:: 0.12 %(reject_by_annotation_epochs)s .. versionadded:: 0.14 %(rank_none)s .. versionadded:: 0.17 .. versionadded:: 0.18 Support for 'info' mode. %(verbose)s Returns ------- cov : instance of Covariance | list The computed covariance. If method equals 'auto' or is a list of str and return_estimators equals True, a list of covariance estimators is returned (sorted by log-likelihood, from high to low, i.e. from best to worst). See Also -------- compute_covariance : Estimate noise covariance matrix from epoched data. Notes ----- This function will: 1. Partition the data into evenly spaced, equal-length epochs. 2. Load them into memory. 3. Subtract the mean across all time points and epochs for each channel. 4. Process the :class:`Epochs` by :func:`compute_covariance`. This will produce a slightly different result compared to using :func:`make_fixed_length_events`, :class:`Epochs`, and :func:`compute_covariance` directly, since that would (with the recommended baseline correction) subtract the mean across time *for each epoch* (instead of across epochs) for each channel. """ tmin = 0. if tmin is None else float(tmin) dt = 1. / raw.info['sfreq'] tmax = raw.times[-1] + dt if tmax is None else float(tmax) tstep = tmax - tmin if tstep is None else float(tstep) tstep_m1 = tstep - dt # inclusive! events = make_fixed_length_events(raw, 1, tmin, tmax, tstep) logger.info('Using up to %s segment%s' % (len(events), _pl(events))) # don't exclude any bad channels, inverses expect all channels present if picks is None: # Need to include all channels e.g. if eog rejection is to be used picks = np.arange(raw.info['nchan']) pick_mask = np.in1d( picks, _pick_data_channels(raw.info, with_ref_meg=False)) else: pick_mask = slice(None) picks = _picks_to_idx(raw.info, picks) epochs = Epochs(raw, events, 1, 0, tstep_m1, baseline=None, picks=picks, reject=reject, flat=flat, verbose=_verbose_safe_false(), preload=False, proj=False, reject_by_annotation=reject_by_annotation) if method is None: method = 'empirical' if isinstance(method, str) and method == 'empirical': # potentially *much* more memory efficient to do it the iterative way picks = picks[pick_mask] data = 0 n_samples = 0 mu = 0 # Read data in chunks for raw_segment in epochs: raw_segment = raw_segment[pick_mask] mu += raw_segment.sum(axis=1) data += np.dot(raw_segment, raw_segment.T) n_samples += raw_segment.shape[1] _check_n_samples(n_samples, len(picks)) data -= mu[:, None] * (mu[None, :] / n_samples) data /= (n_samples - 1.0) logger.info("Number of samples used : %d" % n_samples) logger.info('[done]') ch_names = [raw.info['ch_names'][k] for k in picks] bads = [b for b in raw.info['bads'] if b in ch_names] return Covariance(data, ch_names, bads, raw.info['projs'], nfree=n_samples - 1) del picks, pick_mask # This makes it equivalent to what we used to do (and do above for # empirical mode), treating all epochs as if they were a single long one epochs.load_data() ch_means = epochs._data.mean(axis=0).mean(axis=1) epochs._data -= ch_means[np.newaxis, :, np.newaxis] # fake this value so there are no complaints from compute_covariance epochs.baseline = (None, None) return compute_covariance(epochs, keep_sample_mean=True, method=method, method_params=method_params, cv=cv, scalings=scalings, n_jobs=n_jobs, return_estimators=return_estimators, rank=rank) def _check_method_params(method, method_params, keep_sample_mean=True, name='method', allow_auto=True, rank=None): """Check that method and method_params are usable.""" accepted_methods = ('auto', 'empirical', 'diagonal_fixed', 'ledoit_wolf', 'oas', 'shrunk', 'pca', 'factor_analysis', 'shrinkage') _method_params = { 'empirical': {'store_precision': False, 'assume_centered': True}, 'diagonal_fixed': {'store_precision': False, 'assume_centered': True}, 'ledoit_wolf': {'store_precision': False, 'assume_centered': True}, 'oas': {'store_precision': False, 'assume_centered': True}, 'shrinkage': {'shrinkage': 0.1, 'store_precision': False, 'assume_centered': True}, 'shrunk': {'shrinkage': np.logspace(-4, 0, 30), 'store_precision': False, 'assume_centered': True}, 'pca': {'iter_n_components': None}, 'factor_analysis': {'iter_n_components': None} } for ch_type in _DATA_CH_TYPES_SPLIT: _method_params['diagonal_fixed'][ch_type] = 0.1 if isinstance(method_params, dict): for key, values in method_params.items(): if key not in _method_params: raise ValueError('key (%s) must be "%s"' % (key, '" or "'.join(_method_params))) _method_params[key].update(method_params[key]) shrinkage = method_params.get('shrinkage', {}).get('shrinkage', 0.1) if not 0 <= shrinkage <= 1: raise ValueError('shrinkage must be between 0 and 1, got %s' % (shrinkage,)) was_auto = False if method is None: method = ['empirical'] elif method == 'auto' and allow_auto: was_auto = True method = ['shrunk', 'diagonal_fixed', 'empirical', 'factor_analysis'] if not isinstance(method, (list, tuple)): method = [method] if not all(k in accepted_methods for k in method): raise ValueError( 'Invalid {name} ({method}). Accepted values (individually or ' 'in a list) are any of "{accepted_methods}" or None.'.format( name=name, method=method, accepted_methods=accepted_methods)) if not (isinstance(rank, str) and rank == 'full'): if was_auto: method.pop(method.index('factor_analysis')) for method_ in method: if method_ in ('pca', 'factor_analysis'): raise ValueError('%s can so far only be used with rank="full",' ' got rank=%r' % (method_, rank)) if not keep_sample_mean: if len(method) != 1 or 'empirical' not in method: raise ValueError('`keep_sample_mean=False` is only supported' 'with %s="empirical"' % (name,)) for p, v in _method_params.items(): if v.get('assume_centered', None) is False: raise ValueError('`assume_centered` must be True' ' if `keep_sample_mean` is False') return method, _method_params @verbose def compute_covariance(epochs, keep_sample_mean=True, tmin=None, tmax=None, projs=None, method='empirical', method_params=None, cv=3, scalings=None, n_jobs=None, return_estimators=False, on_mismatch='raise', rank=None, verbose=None): """Estimate noise covariance matrix from epochs. The noise covariance is typically estimated on pre-stimulus periods when the stimulus onset is defined from events. If the covariance is computed for multiple event types (events with different IDs), the following two options can be used and combined: 1. either an Epochs object for each event type is created and a list of Epochs is passed to this function. 