# -*- coding: utf-8 -*- # Authors: Mark Wronkiewicz # Eric Larson # Jussi Nurminen # License: BSD-3-Clause from collections import Counter, OrderedDict from functools import partial from math import factorial from os import path as op import numpy as np from .. import __version__ from ..annotations import _annotations_starts_stops from ..bem import _check_origin from ..transforms import (_str_to_frame, _get_trans, Transform, apply_trans, _find_vector_rotation, _cart_to_sph, _get_n_moments, _sph_to_cart_partials, _deg_ord_idx, _average_quats, _sh_complex_to_real, _sh_real_to_complex, _sh_negate, quat_to_rot, rot_to_quat) from ..forward import _concatenate_coils, _prep_meg_channels, _create_meg_coils from ..surface import _normalize_vectors from ..io.constants import FIFF, FWD from ..io.meas_info import _simplify_info, Info from ..io.proc_history import _read_ctc from ..io.write import _generate_meas_id, DATE_NONE from ..io import (_loc_to_coil_trans, _coil_trans_to_loc, BaseRaw, RawArray, Projection) from ..io.pick import pick_types, pick_info from ..utils import (verbose, logger, _clean_names, warn, _time_mask, _pl, _check_option, _ensure_int, _validate_type, use_log_level) from ..fixes import _safe_svd, bincount from ..channels.channels import _get_T1T2_mag_inds, fix_mag_coil_types # Note: MF uses single precision and some algorithms might use # truncated versions of constants (e.g., μ0), which could lead to small # differences between algorithms @verbose def maxwell_filter_prepare_emptyroom( raw_er, *, raw, bads='from_raw', annotations='from_raw', meas_date='keep', emit_warning=False, verbose=None ): """Prepare an empty-room recording for Maxwell filtering. Empty-room data by default lacks certain properties that are required to ensure running :func:`~mne.preprocessing.maxwell_filter` will process the empty-room recording the same way as the experimental data. This function preconditions an empty-room raw data instance accordingly so it can be used for Maxwell filtering. Please see the ``Notes`` section for details. Parameters ---------- raw_er : instance of Raw The empty-room recording. It will not be modified. raw : instance of Raw The experimental recording, typically this will be the reference run used for Maxwell filtering. bads : 'from_raw' | 'union' | 'keep' How to populate the list of bad channel names to be injected into the empty-room recording. If ``'from_raw'`` (default) the list of bad channels will be overwritten with that of ``raw``. If ``'union'``, will use the union of bad channels in ``raw`` and ``raw_er``. Note that this may lead to additional bad channels in the empty-room in comparison to the experimental recording. If ``'keep'``, don't alter the existing list of bad channels. .. note:: Non-MEG channels are silently dropped from the list of bads. annotations : 'from_raw' | 'union' | 'keep' Whether to copy the annotations over from ``raw`` (default), use the union of the annotations, or to keep them unchanged. meas_date : 'keep' | 'from_raw' Whether to transfer the measurement date from ``raw`` or to keep it as is (default). If you intend to manually transfer annotations from ``raw`` **after** running this function, you should set this to ``'from_raw'``. %(emit_warning)s Unlike :meth:`raw.set_annotations `, the default here is ``False``, as empty-room recordings are often shorter than raw. %(verbose)s Returns ------- raw_er_prepared : instance of Raw A copy of the passed empty-room recording, ready for Maxwell filtering. Notes ----- This function will: * Compile the list of bad channels according to the ``bads`` parameter. * Inject the device-to-head transformation matrix from the experimental recording into the empty-room recording. * Set the following properties of the empty-room recording to match the experimental recording: * Montage * ``raw.first_time`` and ``raw.first_samp`` * Adjust annotations according to the ``annotations`` parameter. * Adjust the measurement date according to the ``meas_date`` parameter. .. versionadded:: 1.1 """ # noqa: E501 _validate_type(item=raw_er, types=BaseRaw, item_name='raw_er') _validate_type(item=raw, types=BaseRaw, item_name='raw') _validate_type(item=bads, types=str, item_name='bads') _check_option( parameter='bads', value=bads, allowed_values=['from_raw', 'union', 'keep'] ) _validate_type(item=annotations, types=str, item_name='annotations') _check_option( parameter='annotations', value=annotations, allowed_values=['from_raw', 'union', 'keep'] ) _validate_type(item=meas_date, types=str, item_name='meas_date') _check_option( parameter='meas_date', value=annotations, allowed_values=['from_raw', 'keep'] ) raw_er_prepared = raw_er.copy() del raw_er # just to be sure # handle bads; only keep MEG channels if bads == 'from_raw': bads = raw.info['bads'] elif bads == 'union': bads = sorted( set(raw.info['bads'] + raw_er_prepared.info['bads']) ) elif bads == 'keep': bads = raw_er_prepared.info['bads'] bads = [ch_name for ch_name in bads if ch_name.startswith('MEG')] raw_er_prepared.info['bads'] = bads # handle dev_head_t raw_er_prepared.info['dev_head_t'] = raw.info['dev_head_t'] # handle montage montage = raw.get_montage() raw_er_prepared.set_montage(montage) # handle first_samp raw_er_prepared.annotations.onset += ( raw.first_time - raw_er_prepared.first_time ) raw_er_prepared._cropped_samp = raw._cropped_samp # handle annotations if annotations != 'keep': er_annot = raw_er_prepared.annotations if annotations == 'from_raw': er_annot.delete(np.arange(len(er_annot))) er_annot.append( raw.annotations.onset, raw.annotations.duration, raw.annotations.description, raw.annotations.ch_names ) if raw_er_prepared.info['meas_date'] is None: er_annot.onset -= raw_er_prepared.first_time raw_er_prepared.set_annotations(er_annot, emit_warning) # handle measurement date if meas_date == 'from_raw': raw_er_prepared.set_meas_date(raw.info['meas_date']) return raw_er_prepared # Changes to arguments here should also be made in find_bad_channels_maxwell @verbose def maxwell_filter(raw, origin='auto', int_order=8, ext_order=3, calibration=None, cross_talk=None, st_duration=None, st_correlation=0.98, coord_frame='head', destination=None, regularize='in', ignore_ref=False, bad_condition='error', head_pos=None, st_fixed=True, st_only=False, mag_scale=100., skip_by_annotation=('edge', 'bad_acq_skip'), extended_proj=(), verbose=None): """Maxwell filter data using multipole moments. Parameters ---------- raw : instance of mne.io.Raw Data to be filtered. .. warning:: It is critical to mark bad channels in ``raw.info['bads']`` prior to processing in order to prevent artifact spreading. Manual inspection and use of :func:`~find_bad_channels_maxwell` is recommended. %(origin_maxwell)s %(int_order_maxwell)s %(ext_order_maxwell)s %(calibration_maxwell_cal)s %(cross_talk_maxwell)s st_duration : float | None If not None, apply spatiotemporal SSS with specified buffer duration (in seconds). MaxFilter™'s default is 10.0 seconds in v2.2. Spatiotemporal SSS acts as implicitly as a high-pass filter where the cut-off frequency is 1/st_duration Hz. For this (and other) reasons, longer buffers are generally better as long as your system can handle the higher memory usage. To ensure that each window is processed identically, choose a buffer length that divides evenly into your data. Any