2. an Epochs object is created for multiple events and passed to this function. .. note:: To estimate the noise covariance from non-epoched raw data, such as an empty-room recording, use :func:`mne.compute_raw_covariance` instead. Parameters ---------- epochs : instance of Epochs, or list of Epochs The epochs. keep_sample_mean : bool (default True) If False, the average response over epochs is computed for each event type and subtracted during the covariance computation. This is useful if the evoked response from a previous stimulus extends into the baseline period of the next. Note. This option is only implemented for method='empirical'. tmin : float | None (default None) Start time for baseline. If None start at first sample. tmax : float | None (default None) End time for baseline. If None end at last sample. projs : list of Projection | None (default None) List of projectors to use in covariance calculation, or None to indicate that the projectors from the epochs should be inherited. If None, then projectors from all epochs must match. method : str | list | None (default 'empirical') The method used for covariance estimation. If 'empirical' (default), the sample covariance will be computed. A list can be passed to perform estimates using multiple methods. If 'auto' or a list of methods, the best estimator will be determined based on log-likelihood and cross-validation on unseen data as described in :footcite:`EngemannGramfort2015`. Valid methods are 'empirical', 'diagonal_fixed', 'shrunk', 'oas', 'ledoit_wolf', 'factor_analysis', 'shrinkage', and 'pca' (see Notes). If ``'auto'``, it expands to:: ['shrunk', 'diagonal_fixed', 'empirical', 'factor_analysis'] ``'factor_analysis'`` is removed when ``rank`` is not 'full'. The ``'auto'`` mode is not recommended if there are many segments of data, since computation can take a long time. .. versionadded:: 0.9.0 method_params : dict | None (default None) Additional parameters to the estimation procedure. Only considered if method is not None. Keys must correspond to the value(s) of ``method``. If None (default), expands to the following (with the addition of ``{'store_precision': False, 'assume_centered': True} for all methods except ``'factor_analysis'`` and ``'pca'``):: {'diagonal_fixed': {'grad': 0.1, 'mag': 0.1, 'eeg': 0.1, ...}, 'shrinkage': {'shrikage': 0.1}, 'shrunk': {'shrinkage': np.logspace(-4, 0, 30)}, 'pca': {'iter_n_components': None}, 'factor_analysis': {'iter_n_components': None}} cv : int | sklearn.model_selection object (default 3) The cross validation method. Defaults to 3, which will internally trigger by default :class:`sklearn.model_selection.KFold` with 3 splits. scalings : dict | None (default None) Defaults to ``dict(mag=1e15, grad=1e13, eeg=1e6)``. These defaults will scale data to roughly the same order of magnitude. %(n_jobs)s return_estimators : bool (default False) Whether to return all estimators or the best. Only considered if method equals 'auto' or is a list of str. Defaults to False. on_mismatch : str What to do when the MEG<->Head transformations do not match between epochs. If "raise" (default) an error is raised, if "warn" then a warning is emitted, if "ignore" then nothing is printed. Having mismatched transforms can in some cases lead to unexpected or unstable results in covariance calculation, e.g. when data have been processed with Maxwell filtering but not transformed to the same head position. %(rank_none)s .. versionadded:: 0.17 .. versionadded:: 0.18 Support for 'info' mode. %(verbose)s Returns ------- cov : instance of Covariance | list The computed covariance. If method equals 'auto' or is a list of str and return_estimators equals True, a list of covariance estimators is returned (sorted by log-likelihood, from high to low, i.e. from best to worst). See Also -------- compute_raw_covariance : Estimate noise covariance from raw data, such as empty-room recordings. Notes ----- Baseline correction or sufficient high-passing should be used when creating the :class:`Epochs` to ensure that the data are zero mean, otherwise the computed covariance matrix will be inaccurate. Valid ``method`` strings are: * ``'empirical'`` The empirical or sample covariance (default) * ``'diagonal_fixed'`` A diagonal regularization based on channel types as in :func:`mne.cov.regularize`. * ``'shrinkage'`` Fixed shrinkage. .. versionadded:: 0.16 * ``'ledoit_wolf'`` The Ledoit-Wolf estimator, which uses an empirical formula for the optimal shrinkage value :footcite:`LedoitWolf2004`. * ``'oas'`` The OAS estimator :footcite:`ChenEtAl2010`, which uses a different empricial formula for the optimal shrinkage value. .. versionadded:: 0.16 * ``'shrunk'`` Like 'ledoit_wolf', but with cross-validation for optimal alpha. * ``'pca'`` Probabilistic PCA with low rank :footcite:`TippingBishop1999`. * ``'factor_analysis'`` Factor analysis with low rank :footcite:`Barber2012`. ``'ledoit_wolf'`` and ``'pca'`` are similar to ``'shrunk'`` and ``'factor_analysis'``, respectively, except that they use cross validation (which is useful when samples are correlated, which is often the case for M/EEG data). The former two are not included in the ``'auto'`` mode to avoid redundancy. For multiple event types, it is also possible to create a single :class:`Epochs` object with events obtained using :func:`mne.merge_events`. However, the resulting covariance matrix will only be correct if ``keep_sample_mean is True``. The covariance can be unstable if the number of samples is small. In that case it is common to regularize the covariance estimate. The ``method`` parameter allows to regularize the covariance in an automated way. It also allows to select between different alternative estimation algorithms which themselves achieve regularization. Details are described in :footcite:`EngemannGramfort2015`. For more information on the advanced estimation methods, see :ref:`the sklearn manual `. References ---------- .. footbibliography:: """ # scale to natural unit for best stability with MEG/EEG scalings = _check_scalings_user(scalings) method, _method_params = _check_method_params( method, method_params, keep_sample_mean, rank=rank) del method_params # for multi condition support epochs is required to refer to a list of # epochs objects def _unpack_epochs(epochs): if len(epochs.event_id) > 1: epochs = [epochs[k] for k in epochs.event_id] else: epochs = [epochs] return epochs if not isinstance(epochs, list): epochs = _unpack_epochs(epochs) else: epochs = sum([_unpack_epochs(epoch) for epoch in epochs], []) # check for baseline correction if any(epochs_t.baseline is None and epochs_t.info['highpass'] < 0.5 and keep_sample_mean for epochs_t in epochs): warn('Epochs are not baseline corrected, covariance ' 'matrix may be inaccurate') orig = epochs[0].info['dev_head_t'] _check_on_missing(on_mismatch, 'on_mismatch') for ei, epoch in enumerate(epochs): epoch.info._check_consistency() if (orig is None) != (epoch.info['dev_head_t'] is None) or \ (orig is not None and not np.allclose(orig['trans'], epoch.info['dev_head_t']['trans'])): msg = ('MEG<->Head transform mismatch between epochs[0]:\n%s\n\n' 'and epochs[%s]:\n%s' % (orig, ei, epoch.info['dev_head_t'])) _on_missing(on_mismatch, msg, 'on_mismatch') bads = epochs[0].info['bads'] if projs is None: projs = epochs[0].info['projs'] # make sure Epochs are compatible for epochs_t in epochs[1:]: if epochs_t.proj != epochs[0].proj: raise ValueError('Epochs must agree on the use of projections') for proj_a, proj_b in zip(epochs_t.info['projs'], projs): if not _proj_equal(proj_a, proj_b): raise ValueError('Epochs must have same projectors') projs = _check_projs(projs) ch_names = epochs[0].ch_names # make sure Epochs are compatible for epochs_t in epochs[1:]: if epochs_t.info['bads'] != bads: raise ValueError('Epochs must have same bad channels') if epochs_t.ch_names != ch_names: raise ValueError('Epochs must have same channel names') picks_list = _picks_by_type(epochs[0].info) picks_meeg = np.concatenate([b for _, b in picks_list]) picks_meeg = np.sort(picks_meeg) ch_names = [epochs[0].ch_names[k] for k in picks_meeg] info = epochs[0].info # we will overwrite 'epochs' if not keep_sample_mean: # prepare mean covs n_epoch_types = len(epochs) data_mean = [0] * n_epoch_types n_samples = np.zeros(n_epoch_types, dtype=np.int64) n_epochs = np.zeros(n_epoch_types, dtype=np.int64) for ii, epochs_t in enumerate(epochs): tslice = _get_tslice(epochs_t, tmin, tmax) for e in epochs_t: e = e[picks_meeg, tslice] if not keep_sample_mean: data_mean[ii] += e n_samples[ii] += e.shape[1] n_epochs[ii] += 1 n_samples_epoch = n_samples // n_epochs norm_const = np.sum(n_samples_epoch * (n_epochs - 1)) data_mean = [1.0 / n_epoch * np.dot(mean, mean.T) for n_epoch, mean in zip(n_epochs, data_mean)] info = pick_info(info, picks_meeg) tslice = _get_tslice(epochs[0], tmin, tmax) epochs = [ee.get_data(picks=picks_meeg)[..., tslice] for ee in epochs] picks_meeg = np.arange(len(picks_meeg)) picks_list = _picks_by_type(info) if len(epochs) > 1: epochs = np.concatenate(epochs, 0) else: epochs = epochs[0] epochs = np.hstack(epochs) n_samples_tot = epochs.shape[-1] _check_n_samples(n_samples_tot, len(picks_meeg)) epochs = epochs.T # sklearn | C-order cov_data = _compute_covariance_auto( epochs, method=method, method_params=_method_params, info=info, cv=cv, n_jobs=n_jobs, stop_early=True, picks_list=picks_list, scalings=scalings, rank=rank) if keep_sample_mean is False: cov = cov_data['empirical']['data'] # undo scaling cov *= (n_samples_tot - 1) # ... apply pre-computed class-wise normalization for mean_cov in data_mean: cov -= mean_cov cov /= norm_const covs = list() for this_method, data in cov_data.items(): cov = Covariance(data.pop('data'), ch_names, info['bads'], projs, nfree=n_samples_tot - 1) # add extra info cov.update(method=this_method, **data) covs.append(cov) logger.info('Number of samples used : %d' % n_samples_tot) covs.sort(key=lambda c: c['loglik'], reverse=True) if len(covs) > 1: msg = ['log-likelihood on unseen data (descending order):'] for c in covs: msg.append('%s: %0.3f' % (c['method'], c['loglik'])) logger.info('\n '.join(msg)) if return_estimators: out = covs else: out = covs[0] logger.info('selecting best estimator: {}'.format(out['method'])) else: out = covs[0] logger.info('[done]') return out def _check_scalings_user(scalings): if isinstance(scalings, dict): for k, v in scalings.items(): _check_option('the keys in `scalings`', k, ['mag', 'grad', 'eeg']) elif scalings is not None and not isinstance(scalings, np.ndarray): raise TypeError('scalings must be a dict, ndarray, or None, got %s' % type(scalings)) scalings = _handle_default('scalings', scalings) return scalings def _eigvec_subspace(eig, eigvec, mask): """Compute the subspace from a subset of eigenvectors.""" # We do the same thing we do with projectors: P = np.eye(len(eigvec)) - np.dot(eigvec[~mask].conj().T, eigvec[~mask]) eig, eigvec = eigh(P) eigvec = eigvec.conj().T return eig, eigvec def _compute_covariance_auto(data, method, info, method_params, cv, scalings, n_jobs, stop_early, picks_list, rank): """Compute covariance auto mode.""" # rescale to improve numerical stability orig_rank = rank rank = compute_rank( RawArray(data.T, info, copy=None, verbose=_verbose_safe_false()), rank, scalings, info) with _scaled_array(data.T, picks_list, scalings): C = np.dot(data.T, data) _, eigvec, mask = _smart_eigh(C, info, rank, proj_subspace=True, do_compute_rank=False) eigvec = eigvec[mask] data = np.dot(data, eigvec.T) used = np.where(mask)[0] sub_picks_list = [(key, np.searchsorted(used, picks)) for key, picks in picks_list] sub_info = pick_info(info, used) if len(used) != len(mask) else info logger.info('Reducing data rank from %s -> %s' % (len(mask), eigvec.shape[0])) estimator_cov_info = list() msg = 'Estimating covariance using %s' ok_sklearn = check_version('sklearn') if not ok_sklearn and (len(method) != 1 or method[0] != 'empirical'): raise ValueError('scikit-learn is not installed, `method` must be ' '`empirical`, got %s' % (method,)) for method_ in method: data_ = data.copy() name = method_.