data at the trailing edge that doesn't fit evenly into a whole buffer window will be lumped into the previous buffer. st_correlation : float Correlation limit between inner and outer subspaces used to reject ovwrlapping intersecting inner/outer signals during spatiotemporal SSS. %(coord_frame_maxwell)s %(destination_maxwell_dest)s %(regularize_maxwell_reg)s %(ignore_ref_maxwell)s %(bad_condition_maxwell_cond)s %(head_pos_maxwell)s .. versionadded:: 0.12 %(st_fixed_maxwell_only)s %(mag_scale_maxwell)s .. versionadded:: 0.13 %(skip_by_annotation_maxwell)s .. versionadded:: 0.17 %(extended_proj_maxwell)s %(verbose)s Returns ------- raw_sss : instance of mne.io.Raw The raw data with Maxwell filtering applied. See Also -------- mne.preprocessing.annotate_amplitude mne.preprocessing.find_bad_channels_maxwell mne.chpi.filter_chpi mne.chpi.read_head_pos mne.epochs.average_movements Notes ----- .. versionadded:: 0.11 Some of this code was adapted and relicensed (with BSD form) with permission from Jussi Nurminen. These algorithms are based on work from :footcite:`TauluKajola2005` and :footcite:`TauluSimola2006`. It will likely use multiple CPU cores, see the :ref:`FAQ ` for more information. .. warning:: Maxwell filtering in MNE is not designed or certified for clinical use. Compared to the MEGIN MaxFilter™ software, the MNE Maxwell filtering routines currently provide the following features: .. table:: :widths: auto +-----------------------------------------------------------------------------+-----+-----------+ | Feature | MNE | MaxFilter | +=============================================================================+=====+===========+ | Maxwell filtering software shielding | ✓ | ✓ | +-----------------------------------------------------------------------------+-----+-----------+ | Bad channel reconstruction | ✓ | ✓ | +-----------------------------------------------------------------------------+-----+-----------+ | Cross-talk cancellation | ✓ | ✓ | +-----------------------------------------------------------------------------+-----+-----------+ | Fine calibration correction (1D) | ✓ | ✓ | +-----------------------------------------------------------------------------+-----+-----------+ | Fine calibration correction (3D) | ✓ | | +-----------------------------------------------------------------------------+-----+-----------+ | Spatio-temporal SSS (tSSS) | ✓ | ✓ | +-----------------------------------------------------------------------------+-----+-----------+ | Coordinate frame translation | ✓ | ✓ | +-----------------------------------------------------------------------------+-----+-----------+ | Regularization using information theory | ✓ | ✓ | +-----------------------------------------------------------------------------+-----+-----------+ | Movement compensation (raw) | ✓ | ✓ | +-----------------------------------------------------------------------------+-----+-----------+ | Movement compensation (:func:`epochs `) | ✓ | | +-----------------------------------------------------------------------------+-----+-----------+ | :func:`cHPI subtraction ` | ✓ | ✓ | +-----------------------------------------------------------------------------+-----+-----------+ | Double floating point precision | ✓ | | +-----------------------------------------------------------------------------+-----+-----------+ | Seamless processing of split (``-1.fif``) and concatenated files | ✓ | | +-----------------------------------------------------------------------------+-----+-----------+ | Automatic bad channel detection (:func:`~find_bad_channels_maxwell`) | ✓ | ✓ | +-----------------------------------------------------------------------------+-----+-----------+ | Head position estimation (:func:`~mne.chpi.compute_head_pos`) | ✓ | ✓ | +-----------------------------------------------------------------------------+-----+-----------+ | Certified for clinical use | | ✓ | +-----------------------------------------------------------------------------+-----+-----------+ | Extended external basis (eSSS) | ✓ | | +-----------------------------------------------------------------------------+-----+-----------+ Epoch-based movement compensation is described in :footcite:`TauluKajola2005`. Use of Maxwell filtering routines with non-Neuromag systems is currently **experimental**. Worse results for non-Neuromag systems are expected due to (at least): * Missing fine-calibration and cross-talk cancellation data for other systems. * Processing with reference sensors has not been vetted. * Regularization of components may not work well for all systems. * Coil integration has not been optimized using Abramowitz/Stegun definitions. .. note:: Various Maxwell filtering algorithm components are covered by patents owned by MEGIN. These patents include, but may not be limited to: - US2006031038 (Signal Space Separation) - US6876196 (Head position determination) - WO2005067789 (DC fields) - WO2005078467 (MaxShield) - WO2006114473 (Temporal Signal Space Separation) These patents likely preclude the use of Maxwell filtering code in commercial applications. Consult a lawyer if necessary. Currently, in order to perform Maxwell filtering, the raw data must not have any projectors applied. During Maxwell filtering, the spatial structure of the data is modified, so projectors are discarded (unless in ``st_only=True`` mode). References ---------- .. footbibliography:: """ # noqa: E501 logger.info('Maxwell filtering raw data') params = _prep_maxwell_filter( raw=raw, origin=origin, int_order=int_order, ext_order=ext_order, calibration=calibration, cross_talk=cross_talk, st_duration=st_duration, st_correlation=st_correlation, coord_frame=coord_frame, destination=destination, regularize=regularize, ignore_ref=ignore_ref, bad_condition=bad_condition, head_pos=head_pos, st_fixed=st_fixed, st_only=st_only, mag_scale=mag_scale, skip_by_annotation=skip_by_annotation, extended_proj=extended_proj) raw_sss = _run_maxwell_filter(raw, **params) # Update info _update_sss_info(raw_sss, **params['update_kwargs']) logger.info('[done]') return raw_sss @verbose def _prep_maxwell_filter( raw, origin='auto', int_order=8, ext_order=3, calibration=None, cross_talk=None, st_duration=None, st_correlation=0.98, coord_frame='head', destination=None, regularize='in', ignore_ref=False, bad_condition='error', head_pos=None, st_fixed=True, st_only=False, mag_scale=100., skip_by_annotation=('edge', 'bad_acq_skip'), extended_proj=(), reconstruct='in', verbose=None): # There are an absurd number of different possible notations for spherical # coordinates, which confounds the notation for spherical harmonics. Here, # we purposefully stay away from shorthand notation in both and use # explicit terms (like 'azimuth' and 'polar') to avoid confusion. # See mathworld.wolfram.com/SphericalHarmonic.html for more discussion. # Our code follows the same standard that ``scipy`` uses for ``sph_harm``. # triage inputs ASAP to avoid late-thrown errors _validate_type(raw, BaseRaw, 'raw') _check_usable(raw) _check_regularize(regularize) st_correlation = float(st_correlation) if st_correlation <= 0. or st_correlation > 1.: raise ValueError('Need 0 < st_correlation <= 1., got %s' % st_correlation) _check_option('coord_frame', coord_frame, ['head', 'meg']) head_frame = True if coord_frame == 'head' else