__name__ if callable(method_) else method_ logger.info(msg % name.upper()) mp = method_params[method_] _info = {} if method_ == 'empirical': est = EmpiricalCovariance(**mp) est.fit(data_) estimator_cov_info.append((est, est.covariance_, _info)) del est elif method_ == 'diagonal_fixed': est = _RegCovariance(info=sub_info, **mp) est.fit(data_) estimator_cov_info.append((est, est.covariance_, _info)) del est elif method_ == 'ledoit_wolf': from sklearn.covariance import LedoitWolf shrinkages = [] lw = LedoitWolf(**mp) for ch_type, picks in sub_picks_list: lw.fit(data_[:, picks]) shrinkages.append((ch_type, lw.shrinkage_, picks)) sc = _ShrunkCovariance(shrinkage=shrinkages, **mp) sc.fit(data_) estimator_cov_info.append((sc, sc.covariance_, _info)) del lw, sc elif method_ == 'oas': from sklearn.covariance import OAS shrinkages = [] oas = OAS(**mp) for ch_type, picks in sub_picks_list: oas.fit(data_[:, picks]) shrinkages.append((ch_type, oas.shrinkage_, picks)) sc = _ShrunkCovariance(shrinkage=shrinkages, **mp) sc.fit(data_) estimator_cov_info.append((sc, sc.covariance_, _info)) del oas, sc elif method_ == 'shrinkage': sc = _ShrunkCovariance(**mp) sc.fit(data_) estimator_cov_info.append((sc, sc.covariance_, _info)) del sc elif method_ == 'shrunk': from sklearn.model_selection import GridSearchCV from sklearn.covariance import ShrunkCovariance shrinkage = mp.pop('shrinkage') tuned_parameters = [{'shrinkage': shrinkage}] shrinkages = [] gs = GridSearchCV(ShrunkCovariance(**mp), tuned_parameters, cv=cv) for ch_type, picks in sub_picks_list: gs.fit(data_[:, picks]) shrinkages.append((ch_type, gs.best_estimator_.shrinkage, picks)) shrinkages = [c[0] for c in zip(shrinkages)] sc = _ShrunkCovariance(shrinkage=shrinkages, **mp) sc.fit(data_) estimator_cov_info.append((sc, sc.covariance_, _info)) del shrinkage, sc elif method_ == 'pca': assert orig_rank == 'full' pca, _info = _auto_low_rank_model( data_, method_, n_jobs=n_jobs, method_params=mp, cv=cv, stop_early=stop_early) pca.fit(data_) estimator_cov_info.append((pca, pca.get_covariance(), _info)) del pca elif method_ == 'factor_analysis': assert orig_rank == 'full' fa, _info = _auto_low_rank_model( data_, method_, n_jobs=n_jobs, method_params=mp, cv=cv, stop_early=stop_early) fa.fit(data_) estimator_cov_info.append((fa, fa.get_covariance(), _info)) del fa else: raise ValueError('Oh no! Your estimator does not have' ' a .fit method') logger.info('Done.') if len(method) > 1: logger.info('Using cross-validation to select the best estimator.') out = dict() for ei, (estimator, cov, runtime_info) in \ enumerate(estimator_cov_info): if len(method) > 1: loglik = _cross_val(data, estimator, cv, n_jobs) else: loglik = None # project back cov = np.dot(eigvec.T, np.dot(cov, eigvec)) # undo bias cov *= data.shape[0] / (data.shape[0] - 1) # undo scaling _undo_scaling_cov(cov, picks_list, scalings) method_ = method[ei] name = method_.__name__ if callable(method_) else method_ out[name] = dict(loglik=loglik, data=cov, estimator=estimator) out[name].update(runtime_info) return out def _gaussian_loglik_scorer(est, X, y=None): """Compute the Gaussian log likelihood of X under the model in est.""" # compute empirical covariance of the test set precision = est.get_precision() n_samples, n_features = X.shape log_like = -.5 * (X * (np.dot(X, precision))).sum(axis=1) log_like -= .5 * (n_features * log(2. * np.pi) - _logdet(precision)) out = np.mean(log_like) return out def _cross_val(data, est, cv, n_jobs): """Compute cross validation.""" from sklearn.model_selection import cross_val_score return np.mean(cross_val_score(est, data, cv=cv, n_jobs=n_jobs, scoring=_gaussian_loglik_scorer)) def _auto_low_rank_model(data, mode, n_jobs, method_params, cv, stop_early=True, verbose=None): """Compute latent variable models.""" method_params = deepcopy(method_params) iter_n_components = method_params.pop('iter_n_components') if iter_n_components is None: iter_n_components = np.arange(5, data.shape[1], 5) from sklearn.decomposition import PCA, FactorAnalysis if mode == 'factor_analysis': est = FactorAnalysis else: assert mode == 'pca' est = PCA est = est(**method_params) est.n_components = 1 scores = np.empty_like(iter_n_components, dtype=np.float64) scores.fill(np.nan) # make sure we don't empty the thing if it's a generator max_n = max(list(deepcopy(iter_n_components))) if max_n > data.shape[1]: warn('You are trying to estimate %i components on matrix ' 'with %i features.' % (max_n, data.shape[1])) for ii, n in enumerate(iter_n_components): est.n_components = n try: # this may fail depending on rank and split score = _cross_val(data=data, est=est, cv=cv, n_jobs=n_jobs) except ValueError: score = np.inf if np.isinf(score) or score > 0: logger.info('... infinite values encountered. stopping estimation') break logger.info('... rank: %i - loglik: %0.3f' % (n, score)) if score != -np.inf: scores[ii] = score if (ii >= 3 and np.all(np.diff(scores[ii - 3:ii]) < 0) and stop_early): # early stop search when loglik has been going down 3 times logger.info('early stopping parameter search.') break # happens if rank is too low right form the beginning if np.isnan(scores).all(): raise RuntimeError('Oh no! Could not estimate covariance because all ' 'scores were NaN. Please contact the MNE-Python ' 'developers.') i_score = np.nanargmax(scores) best = est.n_components = iter_n_components[i_score] logger.info('... best model at rank = %i' % best) runtime_info = {'ranks': np.array(iter_n_components), 'scores': scores, 'best': best, 'cv': cv} return est, runtime_info ############################################################################### # Sklearn Estimators class _RegCovariance(BaseEstimator): """Aux class.""" def __init__(self, info, grad=0.1, mag=0.1, eeg=0.1, seeg=0.1, ecog=0.1, hbo=0.1, hbr=0.1, fnirs_cw_amplitude=0.1, fnirs_fd_ac_amplitude=0.1, fnirs_fd_phase=0.1, fnirs_od=0.1, csd=0.1, dbs=0.1, store_precision=False, assume_centered=False): self.info = info # For sklearn compat, these cannot (easily?) be combined into # a single dictionary self.grad = grad self.mag = mag self.eeg = eeg self.seeg = seeg self.dbs = dbs self.ecog = ecog self.hbo = hbo self.hbr = hbr self.fnirs_cw_amplitude = fnirs_cw_amplitude self.fnirs_fd_ac_amplitude = fnirs_fd_ac_amplitude self.fnirs_fd_phase = fnirs_fd_phase self.fnirs_od = fnirs_od self.csd = csd self.store_precision = store_precision self.assume_centered = assume_centered def fit(self, X): """Fit covariance model with classical diagonal regularization.""" self.estimator_ = EmpiricalCovariance( store_precision=self.store_precision, assume_centered=self.assume_centered) self.covariance_ = self.estimator_.fit(X).covariance_ self.covariance_ = 0.5 * (self.covariance_ + self.covariance_.T) cov_ = Covariance( data=self.covariance_, names=self.info['ch_names'], bads=self.info['bads'], projs=self.info['projs'], nfree=len(self.covariance_)) cov_ = regularize( cov_, self.info, proj=False, exclude='bads', grad=self.grad, mag=self.mag, eeg=self.eeg, ecog=self.ecog, seeg=self.seeg, dbs=self.dbs, hbo=self.hbo, hbr=self.hbr, rank='full') self.estimator_.covariance_ = self.covariance_ = cov_.data return self def score(self, X_test, y=None): """Delegate call to modified EmpiricalCovariance instance.""" return self.estimator_.score(X_test, y=y) def get_precision(self): """Delegate call to modified EmpiricalCovariance instance.""" return self.estimator_.get_precision() class _ShrunkCovariance(BaseEstimator): """Aux class.""" def __init__(self, store_precision, assume_centered, shrinkage=0.1): self.store_precision = store_precision self.assume_centered = assume_centered self.shrinkage = shrinkage def fit(self, X): """Fit covariance model with oracle shrinkage regularization.""" from sklearn.covariance import shrunk_covariance self.estimator_ = EmpiricalCovariance( store_precision=self.store_precision, assume_centered=self.assume_centered) cov = self.estimator_.fit(X).covariance_ if not isinstance(self.shrinkage, (list, tuple)): shrinkage = [('all', self.shrinkage, np.arange(len(cov)))] else: shrinkage = self.shrinkage zero_cross_cov = np.zeros_like(cov, dtype=bool) for a, b in itt.combinations(shrinkage, 2): picks_i, picks_j = a[2], b[2] ch_ = a[0], b[0] if 'eeg' in ch_: zero_cross_cov[np.ix_(picks_i, picks_j)] = True zero_cross_cov[np.ix_(picks_j, picks_i)] = True self.zero_cross_cov_ = zero_cross_cov # Apply shrinkage to blocks for ch_type, c, picks in shrinkage: sub_cov = cov[np.ix_(picks, picks)] cov[np.ix_(picks, picks)] = shrunk_covariance(sub_cov, shrinkage=c) # Apply shrinkage to cross-cov for a, b in itt.combinations(shrinkage, 2): shrinkage_i, shrinkage_j = a[1], b[1] picks_i, picks_j = a[2], b[2] c_ij = np.sqrt((1. - shrinkage_i) * (1. - shrinkage_j)) cov[np.ix_(picks_i, picks_j)] *= c_ij cov[np.ix_(picks_j, picks_i)] *= c_ij # Set to zero the necessary cross-cov if np.any(zero_cross_cov): cov[zero_cross_cov] = 0.0 self.estimator_.covariance_ = self.covariance_ = cov return self def score(self, X_test, y=None): """Delegate to modified EmpiricalCovariance instance.""" # compute empirical covariance of the test set test_cov = empirical_covariance(X_test - self.estimator_.location_, assume_centered=True) if np.any(self.zero_cross_cov_): test_cov[self.zero_cross_cov_] = 0. res = log_likelihood(test_cov, self.estimator_.get_precision()) return res def get_precision(self): """Delegate to modified EmpiricalCovariance instance.""" return self.estimator_.get_precision() ############################################################################### # Writing @verbose def write_cov(fname, cov, *, overwrite=False, verbose=None): """Write a noise covariance matrix. Parameters ---------- fname : str The name of the file. It should end with -cov.fif or -cov.fif.gz. cov : Covariance The noise covariance matrix. %(overwrite)s .. versionadded:: 1.0 %(verbose)s See Also -------- read_cov """ cov.save(fname, overwrite=overwrite, verbose=verbose) ############################################################################### # Prepare for inverse modeling def _unpack_epochs(epochs): """Aux Function.""" if len(epochs.event_id) > 1: epochs = [epochs[k] for k in epochs.event_id] else: epochs = [epochs] return epochs def _get_ch_whitener(A, pca, ch_type, rank): """Get whitener params for a set of channels.""" # whitening operator eig, eigvec = eigh(A, overwrite_a=True) eigvec = eigvec.conj().T mask = np.ones(len(eig), bool) eig[:-rank] = 0.0 mask[:-rank] = False logger.info(' Setting small %s eigenvalues to zero (%s)' % (ch_type, 'using PCA' if pca else 'without PCA')) if pca: # No PCA case. # This line will reduce the actual number of variables in data # and leadfield to the true rank. eigvec = eigvec[:-rank].copy() return eig, eigvec, mask @verbose def prepare_noise_cov(noise_cov, info, ch_names=None, rank=None, scalings=None, on_rank_mismatch='ignore', verbose=None): """Prepare noise covariance matrix. Parameters ---------- noise_cov : instance of Covariance The noise covariance to process. %(info_not_none)s (Used to get channel types and bad channels). ch_names : list | None The channel names to be considered. Can be None to use ``info['ch_names']``. %(rank_none)s .. versionadded:: 0.18 Support for 'info' mode. scalings : dict | None Data will be rescaled before rank estimation to improve accuracy. If dict, it will override the following dict (default if None):: dict(mag=1e12, grad=1e11, eeg=1e5) %(on_rank_mismatch)s %(verbose)s Returns ------- cov : instance of Covariance A copy of the covariance with the good channels subselected and parameters updated. """ # reorder C and info to match ch_names order noise_cov_idx = list() missing = list() ch_names = info['ch_names'] if ch_names is None else ch_names for c in ch_names: # this could be try/except ValueError, but it is not the preferred way if c in noise_cov.ch_names: noise_cov_idx.append(noise_cov.ch_names.index(c)) else: missing.append(c) if len(missing): raise RuntimeError('Not all channels present in noise covariance:\n%s' % missing) C = noise_cov._get_square()[np.ix_(noise_cov_idx, noise_cov_idx)] info = pick_info(info, pick_channels(info['ch_names'], ch_names)) projs = info['projs'] + noise_cov['projs'] noise_cov = Covariance( data=C, names=ch_names, bads=list(noise_cov['bads']), projs=deepcopy(noise_cov['projs']), nfree=noise_cov['nfree'], method=noise_cov.get('method', None), loglik=noise_cov.get('loglik', None)) eig, eigvec, _ = _smart_eigh(noise_cov, info, rank, scalings, projs, ch_names, on_rank_mismatch=on_rank_mismatch) noise_cov.update(eig=eig, eigvec=eigvec) return noise_cov @verbose def _smart_eigh(C, info, rank, scalings=None, projs=None, ch_names=None, proj_subspace=False, do_compute_rank=True, on_rank_mismatch='ignore', verbose=None): """Compute eigh of C taking into account rank and ch_type scalings.""" scalings = _handle_default('scalings_cov_rank', scalings) projs = info['projs'] if projs is None else projs ch_names = info['ch_names'] if ch_names is None else ch_names if info['ch_names'] != ch_names: info = pick_info(info, [info['ch_names'].index(c) for c in ch_names]) assert info['ch_names'] == ch_names n_chan = len(ch_names) # Create the projection operator proj, ncomp, _ = make_projector(projs, ch_names) if isinstance(C, Covariance): C = C['data'] if ncomp > 0: logger.info(' Created an SSP operator (subspace dimension = %d)' % ncomp) C = np.dot(proj, np.dot(C, proj.T)) noise_cov = Covariance(C, ch_names, [], projs, 0) if do_compute_rank: # if necessary rank = compute_rank( noise_cov, rank, scalings, info, on_rank_mismatch=on_rank_mismatch) assert C.ndim == 2 and C.shape[0] == C.shape[1] # time saving short-circuit if proj_subspace and sum(rank.values()) == C.shape[0]: return np.ones(n_chan), np.eye(n_chan), np.ones(n_chan, bool) dtype = complex if C.dtype == np.complex_ else float eig = np.zeros(n_chan, dtype) eigvec = np.zeros((n_chan, n_chan), dtype) mask = np.zeros(n_chan, bool) for ch_type, picks in _picks_by_type(info, meg_combined=True, ref_meg=False, exclude=[]): if len(picks) == 0: continue this_C = C[np.ix_(picks, picks)] if ch_type not in rank and ch_type in ('mag', 'grad'): this_rank = rank['meg'] # if there is only one or the other else: this_rank = rank[ch_type] e, ev, m = _get_ch_whitener(this_C, False, ch_type.upper(), this_rank) if proj_subspace: # Choose the subspace the same way we do for projections e, ev = _eigvec_subspace(e, ev, m) eig[picks], eigvec[np.ix_(picks, picks)], mask[picks] = e, ev, m # XXX : also handle ref for sEEG and ECoG if ch_type == 'eeg' and _needs_eeg_average_ref_proj(info) and not \ _has_eeg_average_ref_proj(info, projs=projs): warn('No average EEG reference present in info["projs"], ' 'covariance may be adversely affected. Consider recomputing ' 'covariance using with an average eeg reference projector ' 'added.') return eig, eigvec, mask @verbose def regularize(cov, info, mag=0.1, grad=0.1, eeg=0.1, exclude='bads', proj=True, seeg=0.1, ecog=0.1, hbo=0.1, hbr=0.1, fnirs_cw_amplitude=0.1, fnirs_fd_ac_amplitude=0.1, fnirs_fd_phase=0.1, fnirs_od=0.1, csd=0.1, dbs=0.1, rank=None, scalings=None, verbose=None): """Regularize noise covariance matrix. This method works by adding a constant to the diagonal for each channel type separately. Special care is taken to keep the rank of the data constant. .. note:: This function is kept for reasons of backward-compatibility. Please consider explicitly using the ``method`` parameter in :func:`mne.compute_covariance` to directly combine estimation with regularization in a data-driven fashion. See the `faq `_ for more information. Parameters ---------- cov : Covariance The noise covariance matrix. %(info_not_none)s (Used to get channel types and bad channels). mag : float (default 0.1) Regularization factor for MEG magnetometers. grad : float (default 0.1) Regularization factor for MEG gradiometers. Must be the same as ``mag`` if data have been processed with SSS. eeg : float (default 0.1) Regularization factor for EEG. exclude : list | 'bads' (default 'bads') List of channels to mark as bad. If 'bads', bads channels are extracted from both info['bads'] and cov['bads']. proj : bool (default True) Apply projections to keep rank of data. seeg : float (default 0.1) Regularization factor for sEEG signals. ecog : float (default 0.1) Regularization factor for ECoG signals. hbo : float (default 0.1) Regularization factor for HBO signals. hbr : float (default 0.1) Regularization factor for HBR signals. fnirs_cw_amplitude : float (default 0.1) Regularization factor for fNIRS CW raw signals. fnirs_fd_ac_amplitude : float (default 0.1) Regularization factor for fNIRS FD AC raw signals. fnirs_fd_phase : float (default 0.1) Regularization factor for fNIRS raw phase signals. fnirs_od : float (default 0.1) Regularization factor for fNIRS optical density signals. csd : float (default 0.1) Regularization factor for EEG-CSD signals. dbs : float (default 0.1) Regularization factor for DBS signals. %(rank_none)s .. versionadded:: 0.17 .. versionadded:: 0.18 Support for 'info' mode. scalings : dict | None Data will be rescaled before rank estimation to improve accuracy. See :func:`mne.compute_covariance`. .. versionadded:: 0.17 %(verbose)s Returns ------- reg_cov : Covariance The regularized covariance matrix. See Also -------- mne.compute_covariance """ # noqa: E501 from scipy import linalg cov = cov.copy() info._check_consistency() scalings = _handle_default('scalings_cov_rank', scalings) regs = dict(eeg=eeg, seeg=seeg, dbs=dbs, ecog=ecog, hbo=hbo, hbr=hbr, fnirs_cw_amplitude=fnirs_cw_amplitude, fnirs_fd_ac_amplitude=fnirs_fd_ac_amplitude, fnirs_fd_phase=fnirs_fd_phase, fnirs_od=fnirs_od, csd=csd) if exclude is None: raise ValueError('exclude must be a list of strings or "bads"') if exclude == 'bads': exclude = info['bads'] + cov['bads'] picks_dict = {ch_type: [] for ch_type in _DATA_CH_TYPES_SPLIT} meg_combined = 'auto' if rank != 'full' else False picks_dict.update(dict(_picks_by_type( info, meg_combined=meg_combined, exclude=exclude, ref_meg=False))) if len(picks_dict.get('meg', [])) > 0 and rank != 'full': # combined if mag != grad: raise ValueError('On data where magnetometers and gradiometers ' 'are dependent (e.g., SSSed data), mag (%s) must ' 'equal grad (%s)' % (mag, grad)) logger.info('Regularizing MEG channels jointly') regs['meg'] = mag