False recon_trans = _check_destination(destination, raw.info, head_frame) if st_duration is not None: st_duration = float(st_duration) st_correlation = float(st_correlation) st_duration = int(round(st_duration * raw.info['sfreq'])) if not 0. < st_correlation <= 1: raise ValueError('st_correlation must be between 0. and 1.') _check_option('bad_condition', bad_condition, ['error', 'warning', 'ignore', 'info']) if raw.info['dev_head_t'] is None and coord_frame == 'head': raise RuntimeError('coord_frame cannot be "head" because ' 'info["dev_head_t"] is None; if this is an ' 'empty room recording, consider using ' 'coord_frame="meg"') if st_only and st_duration is None: raise ValueError('st_duration must not be None if st_only is True') head_pos = _check_pos(head_pos, head_frame, raw, st_fixed, raw.info['sfreq']) _check_info(raw.info, sss=not st_only, tsss=st_duration is not None, calibration=not st_only and calibration is not None, ctc=not st_only and cross_talk is not None) # Now we can actually get moving info = raw.info.copy() meg_picks, mag_picks, grad_picks, good_mask, mag_or_fine = \ _get_mf_picks_fix_mags(info, int_order, ext_order, ignore_ref) # Magnetometers are scaled to improve numerical stability coil_scale, mag_scale = _get_coil_scale( meg_picks, mag_picks, grad_picks, mag_scale, info) # # Extended projection vectors # _validate_type(extended_proj, (list, tuple), 'extended_proj') good_names = [info['ch_names'][c] for c in meg_picks[good_mask]] if len(extended_proj) > 0: extended_proj_ = list() for pi, proj in enumerate(extended_proj): item = 'extended_proj[%d]' % (pi,) _validate_type(proj, Projection, item) got_names = proj['data']['col_names'] missing = sorted(set(good_names) - set(got_names)) if missing: raise ValueError('%s channel names were missing some ' 'good MEG channel names:\n%s' % (item, ', '.join(missing))) idx = [got_names.index(name) for name in good_names] extended_proj_.append(proj['data']['data'][:, idx]) extended_proj = np.concatenate(extended_proj_) logger.info(' Extending external SSS basis using %d projection ' 'vectors' % (len(extended_proj),)) # # Fine calibration processing (load fine cal and overwrite sensor geometry) # sss_cal = dict() if calibration is not None: calibration, sss_cal = _update_sensor_geometry( info, calibration, ignore_ref) mag_or_fine.fill(True) # all channels now have some mag-type data # Determine/check the origin of the expansion origin = _check_origin(origin, info, coord_frame, disp=True) # Convert to the head frame if coord_frame == 'meg' and info['dev_head_t'] is not None: origin_head = apply_trans(info['dev_head_t'], origin) else: origin_head = origin update_kwargs = dict( origin=origin, coord_frame=coord_frame, sss_cal=sss_cal, int_order=int_order, ext_order=ext_order, extended_proj=extended_proj) del origin, coord_frame, sss_cal origin_head.setflags(write=False) # # Cross-talk processing # meg_ch_names = [info['ch_names'][p] for p in meg_picks] ctc, sss_ctc = _read_cross_talk(cross_talk, meg_ch_names) update_kwargs['sss_ctc'] = sss_ctc del sss_ctc # # Translate to destination frame (always use non-fine-cal bases) # exp = dict(origin=origin_head, int_order=int_order, ext_order=0) all_coils = _prep_mf_coils(info, ignore_ref) S_recon = _trans_sss_basis(exp, all_coils, recon_trans, coil_scale) exp['ext_order'] = ext_order exp['extended_proj'] = extended_proj del extended_proj # Reconstruct data from internal space only (Eq. 38), and rescale S_recon S_recon /= coil_scale if recon_trans is not None: # warn if we have translated too far diff = 1000 * (info['dev_head_t']['trans'][:3, 3] - recon_trans['trans'][:3, 3]) dist = np.sqrt(np.sum(_sq(diff))) if dist > 25.: warn('Head position change is over 25 mm (%s) = %0.1f mm' % (', '.join('%0.1f' % x for x in diff), dist)) # Reconstruct raw file object with spatiotemporal processed data max_st = dict() if st_duration is not None: if st_only: job = FIFF.FIFFV_SSS_JOB_TPROJ else: job = FIFF.FIFFV_SSS_JOB_ST max_st.update(job=job, subspcorr=st_correlation, buflen=st_duration / info['sfreq']) logger.info(' Processing data using tSSS with st_duration=%s' % max_st['buflen']) st_when = 'before' if st_fixed else 'after' # relative to movecomp else: # st_duration from here on will act like the chunk size st_duration = min(max(int(round(10. * info['sfreq'])), 1), len(raw.times)) st_correlation = None st_when = 'never' update_kwargs['max_st'] = max_st del st_fixed, max_st # Figure out which transforms we need for each tSSS block # (and transform pos[1] to times) head_pos[1] = raw.time_as_index(head_pos[1], use_rounding=True) # Compute the first bit of pos_data for cHPI reporting if info['dev_head_t'] is not None and head_pos[0] is not None: this_pos_quat = np.concatenate([ rot_to_quat(info['dev_head_t']['trans'][:3, :3]), info['dev_head_t']['trans'][:3, 3], np.zeros(3)]) else: this_pos_quat = None _get_this_decomp_trans = partial( _get_decomp, all_coils=all_coils, cal=calibration, regularize=regularize, exp=exp, ignore_ref=ignore_ref, coil_scale=coil_scale, grad_picks=grad_picks, mag_picks=mag_picks, good_mask=good_mask, mag_or_fine=mag_or_fine, bad_condition=bad_condition, mag_scale=mag_scale) update_kwargs.update( nchan=good_mask.sum(), st_only=st_only, recon_trans=recon_trans) params = dict( skip_by_annotation=skip_by_annotation, st_duration=st_duration, st_correlation=st_correlation, st_only=st_only, st_when=st_when, ctc=ctc, coil_scale=coil_scale, this_pos_quat=this_pos_quat, meg_picks=meg_picks, good_mask=good_mask, grad_picks=grad_picks, head_pos=head_pos, info=info, _get_this_decomp_trans=_get_this_decomp_trans, S_recon=S_recon, update_kwargs=update_kwargs) return params def _run_maxwell_filter( raw, skip_by_annotation, st_duration, st_correlation, st_only, st_when, ctc, coil_scale, this_pos_quat, meg_picks, good_mask, grad_picks, head_pos, info, _get_this_decomp_trans, S_recon, update_kwargs, reconstruct='in', copy=True): # Eventually find_bad_channels_maxwell could be sped up by moving this # outside the loop (e.g., in the prep function) but regularization depends # on which channels are being used, so easier just to include it here. # The time it takes to recompute S and pS themselves is roughly on par # with the np.dot with the data, so not a huge gain to be made there. S_decomp, S_decomp_full, pS_decomp, reg_moments, n_use_in = \ _get_this_decomp_trans(info['dev_head_t'], t=0.) update_kwargs.update(reg_moments=reg_moments.copy()) if ctc is not None: ctc = ctc[good_mask][:, good_mask] add_channels = (head_pos[0] is not None) and (not st_only) and copy raw_sss, pos_picks = _copy_preload_add_channels( raw, add_channels, copy, info) sfreq = info['sfreq'] del raw if not st_only: # remove MEG projectors, they won't apply now _remove_meg_projs(raw_sss) # Figure out which segments of data we can use onsets, ends = _annotations_starts_stops( raw_sss, skip_by_annotation, invert=True) max_samps = (ends - onsets).max() if not 0. < st_duration <= max_samps + 1.: raise ValueError('st_duration (%0.1fs) must be between 0 and the ' 'longest contiguous duration of the data ' '(%0.1fs).' % (st_duration / sfreq, max_samps / sfreq)) # Generate time points to break up data into equal-length windows starts, stops = list(), list() for onset, end in zip(onsets, ends): read_lims = np.arange(onset, end + 1, st_duration) if