else: regs.update(mag=mag, grad=grad) if rank != 'full': rank = compute_rank(cov, rank, scalings, info) info_ch_names = info['ch_names'] ch_names_by_type = dict() for ch_type, picks_type in picks_dict.items(): ch_names_by_type[ch_type] = [info_ch_names[i] for i in picks_type] # This actually removes bad channels from the cov, which is not backward # compatible, so let's leave all channels in cov_good = pick_channels_cov(cov, include=info_ch_names, exclude=exclude) ch_names = cov_good.ch_names # Now get the indices for each channel type in the cov idx_cov = {ch_type: [] for ch_type in ch_names_by_type} for i, ch in enumerate(ch_names): for ch_type in ch_names_by_type: if ch in ch_names_by_type[ch_type]: idx_cov[ch_type].append(i) break else: raise Exception('channel %s is unknown type' % ch) C = cov_good['data'] assert len(C) == sum(map(len, idx_cov.values())) if proj: projs = info['projs'] + cov_good['projs'] projs = activate_proj(projs) for ch_type in idx_cov: desc = ch_type.upper() idx = idx_cov[ch_type] if len(idx) == 0: continue reg = regs[ch_type] if reg == 0.0: logger.info(" %s regularization : None" % desc) continue logger.info(" %s regularization : %s" % (desc, reg)) this_C = C[np.ix_(idx, idx)] U = np.eye(this_C.shape[0]) this_ch_names = [ch_names[k] for k in idx] if rank == 'full': if proj: P, ncomp, _ = make_projector(projs, this_ch_names) if ncomp > 0: # This adjustment ends up being redundant if rank is None: U = linalg.svd(P)[0][:, :-ncomp] logger.info(' Created an SSP operator for %s ' '(dimension = %d)' % (desc, ncomp)) else: this_picks = pick_channels(info['ch_names'], this_ch_names) this_info = pick_info(info, this_picks) # Here we could use proj_subspace=True, but this should not matter # since this is already in a loop over channel types _, eigvec, mask = _smart_eigh(this_C, this_info, rank) U = eigvec[mask].T this_C = np.dot(U.T, np.dot(this_C, U)) sigma = np.mean(np.diag(this_C)) this_C.flat[::len(this_C) + 1] += reg * sigma # modify diag inplace this_C = np.dot(U, np.dot(this_C, U.T)) C[np.ix_(idx, idx)] = this_C # Put data back in correct locations idx = pick_channels(cov.ch_names, info_ch_names, exclude=exclude) cov['data'][np.ix_(idx, idx)] = C return cov def _regularized_covariance(data, reg=None, method_params=None, info=None, rank=None): """Compute a regularized covariance from data using sklearn. This is a convenience wrapper for mne.decoding functions, which adopted a slightly different covariance API. Returns ------- cov : ndarray, shape (n_channels, n_channels) The covariance matrix. """ _validate_type(reg, (str, 'numeric', None)) if reg is None: reg = 'empirical' elif not isinstance(reg, str): reg = float(reg) if method_params is not None: raise ValueError('If reg is a float, method_params must be None ' '(got %s)' % (type(method_params),)) method_params = dict(shrinkage=dict( shrinkage=reg, assume_centered=True, store_precision=False)) reg = 'shrinkage' method, method_params = _check_method_params( reg, method_params, name='reg', allow_auto=False, rank=rank) # use mag instead of eeg here to avoid the cov EEG projection warning info = create_info(data.shape[-2], 1000., 'mag') if info is None else info picks_list = _picks_by_type(info) scalings = _handle_default('scalings_cov_rank', None) cov = _compute_covariance_auto( data.T, method=method, method_params=method_params, info=info, cv=None, n_jobs=None, stop_early=True, picks_list=picks_list, scalings=scalings, rank=rank)[reg]['data'] return cov @verbose def compute_whitener(noise_cov, info=None, picks=None, rank=None, scalings=None, return_rank=False, pca=False, return_colorer=False, on_rank_mismatch='warn', verbose=None): """Compute whitening matrix. Parameters ---------- noise_cov : Covariance The noise covariance. %(info)s Can be None if ``noise_cov`` has already been prepared with :func:`prepare_noise_cov`. %(picks_good_data_noref)s %(rank_none)s .. versionadded:: 0.18 Support for 'info' mode. scalings : dict | None The rescaling method to be applied. See documentation of ``prepare_noise_cov`` for details. return_rank : bool If True, return the rank used to compute the whitener. .. versionadded:: 0.15 pca : bool | str Space to project the data into. Options: :data:`python:True` Whitener will be shape (n_nonzero, n_channels). ``'white'`` Whitener will be shape (n_channels, n_channels), potentially rank deficient, and have the first ``n_channels - n_nonzero`` rows and columns set to zero. :data:`python:False` (default) Whitener will be shape (n_channels, n_channels), potentially rank deficient, and rotated back to the space of the original data. .. versionadded:: 0.18 return_colorer : bool If True, return the colorer as well. %(on_rank_mismatch)s %(verbose)s Returns ------- W : ndarray, shape (n_channels, n_channels) or (n_nonzero, n_channels) The whitening matrix. ch_names : list The channel names. rank : int Rank reduction of the whitener. Returned only if return_rank is True. colorer : ndarray, shape (n_channels, n_channels) or (n_channels, n_nonzero) The coloring matrix. """ # noqa: E501 _validate_type(pca, (str, bool), 'space') _valid_pcas = (True, 'white', False) if pca not in _valid_pcas: raise ValueError('space must be one of %s, got %s' % (_valid_pcas, pca)) if info is None: if 'eig' not in noise_cov: raise ValueError('info can only be None if the noise cov has ' 'already been prepared with prepare_noise_cov') ch_names = deepcopy(noise_cov['names']) else: picks = _picks_to_idx(info, picks, with_ref_meg=False) ch_names = [info['ch_names'][k] for k in picks] del picks noise_cov = prepare_noise_cov( noise_cov, info, ch_names, rank, scalings, on_rank_mismatch=on_rank_mismatch) n_chan = len(ch_names) assert n_chan == len(noise_cov['eig']) # Omit the zeroes due to projection eig = noise_cov['eig'].copy() nzero = (eig > 0) eig[~nzero] = 0. # get rid of numerical noise (negative) ones if noise_cov['eigvec'].dtype.kind == 'c': dtype = np.complex128 else: dtype = np.float64 W = np.zeros((n_chan, 1), dtype) W[nzero, 0] = 1.0 / np.sqrt(eig[nzero]) # Rows of eigvec are the eigenvectors W = W * noise_cov['eigvec'] # C ** -0.5 C = np.sqrt(eig) * noise_cov['eigvec'].conj().T # C ** 0.5 n_nzero = nzero.sum() logger.info(' Created the whitener using a noise covariance matrix ' 'with rank %d (%d small eigenvalues omitted)' % (n_nzero, noise_cov['dim'] - n_nzero)) # Do the requested projection if pca is True: W = W[nzero] C = C[:, nzero] elif pca is False: W = np.dot(noise_cov['eigvec'].conj().T, W) C = np.dot(C, noise_cov['eigvec']) # Triage return out = W, ch_names if return_rank: out += (n_nzero,) if return_colorer: out += (C,) return out @verbose def whiten_evoked(evoked, noise_cov, picks=None, diag=None, rank=None, scalings=None, verbose=None): """Whiten evoked data using given noise covariance. Parameters ---------- evoked : instance of Evoked The evoked data. noise_cov : instance of Covariance The noise covariance. %(picks_good_data)s diag : bool (default False) If True, whiten using only the diagonal of the covariance. %(rank_none)s .. versionadded:: 0.18 Support for 'info' mode. scalings : dict | None (default None) To achieve reliable rank estimation on multiple sensors, sensors have to be rescaled. This parameter controls the rescaling. If dict, it will override the following default dict (default if None): dict(mag=1e12, grad=1e11, eeg=1e5) %(verbose)s Returns ------- evoked_white : instance of Evoked The whitened evoked data. """ evoked = evoked.copy() picks = _picks_to_idx(evoked.info, picks) if diag: noise_cov = noise_cov.as_diag() W, _ = compute_whitener(noise_cov, evoked.info, picks=picks, rank=rank, scalings=scalings) evoked.data[picks] = np.sqrt(evoked.nave) * np.dot(W, evoked.data[picks]) return evoked @verbose def _read_cov(fid, node, cov_kind, limited=False, verbose=None): """Read a noise covariance matrix.""" # Find all covariance matrices from scipy import sparse covs = dir_tree_find(node, FIFF.FIFFB_MNE_COV) if len(covs) == 0: raise ValueError('No covariance matrices found') # Is any of the covariance matrices a noise covariance for p in range(len(covs)): tag = find_tag(fid, covs[p], FIFF.FIFF_MNE_COV_KIND) if tag is not None and int(tag.data) == cov_kind: this = covs[p] # Find all the necessary data tag = find_tag(fid, this, FIFF.FIFF_MNE_COV_DIM) if tag is None: raise ValueError('Covariance matrix dimension not found') dim = int(tag.data) tag = find_tag(fid, this, FIFF.FIFF_MNE_COV_NFREE) if tag is None: nfree = -1 else: nfree = int(tag.data) tag = find_tag(fid, this, FIFF.FIFF_MNE_COV_METHOD) if tag is None: method = None else: method = tag.data tag = find_tag(fid, this, FIFF.FIFF_MNE_COV_SCORE) if tag is None: score = None else: score = tag.data[0] tag = find_tag(fid, this, FIFF.FIFF_MNE_ROW_NAMES) if tag is None: names = [] else: names = tag.data.split(':') if len(names) != dim: raise ValueError('Number of names does not match ' 'covariance matrix dimension') tag = find_tag(fid, this, FIFF.FIFF_MNE_COV) if tag is None: tag = find_tag(fid, this, FIFF.FIFF_MNE_COV_DIAG) if tag is None: raise ValueError('No covariance matrix data found') else: # Diagonal is stored data = tag.data diag = True logger.info(' %d x %d diagonal covariance (kind = ' '%d) found.' % (dim, dim, cov_kind)) else: if not sparse.issparse(tag.data): # Lower diagonal is stored vals = tag.data data = np.zeros((dim, dim)) data[np.tril(np.ones((dim, dim))) > 0] = vals data = data + data.T data.flat[::dim + 1] /= 2.0 diag = False logger.info(' %d x %d full covariance (kind = %d) ' 'found.' % (dim, dim, cov_kind)) else: diag = False data = tag.data logger.info(' %d x %d sparse covariance (kind = %d)' ' found.' % (dim, dim, cov_kind)) # Read the possibly precomputed decomposition tag1 = find_tag(fid, this, FIFF.FIFF_MNE_COV_EIGENVALUES) tag2 = find_tag(fid, this, FIFF.FIFF_MNE_COV_EIGENVECTORS) if tag1 is not None and tag2 is not None: eig = tag1.data eigvec = tag2.data else: eig = None eigvec = None # Read the projection operator projs = _read_proj(fid, this) # Read the bad channel list bads = _read_bad_channels(fid, this, None) # Put it together assert dim == len(data) assert data.ndim == (1 if diag else 2) cov = dict(kind=cov_kind, diag=diag, dim=dim, names=names, data=data, projs=projs, bads=bads, nfree=nfree, eig=eig, eigvec=eigvec) if score is not None: cov['loglik'] = score if method is not None: cov['method'] = method if limited: del cov['kind'], cov['dim'], cov['diag'] return cov logger.info(' Did not find the desired covariance matrix (kind = %d)' % cov_kind) return None def _write_cov(fid, cov): """Write a noise covariance matrix.""" start_block(fid, FIFF.FIFFB_MNE_COV) # Dimensions etc. write_int(fid, FIFF.FIFF_MNE_COV_KIND, cov['kind']) write_int(fid, FIFF.FIFF_MNE_COV_DIM, cov['dim']) if cov['nfree'] > 0: write_int(fid, FIFF.FIFF_MNE_COV_NFREE, cov['nfree']) # Channel names if cov['names'] is not None and len(cov['names']) > 0: write_name_list(fid, FIFF.FIFF_MNE_ROW_NAMES, cov['names']) # Data if cov['diag']: write_double(fid, FIFF.FIFF_MNE_COV_DIAG, cov['data']) else: # Store only lower part of covariance matrix dim = cov['dim'] mask = np.tril(np.ones((dim, dim), dtype=bool)) > 0 vals = cov['data'][mask].ravel() write_double(fid, FIFF.FIFF_MNE_COV, vals) # Eigenvalues and vectors if present if cov['eig'] is not None and cov['eigvec'] is not None: write_float_matrix(fid, FIFF.FIFF_MNE_COV_EIGENVECTORS, cov['eigvec']) write_double(fid, FIFF.FIFF_MNE_COV_EIGENVALUES, cov['eig']) # Projection operator if cov['projs'] is not None and len(cov['projs']) > 0: _write_proj(fid, cov['projs']) # Bad channels if cov['bads'] is not None and len(cov['bads']) > 0: start_block(fid, FIFF.FIFFB_MNE_BAD_CHANNELS) write_name_list(fid, FIFF.FIFF_MNE_CH_NAME_LIST, cov['bads']) end_block(fid, FIFF.FIFFB_MNE_BAD_CHANNELS) # estimator method if 'method' in cov: write_string(fid, FIFF.FIFF_MNE_COV_METHOD, cov['method']) # negative log-likelihood score if 'loglik' in cov: write_double( fid, FIFF.FIFF_MNE_COV_SCORE, np.array(cov['loglik'])) # Done! end_block(fid, FIFF.FIFFB_MNE_COV) @verbose def _ensure_cov(cov, name='cov', *, verbose=None): _validate_type(cov, ('path-like', Covariance), name) logger.info('Noise covariance : %s' % (cov,)) if not isinstance(cov, Covariance): cov = read_cov(cov, verbose=_verbose_safe_false()) return cov