len(read_lims) == 1: read_lims = np.concatenate([read_lims, [end]]) if read_lims[-1] != end: read_lims[-1] = end # fold it into the previous buffer n_last_buf = read_lims[-1] - read_lims[-2] if st_correlation is not None and len(read_lims) > 2: if n_last_buf >= st_duration: logger.info( ' Spatiotemporal window did not fit evenly into' 'contiguous data segment. %0.2f seconds were lumped ' 'into the previous window.' % ((n_last_buf - st_duration) / sfreq,)) else: logger.info( ' Contiguous data segment of duration %0.2f ' 'seconds is too short to be processed with tSSS ' 'using duration %0.2f' % (n_last_buf / sfreq, st_duration / sfreq)) assert len(read_lims) >= 2 assert read_lims[0] == onset and read_lims[-1] == end starts.extend(read_lims[:-1]) stops.extend(read_lims[1:]) del read_lims st_duration = min(max_samps, st_duration) # Loop through buffer windows of data n_sig = int(np.floor(np.log10(max(len(starts), 0)))) + 1 logger.info( ' Processing %s data chunk%s' % (len(starts), _pl(starts))) for ii, (start, stop) in enumerate(zip(starts, stops)): if start == stop: continue # Skip zero-length annotations tsss_valid = (stop - start) >= st_duration rel_times = raw_sss.times[start:stop] t_str = '%8.3f - %8.3f sec' % tuple(rel_times[[0, -1]]) t_str += ('(#%d/%d)' % (ii + 1, len(starts))).rjust(2 * n_sig + 5) # Get original data orig_data = raw_sss._data[meg_picks[good_mask], start:stop] # This could just be np.empty if not st_only, but shouldn't be slow # this way so might as well just always take the original data out_meg_data = raw_sss._data[meg_picks, start:stop] # Apply cross-talk correction if ctc is not None: orig_data = ctc.dot(orig_data) out_pos_data = np.empty((len(pos_picks), stop - start)) # Figure out which positions to use t_s_s_q_a = _trans_starts_stops_quats(head_pos, start, stop, this_pos_quat) n_positions = len(t_s_s_q_a[0]) # Set up post-tSSS or do pre-tSSS if st_correlation is not None: # If doing tSSS before movecomp... resid = orig_data.copy() # to be safe let's operate on a copy if st_when == 'after': orig_in_data = np.empty((len(meg_picks), stop - start)) else: # 'before' avg_trans = t_s_s_q_a[-1] if avg_trans is not None: # if doing movecomp S_decomp_st, _, pS_decomp_st, _, n_use_in_st = \ _get_this_decomp_trans(avg_trans, t=rel_times[0]) else: S_decomp_st, pS_decomp_st = S_decomp, pS_decomp n_use_in_st = n_use_in orig_in_data = np.dot(np.dot(S_decomp_st[:, :n_use_in_st], pS_decomp_st[:n_use_in_st]), resid) resid -= np.dot(np.dot(S_decomp_st[:, n_use_in_st:], pS_decomp_st[n_use_in_st:]), resid) resid -= orig_in_data # Here we operate on our actual data proc = out_meg_data if st_only else orig_data _do_tSSS(proc, orig_in_data, resid, st_correlation, n_positions, t_str, tsss_valid) if not st_only or st_when == 'after': # Do movement compensation on the data for trans, rel_start, rel_stop, this_pos_quat in \ zip(*t_s_s_q_a[:4]): # Recalculate bases if necessary (trans will be None iff the # first position in this interval is the same as last of the # previous interval) if trans is not None: S_decomp, S_decomp_full, pS_decomp, reg_moments, \ n_use_in = _get_this_decomp_trans( trans, t=rel_times[rel_start]) # Determine multipole moments for this interval mm_in = np.dot(pS_decomp[:n_use_in], orig_data[:, rel_start:rel_stop]) # Our output data if not st_only: if reconstruct == 'in': proj = S_recon.take(reg_moments[:n_use_in], axis=1) mult = mm_in else: assert reconstruct == 'orig' proj = S_decomp_full # already picked reg mm_out = np.dot(pS_decomp[n_use_in:], orig_data[:, rel_start:rel_stop]) mult = np.concatenate((mm_in, mm_out)) out_meg_data[:, rel_start:rel_stop] = \ np.dot(proj, mult) if len(pos_picks) > 0: out_pos_data[:, rel_start:rel_stop] = \ this_pos_quat[:, np.newaxis] # Transform orig_data to store just the residual if st_when == 'after': # Reconstruct data using original location from external # and internal spaces and compute residual rel_resid_data = resid[:, rel_start:rel_stop] orig_in_data[:, rel_start:rel_stop] = \ np.dot(S_decomp[:, :n_use_in], mm_in) rel_resid_data -= np.dot(np.dot(S_decomp[:, n_use_in:], pS_decomp[n_use_in:]), rel_resid_data) rel_resid_data -= orig_in_data[:, rel_start:rel_stop] # If doing tSSS at the end if st_when == 'after': _do_tSSS(out_meg_data, orig_in_data, resid, st_correlation, n_positions, t_str, tsss_valid) elif st_when == 'never' and head_pos[0] is not None: logger.info(' Used % 2d head position%s for %s' % (n_positions, _pl(n_positions), t_str)) raw_sss._data[meg_picks, start:stop] = out_meg_data raw_sss._data[pos_picks, start:stop] = out_pos_data return raw_sss def _get_coil_scale(meg_picks, mag_picks, grad_picks, mag_scale, info): """Get the magnetometer scale factor.""" if isinstance(mag_scale, str): if mag_scale != 'auto': raise ValueError('mag_scale must be a float or "auto", got "%s"' % mag_scale) if len(mag_picks) in (0, len(meg_picks)): mag_scale = 100. # only one coil type, doesn't matter logger.info(' Setting mag_scale=%0.2f because only one ' 'coil type is present' % mag_scale) else: # Find our physical distance between gradiometer pickup loops # ("base line") coils = _create_meg_coils([info['chs'][pick] for pick in meg_picks], 'accurate') grad_base = {coils[pick]['base'] for pick in grad_picks} if len(grad_base) != 1 or list(grad_base)[0] <= 0: raise RuntimeError('Could not automatically determine ' 'mag_scale, could not find one ' 'proper gradiometer distance from: %s' % list(grad_base)) grad_base = list(grad_base)[0] mag_scale = 1. / grad_base logger.info(' Setting mag_scale=%0.2f based on gradiometer ' 'distance %0.2f mm' % (mag_scale, 1000 * grad_base)) mag_scale = float(mag_scale) coil_scale = np.ones((len(meg_picks), 1)) coil_scale[mag_picks] = mag_scale return coil_scale, mag_scale def _remove_meg_projs(inst): """Remove inplace existing MEG projectors (assumes inactive).""" meg_picks = pick_types(inst.info, meg=True, exclude=[]) meg_channels = [inst.ch_names[pi] for pi in meg_picks] non_meg_proj = list() for proj in inst.info['projs']: if not any(c in meg_channels for c in proj['data']['col_names']): non_meg_proj.append(proj) inst.add_proj(non_meg_proj, remove_existing=True, verbose=False) def _check_destination(destination, info, head_frame): """Triage our reconstruction trans.""" if destination is None: return info['dev_head_t'] if not head_frame: raise RuntimeError('destination can only be set if using the ' 'head coordinate frame') if isinstance(destination, str): recon_trans = _get_trans(destination, 'meg', 'head')[0] elif isinstance(destination, Transform): recon_trans = destination else: destination = np.array(destination, float) if destination.shape != (3,): raise ValueError('destination must be a 3-element vector, ' 'str, or None') recon_trans = np.eye(4) recon_trans[:3, 3] = destination recon_trans = Transform('meg', 'head', recon_trans) if recon_trans.to_str != 'head' or recon_trans.from_str != 'MEG device': raise RuntimeError('Destination transform is not MEG device -> head, ' 'got %s -> %s' % (recon_trans.from_str, recon_trans.to_str)) return recon_trans @verbose def _prep_mf_coils(info, ignore_ref=True, verbose=None): """Get all coil integration information loaded and sorted.""" coils, comp_coils = _prep_meg_channels( info, head_frame=False, ignore_ref=ignore_ref, do_picking=False, verbose=False)[:2] mag_mask = _get_mag_mask(coils) if len(comp_coils) > 0: meg_picks = pick_types(info, meg=True, ref_meg=False, exclude=[]) ref_picks = pick_types(info, meg=False, ref_meg=True, exclude=[]) inserts = np.searchsorted(meg_picks, ref_picks) # len(inserts) == len(comp_coils) for idx, comp_coil in zip(inserts[::-1], comp_coils[::-1]): coils.insert(idx, comp_coil) # Now we have: # [c['chname'] for c in coils] == # [info['ch_names'][ii] # for ii in pick_types(info, meg=True, ref_meg=True)] # Now coils is a sorted list of coils. Time to do some vectorization. n_coils = len(coils) rmags = np.concatenate([coil['rmag'] for coil in coils]) cosmags = np.concatenate([coil['cosmag'] for coil in coils]) ws = np.concatenate([coil['w'] for coil in coils]) cosmags *= ws[:, np.newaxis] del ws n_int = np.array([len(coil['rmag']) for coil in coils]) bins = np.repeat(np.arange(len(n_int)), n_int) bd = np.concatenate(([0], np.cumsum(n_int))) slice_map = {ii: slice(start, stop) for ii, (start, stop) in enumerate(zip(bd[:-1], bd[1:]))} return rmags, cosmags, bins, n_coils, mag_mask, slice_map def _trans_starts_stops_quats(pos, start, stop, this_pos_data): """Get all trans and limits we need.""" pos_idx = np.arange(*np.searchsorted(pos[1], [start, stop])) used = np.zeros(stop - start, bool) trans = list() rel_starts = list() rel_stops = list() quats = list() weights = list() for ti in range(-1, len(pos_idx)): # first iteration for this block of data if ti < 0: rel_start = 0 rel_stop = pos[1][pos_idx[0]] if len(pos_idx) > 0 else stop rel_stop = rel_stop - start if rel_start == rel_stop: continue # our first pos occurs on first time sample # Don't calculate S_decomp here, use the last one trans.append(None) # meaning: use previous quats.append(this_pos_data) else: rel_start = pos[1][pos_idx[ti]] - start if ti == len(pos_idx) - 1: rel_stop = stop - start else: rel_stop = pos[1][pos_idx[ti + 1]] - start trans.append(pos[0][pos_idx[ti]]) quats.append(pos[2][pos_idx[ti]]) assert 0 <= rel_start assert rel_start < rel_stop assert rel_stop <= stop - start assert not used[rel_start:rel_stop].any() used[rel_start:rel_stop] = True rel_starts.append(rel_start) rel_stops.append(rel_stop) weights.append(rel_stop - rel_start) assert used.all() # Use weighted average for average trans over the window if this_pos_data is None: avg_trans = None else: weights = np.array(weights) quats = np.array(quats) weights = weights / weights.sum().astype(float) # int -> float avg_quat = _average_quats(quats[:, :3], weights) avg_t = np.dot(weights, quats[:, 3:6]) avg_trans = np.vstack([ np.hstack([quat_to_rot(avg_quat), avg_t[:, np.newaxis]]), [[0., 0., 0., 1.]]]) return trans, rel_starts, rel_stops, quats, avg_trans def _do_tSSS(clean_data, orig_in_data, resid, st_correlation, n_positions, t_str, tsss_valid): """Compute and apply SSP-like projection vectors based on min corr.""" if not tsss_valid: t_proj = np.empty((clean_data.shape[1], 0)) else: np.asarray_chkfinite(resid) t_proj = _overlap_projector(orig_in_data, resid, st_correlation) # Apply projector according to Eq. 12 in :footcite:`TauluSimola2006` msg = (' Projecting %2d intersecting tSSS component%s ' 'for %s' % (t_proj.shape[1], _pl(t_proj.shape[1], ' '), t_str)) if n_positions > 1: msg += ' (across %2d position%s)' % (n_positions, _pl(n_positions, ' ')) logger.info(msg) clean_data -= np.dot(np.dot(clean_data, t_proj), t_proj.T) def _copy_preload_add_channels(raw, add_channels, copy, info): """Load data for processing and (maybe) add cHPI pos channels.""" if copy: raw = raw.copy() with raw.info._unlock(): raw.info['chs'] = info['chs'] # updated coil types if add_channels: kinds = [FIFF.FIFFV_QUAT_1, FIFF.FIFFV_QUAT_2, FIFF.FIFFV_QUAT_3, FIFF.FIFFV_QUAT_4, FIFF.FIFFV_QUAT_5, FIFF.FIFFV_QUAT_6, FIFF.FIFFV_HPI_G, FIFF.FIFFV_HPI_ERR, FIFF.FIFFV_HPI_MOV] out_shape = (len(raw.ch_names) + len(kinds), len(raw.times)) out_data = np.zeros(out_shape, np.float64) msg = ' Appending head position result channels and ' if raw.preload: logger.info(msg + 'copying original raw data') out_data[:len(raw.ch_names)] = raw._data raw._data = out_data else: logger.info(msg + 'loading raw data from disk') with use_log_level(False): raw._preload_data(out_data[:len(raw.ch_names)]) raw._data = out_data assert raw.preload is True off = len(raw.ch_names) chpi_chs = [ dict(ch_name='CHPI%03d' % (ii + 1), logno=ii + 1, scanno=off + ii + 1, unit_mul=-1, range=1., unit=-1, kind=kinds[ii], coord_frame=FIFF.FIFFV_COORD_UNKNOWN, cal=1e-4, coil_type=FWD.COIL_UNKNOWN, loc=np.zeros(12)) for ii in range(len(kinds))] raw.info['chs'].extend(chpi_chs) raw.info._update_redundant() raw.info._check_consistency() assert raw._data.shape == (raw.info['nchan'], len(raw.times)) # Return the pos picks pos_picks = np.arange(len(raw.ch_names) - len(chpi_chs), len(raw.ch_names)) return raw, pos_picks else: if copy: if not raw.preload: logger.info(' Loading raw data from disk') raw.load_data(verbose=False) else: logger.info(' Using loaded raw data') return raw, np.array([], int) def _check_pos(pos, head_frame, raw, st_fixed, sfreq): """Check for a valid pos array and transform it to a more usable form.""" _validate_type(pos, (np.ndarray, None), 'head_pos') if pos is None: return [None, np.array([-1])] if not head_frame: raise ValueError('positions can only be used if coord_frame="head"') if not st_fixed: warn('st_fixed=False is untested, use with caution!') if not isinstance(pos, np.ndarray): raise TypeError('pos must be an ndarray') if pos.ndim != 2 or pos.shape[1] != 10: raise ValueError('pos must be an array of shape (N, 10)') t = pos[:, 0] if not np.array_equal(t, np.unique(t)): raise ValueError('Time points must unique and in ascending order') # We need an extra 1e-3 (1 ms) here because MaxFilter outputs values # only out to 3 decimal places if not _time_mask(t, tmin=raw._first_time - 1e-3, tmax=None, sfreq=sfreq).all(): raise ValueError('Head position time points must be greater than ' 'first sample offset, but found %0.4f < %0.4f' % (t[0], raw._first_time)) max_dist = np.sqrt(np.sum(pos[:, 4:7] ** 2, axis=1)).max() if max_dist > 1.: warn('Found a distance greater than 1 m (%0.3g m) from the device ' 'origin, positions may be invalid and Maxwell filtering could ' 'fail' % (max_dist,)) dev_head_ts = np.zeros((len(t), 4, 4)) dev_head_ts[:, 3, 3] = 1. dev_head_ts[:, :3, 3] = pos[:, 4:7] dev_head_ts[:, :3, :3] = quat_to_rot(pos[:, 1:4]) pos = [dev_head_ts, t - raw._first_time, pos[:, 1:]] return pos def _get_decomp(trans, all_coils, cal, regularize, exp, ignore_ref, coil_scale, grad_picks, mag_picks, good_mask, mag_or_fine, bad_condition, t, mag_scale): """Get a decomposition matrix and pseudoinverse matrices.""" from scipy import linalg # # Fine calibration processing (point-like magnetometers and calib. coeffs) # S_decomp_full = _get_s_decomp( exp, all_coils, trans, coil_scale, cal, ignore_ref, grad_picks, mag_picks, mag_scale) S_decomp = S_decomp_full[good_mask] # # Extended SSS basis (eSSS) # extended_proj = exp.get('extended_proj', ()) if len(extended_proj) > 0: rcond = 1e-4 thresh = 1e-4 extended_proj = extended_proj.T * coil_scale[good_mask] extended_proj /= np.linalg.norm(extended_proj, axis=0) n_int = _get_n_moments(exp['int_order']) if S_decomp.shape[1] > n_int: S_ext = S_decomp[:, n_int:].copy() S_ext /= np.linalg.norm(S_ext, axis=0) S_ext_orth = linalg.orth(S_ext, rcond=rcond) assert S_ext_orth.shape[1] == S_ext.shape[1] extended_proj -= np.dot(S_ext_orth, np.dot(S_ext_orth.T, extended_proj)) scale = np.mean(np.linalg.norm(S_decomp[n_int:], axis=0)) else: scale = np.mean(np.linalg.norm(S_decomp[:n_int], axis=0)) mask = np.linalg.norm(extended_proj, axis=0) > thresh extended_remove = list(np.where(~mask)[0] + S_decomp.shape[1]) logger.debug(' Reducing %d -> %d' % (extended_proj.shape[1], mask.sum())) extended_proj /= np.linalg.norm(extended_proj, axis=0) / scale S_decomp = np.concatenate([S_decomp, extended_proj], axis=-1) if extended_proj.shape[1]: S_decomp_full = np.pad( S_decomp_full, ((0, 0), (0, extended_proj.shape[1])), 'constant') S_decomp_full[good_mask, -extended_proj.shape[1]:] = extended_proj else: extended_remove = list() del extended_proj # # Regularization # S_decomp, reg_moments, n_use_in = _regularize( regularize, exp, S_decomp, mag_or_fine, extended_remove, t=t) S_decomp_full = S_decomp_full.take(reg_moments, axis=1) # # Pseudo-inverse of total multipolar moment basis set (Part of Eq. 37) # pS_decomp, sing = _col_norm_pinv(S_decomp.copy()) cond = sing[0] / sing[-1] if bad_condition != 'ignore' and cond >= 1000.: msg = 'Matrix is badly conditioned: %0.0f >= 1000' % cond if bad_condition == 'error': raise RuntimeError(msg) elif bad_condition == 'warning': warn(msg) else: # condition == 'info' logger.info(msg) # Build in our data scaling here pS_decomp *= coil_scale[good_mask].T S_decomp /= coil_scale[good_mask] S_decomp_full /= coil_scale return S_decomp, S_decomp_full, pS_decomp, reg_moments, n_use_in def _get_s_decomp(exp, all_coils, trans, coil_scale, cal, ignore_ref, grad_picks, mag_picks, mag_scale): """Get S_decomp.""" S_decomp = _trans_sss_basis(exp, all_coils, trans, coil_scale) if cal is not None: # Compute point-like mags to incorporate gradiometer imbalance grad_cals = _sss_basis_point(exp, trans, cal, ignore_ref, mag_scale) # Add point like magnetometer data to bases. if len(grad_picks) > 0: S_decomp[grad_picks, :] += grad_cals # Scale magnetometers by calibration coefficient if len(mag_picks) > 0: S_decomp[mag_picks, :] /= cal['mag_cals'] # We need to be careful about KIT gradiometers return S_decomp @verbose def _regularize(regularize, exp, S_decomp, mag_or_fine, extended_remove, t, verbose=None): """Regularize a decomposition matrix.""" # ALWAYS regularize the out components according to norm, since # gradiometer-only setups (e.g., KIT) can have zero first-order # (homogeneous field) components int_order, ext_order = exp['int_order'], exp['ext_order'] n_in = _get_n_moments(int_order) n_out = S_decomp.shape[1] - n_in t_str = '%8.3f' % t if regularize is not None: # regularize='in' in_removes, out_removes = _regularize_in( int_order, ext_order, S_decomp, mag_or_fine, extended_remove) else: in_removes = [] out_removes = _regularize_out(int_order, ext_order, mag_or_fine, extended_remove) reg_in_moments = np.setdiff1d(np.arange(n_in), in_removes) reg_out_moments = np.setdiff1d(np.arange(n_in, S_decomp.shape[1]), out_removes) n_use_in = len(reg_in_moments) n_use_out = len(reg_out_moments) reg_moments = np.concatenate((reg_in_moments, reg_out_moments)) S_decomp = S_decomp.take(reg_moments, axis=1) if regularize is not None or n_use_out != n_out: logger.info(' Using %s/%s harmonic components for %s ' '(%s/%s in, %s/%s out)' % (n_use_in + n_use_out, n_in + n_out, t_str, n_use_in, n_in, n_use_out, n_out)) return S_decomp, reg_moments, n_use_in @verbose def _get_mf_picks_fix_mags(info, int_order, ext_order, ignore_ref=False, verbose=None): """Pick types for Maxwell filtering and fix magnetometers.""" # Check for T1/T2 mag types mag_inds_T1T2 = _get_T1T2_mag_inds(info, use_cal=True) if len(mag_inds_T1T2) > 0: fix_mag_coil_types(info, use_cal=True) # Get indices of channels to use in multipolar moment calculation ref = not ignore_ref meg_picks = pick_types(info, meg=True, ref_meg=ref, exclude=[]) meg_info = pick_info(_simplify_info(info), meg_picks) del info good_mask = np.zeros(len(meg_picks,), bool) good_mask[pick_types(meg_info, meg=True, ref_meg=ref, exclude='bads')] = 1 n_bases = _get_n_moments([int_order, ext_order]).sum() if n_bases > good_mask.sum(): raise ValueError('Number of requested bases (%s) exceeds number of ' 'good sensors (%s)' % (str(n_bases), good_mask.sum())) recons = [ch for ch in meg_info['bads']] if len(recons) > 0: msg = ' Bad MEG channels being reconstructed: %s' % recons else: msg = ' No bad MEG channels' logger.info(msg) ref_meg = False if ignore_ref else 'mag' mag_picks = pick_types(meg_info, meg='mag', ref_meg=ref_meg, exclude=[]) ref_meg = False if ignore_ref else 'grad' grad_picks = pick_types(meg_info, meg='grad', ref_meg=ref_meg, exclude=[]) assert len(mag_picks) + len(grad_picks) == len(meg_info['ch_names']) # Determine which are magnetometers for external basis purposes mag_or_fine = np.zeros(len(meg_picks), bool) mag_or_fine[mag_picks] = True # KIT gradiometers are marked as having units T, not T/M (argh) # We need a separate variable for this because KIT grads should be # treated mostly like magnetometers (e.g., scaled by 100) for reg coil_types = np.array([ch['coil_type'] for ch in meg_info['chs']]) mag_or_fine[(coil_types & 0xFFFF) == FIFF.FIFFV_COIL_KIT_GRAD] = False # The same thing goes for CTF gradiometers... ctf_grads = [FIFF.FIFFV_COIL_CTF_GRAD, FIFF.FIFFV_COIL_CTF_REF_GRAD, FIFF.FIFFV_COIL_CTF_OFFDIAG_REF_GRAD] mag_or_fine[np.in1d(coil_types, ctf_grads)] = False msg = (' Processing %s gradiometers and %s magnetometers' % (len(grad_picks), len(mag_picks))) n_kit = len(mag_picks) - mag_or_fine.sum() if n_kit > 0: msg += ' (of which %s are actually KIT gradiometers)' % n_kit logger.info(msg) return meg_picks, mag_picks, grad_picks, good_mask, mag_or_fine def _check_regularize(regularize): """Ensure regularize is valid.""" if not (regularize is None or (isinstance(regularize, str) and regularize in ('in',))): raise ValueError('regularize must be None or "in"') def _check_usable(inst): """Ensure our data are clean.""" if inst.proj: raise RuntimeError('Projectors cannot be applied to data during ' 'Maxwell filtering.') current_comp = inst.compensation_grade if current_comp not in (0, None): raise RuntimeError('Maxwell filter cannot be done on compensated ' 'channels, but data have been compensated with ' 'grade %s.' % current_comp) def _col_norm_pinv(x): """Compute the pinv with column-normalization to stabilize calculation. Note: will modify/overwrite x. """ norm = np.sqrt(np.sum(x * x, axis=0)) x /= norm u, s, v = _safe_svd(x, full_matrices=False, **check_disable) v /= norm return np.dot(v.T * 1. / s, u.T), s def _sq(x): """Square quickly.""" return x * x def _check_finite(data): """Ensure data is finite.""" if not np.isfinite(data).all(): raise RuntimeError('data contains non-finite numbers') def _sph_harm_norm(order, degree): """Compute normalization factor for spherical harmonics.""" # we could use scipy.special.poch(degree + order + 1, -2 * order) # here, but it's slower for our fairly small degree norm = np.sqrt((2 * degree + 1.) / (4 * np.pi)) if order != 0: norm *= np.sqrt(factorial(degree - order) / float(factorial(degree + order))) return norm def _concatenate_sph_coils(coils): """Concatenate MEG coil parameters for spherical harmoncs.""" rs = np.concatenate([coil['r0_exey'] for coil in coils]) wcoils = np.concatenate([coil['w'] for coil in coils]) ezs = np.concatenate([np.tile(coil['ez'][np.newaxis, :], (len(coil['rmag']), 1)) for coil in coils]) bins = np.repeat(np.arange(len(coils)), [len(coil['rmag']) for coil in coils]) return rs, wcoils, ezs, bins _mu_0 = 4e-7 * np.pi # magnetic permeability def _get_mag_mask(coils): """Get the coil_scale for Maxwell filtering.""" return np.array([coil['coil_class'] == FWD.COILC_MAG for coil in coils]) def _sss_basis_basic(exp, coils, mag_scale=100., method='standard'): """Compute SSS basis using non-optimized (but more readable) algorithms.""" from scipy.special import sph_harm int_order, ext_order = exp['int_order'], exp['ext_order'] origin = exp['origin'] assert 'extended_proj' not in exp # advanced option not supported # Compute vector between origin and coil, convert to spherical coords if method == 'standard': # Get position, normal, weights, and number of integration pts. rmags, cosmags, ws, bins = _concatenate_coils(coils) rmags -= origin # Convert points to spherical coordinates rad, az, pol = _cart_to_sph(rmags).T cosmags *= ws[:, np.newaxis] del rmags, ws out_type = np.float64 else: # testing equivalence method rs, wcoils, ezs, bins = _concatenate_sph_coils(coils) rs -= origin rad, az, pol = _cart_to_sph(rs).T ezs *= wcoils[:, np.newaxis] del rs, wcoils out_type = np.complex128 del origin # Set up output matrices n_in, n_out = _get_n_moments([int_order, ext_order]) S_tot = np.empty((len(coils), n_in + n_out), out_type) S_in = S_tot[:, :n_in] S_out = S_tot[:, n_in:] coil_scale = np.ones((len(coils), 1)) coil_scale[_get_mag_mask(coils)] = mag_scale # Compute internal/external basis vectors (exclude degree 0; L/RHS Eq. 5) for degree in range(1, max(int_order, ext_order) + 1): # Only loop over positive orders, negative orders are handled # for efficiency within for order in range(degree + 1): S_in_out = list() grads_in_out = list() # Same spherical harmonic is used for both internal and external sph = sph_harm(order, degree, az, pol) sph_norm = _sph_harm_norm(order, degree) # Compute complex gradient for all integration points # in spherical coordinates (Eq. 6). The gradient for rad, az, pol # is obtained by taking the partial derivative of Eq. 4 w.r.t. each # coordinate. az_factor = 1j * order * sph / np.sin(np.maximum(pol, 1e-16)) pol_factor = (-sph_norm * np.sin(pol) * np.exp(1j * order * az) * _alegendre_deriv(order, degree, np.cos(pol))) if degree <= int_order: S_in_out.append(S_in) in_norm = _mu_0 * rad ** -(degree + 2) g_rad = in_norm * (-(degree + 1.) * sph) g_az = in_norm * az_factor g_pol = in_norm * pol_factor grads_in_out.append(_sph_to_cart_partials(az, pol, g_rad, g_az, g_pol)) if degree <= ext_order: S_in_out.append(S_out) out_norm = _mu_0 * rad ** (degree - 1) g_rad = out_norm * degree * sph g_az = out_norm * az_factor g_pol = out_norm * pol_factor grads_in_out.append(_sph_to_cart_partials(az, pol, g_rad, g_az, g_pol)) for spc, grads in zip(S_in_out, grads_in_out): # We could convert to real at the end, but it's more efficient # to do it now if method == 'standard': grads_pos_neg = [_sh_complex_to_real(grads, order)] orders_pos_neg = [order] # Deal with the negative orders if order > 0: # it's faster to use the conjugation property for # our normalized spherical harmonics than recalculate grads_pos_neg.append(_sh_complex_to_real( _sh_negate(grads, order), -order)) orders_pos_neg.append(-order) for gr, oo in zip(grads_pos_neg, orders_pos_neg): # Gradients dotted w/integration point weighted normals gr = np.einsum('ij,ij->i', gr, cosmags) vals = np.bincount(bins, gr, len(coils)) spc[:, _deg_ord_idx(degree, oo)] = -vals else: grads = np.einsum('ij,ij->i', grads, ezs) v = (np.bincount(bins, grads.real, len(coils)) + 1j * np.bincount(bins, grads.imag, len(coils))) spc[:, _deg_ord_idx(degree, order)] = -v if order > 0: spc[:, _deg_ord_idx(degree, -order)] = \ -_sh_negate(v, order) # Scale magnetometers S_tot *= coil_scale if method != 'standard': # Eventually we could probably refactor this for 2x mem (and maybe CPU) # savings by changing how spc/S_tot is assigned above (real only) S_tot = _bases_complex_to_real(S_tot, int_order, ext_order) return S_tot def _sss_basis(exp, all_coils): """Compute SSS basis for given conditions. Parameters ---------- exp : dict Must contain the following keys: origin : ndarray, shape (3,) Origin of the multipolar moment space in meters int_order : int Order of the internal multipolar moment space ext_order : int Order of the external multipolar moment space coils : list List of MEG coils. Each should contain coil information dict specifying position, normals, weights, number of integration points and channel type. All coil geometry must be in the same coordinate frame as ``origin`` (``head`` or ``meg``). Returns ------- bases : ndarray, shape (n_coils, n_mult_moments) Internal and external basis sets as a single ndarray. Notes ----- Does not incorporate magnetometer scaling factor or normalize spaces. Adapted from code provided by Jukka Nenonen. """ rmags, cosmags, bins, n_coils = all_coils[:4] int_order, ext_order = exp['int_order'], exp['ext_order'] n_in, n_out = _get_n_moments([int_order, ext_order]) rmags = rmags - exp['origin'] # do the heavy lifting max_order = max(int_order, ext_order) L = _tabular_legendre(rmags, max_order) phi = np.arctan2(rmags[:, 1], rmags[:, 0]) r_n = np.sqrt(np.sum(rmags * rmags, axis=1)) r_xy = np.sqrt(rmags[:, 0] * rmags[:, 0] + rmags[:, 1] * rmags[:, 1]) cos_pol = rmags[:, 2] / r_n # cos(theta); theta 0...pi sin_pol = np.sqrt(1. - cos_pol * cos_pol) # sin(theta) z_only = (r_xy <= 1e-16) sin_pol_nz = sin_pol.copy() sin_pol_nz[z_only] = 1. # will be overwritten later r_xy[z_only] = 1. cos_az = rmags[:, 0] / r_xy # cos(phi) cos_az[z_only] = 1. sin_az = rmags[:, 1] / r_xy # sin(phi) sin_az[z_only] = 0. # Appropriate vector spherical harmonics terms # JNE 2012-02-08: modified alm -> 2*alm, blm -> -2*blm r_nn2 = r_n.copy() r_nn1 = 1.0 / (r_n * r_n) S_tot = np.empty((n_coils, n_in + n_out), np.float64) S_in = S_tot[:, :n_in] S_out = S_tot[:, n_in:] for degree in range(max_order + 1): if degree <= ext_order: r_nn1 *= r_n # r^(l-1) if degree <= int_order: r_nn2 *= r_n # r^(l+2) # mu_0*sqrt((2l+1)/4pi (l-m)!/(l+m)!) mult = 2e-7 * np.sqrt((2 * degree + 1) * np.pi) if degree > 0: idx = _deg_ord_idx(degree, 0) # alpha if degree <= int_order: b_r = mult * (degree + 1) * L[degree][0] / r_nn2 b_pol = -mult * L[degree][1] / r_nn2 S_in[:, idx] = _integrate_points( cos_az, sin_az, cos_pol, sin_pol, b_r, 0., b_pol, cosmags, bins, n_coils) # beta if degree <= ext_order: b_r = -mult * degree * L[degree][0] * r_nn1 b_pol = -mult * L[degree][1] * r_nn1 S_out[:, idx] = _integrate_points( cos_az, sin_az, cos_pol, sin_pol, b_r, 0., b_pol, cosmags, bins, n_coils) for order in range(1, degree + 1): ord_phi = order * phi sin_order = np.sin(ord_phi) cos_order = np.cos(ord_phi) mult /= np.sqrt((degree - order + 1) * (degree + order)) factor = mult * np.sqrt(2) # equivalence fix (MF uses 2.) # Real idx = _deg_ord_idx(degree, order) r_fact = factor * L[degree][order] * cos_order az_fact = factor * order * sin_order * L[degree][order] pol_fact = -factor * (L[degree][order + 1] - (degree + order) * (degree - order + 1) * L[degree][order - 1]) * cos_order # alpha if degree <= int_order: b_r = (degree + 1) * r_fact / r_nn2 b_az = az_fact / (sin_pol_nz * r_nn2) b_az[z_only] = 0. b_pol = pol_fact / (2 * r_nn2) S_in[:, idx] = _integrate_points( cos_az, sin_az, cos_pol, sin_pol, b_r, b_az, b_pol, cosmags, bins, n_coils) # beta if degree <= ext_order: b_r = -degree * r_fact * r_nn1 b_az = az_fact * r_nn1 / sin_pol_nz b_az[z_only] = 0. b_pol = pol_fact * r_nn1 / 2. S_out[:, idx] = _integrate_points( cos_az, sin_az, cos_pol, sin_pol, b_r, b_az, b_pol, cosmags, bins, n_coils) # Imaginary idx = _deg_ord_idx(degree, -order) r_fact = factor * L[degree][order] * sin_order az_fact = factor * order * cos_order * L[degree][order] pol_fact = factor * (L[degree][order + 1] - (degree + order) * (degree - order + 1) * L[degree][order - 1]) * sin_order # alpha if degree <= int_order: b_r = -(degree + 1) * r_fact / r_nn2 b_az = az_fact / (sin_pol_nz * r_nn2) b_az[z_only] = 0. b_pol = pol_fact / (2 * r_nn2) S_in[:, idx] = _integrate_points( cos_az, sin_az, cos_pol, sin_pol, b_r, b_az, b_pol, cosmags, bins, n_coils) # beta if degree <= ext_order: b_r = degree * r_fact * r_nn1 b_az = az_fact * r_nn1 / sin_pol_nz b_az[z_only] = 0. b_pol = pol_fact * r_nn1 / 2. S_out[:, idx] = _integrate_points( cos_az, sin_az, cos_pol, sin_pol, b_r, b_az, b_pol, cosmags, bins, n_coils) return S_tot def _integrate_points(cos_az, sin_az, cos_pol, sin_pol, b_r, b_az, b_pol, cosmags, bins, n_coils): """Integrate points in spherical coords.""" grads = _sp_to_cart(cos_az, sin_az, cos_pol, sin_pol, b_r, b_az, b_pol).T grads = (grads * cosmags).sum(axis=1) return bincount(bins, grads, n_coils) def _tabular_legendre(r, nind): """Compute associated Legendre polynomials.""" r_n = np.sqrt(np.sum(r * r, axis=1)) x = r[:, 2] / r_n # cos(theta) L = list() for degree in range(nind + 1): L.append(np.zeros((degree + 2, len(r)))) L[0][0] = 1. pnn = np.ones(x.shape) fact = 1. sx2 = np.sqrt((1. - x) * (1. + x)) for degree in range(nind + 1): L[degree][degree] = pnn pnn *= (-fact * sx2) fact += 2. if degree < nind: L[degree + 1][degree] = x * (2 * degree + 1) * L[degree][degree] if degree >= 2: for order in range(degree - 1): L[degree][order] = (x * (2 * degree - 1) * L[degree - 1][order] - (degree + order - 1) * L[degree - 2][order]) / (degree - order) return L def _sp_to_cart(cos_az, sin_az, cos_pol, sin_pol, b_r, b_az, b_pol): """Convert spherical coords to cartesian.""" out = np.empty((3,) + sin_pol.shape) out[0] = sin_pol * cos_az * b_r + cos_pol * cos_az * b_pol - sin_az * b_az out[1] = sin_pol * sin_az * b_r + cos_pol * sin_az * b_pol + cos_az * b_az out[2] = cos_pol * b_r - sin_pol * b_pol return out def _get_degrees_orders(order): """Get the set of degrees used in our basis functions.""" degrees = np.zeros(_get_n_moments(order), int) orders = np.zeros_like(degrees) for degree in range(1, order + 1): # Only loop over positive orders, negative orders are handled # for efficiency within for order in range(degree + 1): ii = _deg_ord_idx(degree, order) degrees[ii] = degree orders[ii] = order ii = _deg_ord_idx(degree, -order) degrees[ii] = degree orders[ii] = -order return degrees, orders def _alegendre_deriv(order, degree, val): """Compute the derivative of the associated Legendre polynomial at a value. Parameters ---------- order : int Order of spherical harmonic. (Usually) corresponds to 'm'. degree : int Degree of spherical harmonic. (Usually) corresponds to 'l'. val : float Value to evaluate the derivative at. Returns ------- dPlm : float Associated Legendre function derivative """ from scipy.special import lpmv assert order >= 0 return (order * val * lpmv(order, degree, val) + (degree + order) * (degree - order + 1.) * np.sqrt(1. - val * val) * lpmv(order - 1, degree, val)) / (1. - val * val) def _bases_complex_to_real(complex_tot, int_order, ext_order): """Convert complex spherical harmonics to real.""" n_in, n_out = _get_n_moments([int_order, ext_order]) complex_in = complex_tot[:, :n_in] complex_out = complex_tot[:, n_in:] real_tot = np.empty(complex_tot.shape, np.float64) real_in = real_tot[:, :n_in] real_out = real_tot[:, n_in:] for comp, real, exp_order in zip([complex_in, complex_out], [real_in, real_out], [int_order, ext_order]): for deg in range(1, exp_order + 1): for order in range(deg + 1): idx_pos = _deg_ord_idx(deg, order) idx_neg = _deg_ord_idx(deg, -order) real[:, idx_pos] = _sh_complex_to_real(comp[:, idx_pos], order) if order != 0: # This extra mult factor baffles me a bit, but it works # in round-trip testing, so we'll keep it :( mult = (-1 if order % 2 == 0 else 1) real[:, idx_neg] = mult * _sh_complex_to_real( comp[:, idx_neg], -order) return real_tot def _bases_real_to_complex(real_tot, int_order, ext_order): """Convert real spherical harmonics to complex.""" n_in, n_out = _get_n_moments([int_order, ext_order]) real_in = real_tot[:, :n_in] real_out = real_tot[:, n_in:] comp_tot = np.empty(real_tot.shape, np.complex128) comp_in = comp_tot[:, :n_in] comp_out = comp_tot[:, n_in:] for real, comp, exp_order in zip([real_in, real_out], [comp_in, comp_out], [int_order, ext_order]): for deg in range(1, exp_order + 1): # only loop over positive orders, figure out neg from pos for order in range(deg + 1): idx_pos = _deg_ord_idx(deg, order) idx_neg = _deg_ord_idx(deg, -order) this_comp = _sh_real_to_complex([real[:, idx_pos], real[:, idx_neg]], order) comp[:, idx_pos] = this_comp comp[:, idx_neg] = _sh_negate(this_comp, order) return comp_tot def _check_info(info, sss=True, tsss=True, calibration=True, ctc=True): """Ensure that Maxwell filtering has not been applied yet.""" for ent in info['proc_history']: for msg, key, doing in (('SSS', 'sss_info', sss), ('tSSS', 'max_st', tsss), ('fine calibration', 'sss_cal', calibration), ('cross-talk cancellation', 'sss_ctc', ctc)): if not doing: continue if len(ent['max_info'][key]) > 0: raise RuntimeError('Maxwell filtering %s step has already ' 'been applied, cannot reapply' % msg) def _update_sss_info(raw, origin, int_order, ext_order, nchan, coord_frame, sss_ctc, sss_cal, max_st, reg_moments, st_only, recon_trans, extended_proj): """Update info inplace after Maxwell filtering. Parameters ---------- raw : instance of mne.io.Raw Data to be filtered origin : array-like, shape (3,) Origin of internal and external multipolar moment space in head coords (in meters) int_order : int Order of internal component of spherical expansion ext_order : int Order of external component of spherical expansion nchan : int Number of sensors sss_ctc : dict The cross talk information. sss_cal : dict The calibration information. max_st : dict The tSSS information. reg_moments : ndarray | slice The moments that were used. st_only : bool Whether tSSS only was performed. recon_trans : instance of Transformation The reconstruction trans. extended_proj : ndarray Extended external bases. """ n_in, n_out = _get_n_moments([int_order, ext_order]) with raw.info._unlock(): raw.info['maxshield'] = False components = np.zeros(n_in + n_out + len(extended_proj)).astype('int32') components[reg_moments] = 1 sss_info_dict = dict(in_order=int_order, out_order=ext_order, nchan=nchan, origin=origin.astype('float32'), job=FIFF.FIFFV_SSS_JOB_FILTER, nfree=np.sum(components[:n_in]), frame=_str_to_frame[coord_frame], components=components) max_info_dict = dict(max_st=max_st) if st_only: max_info_dict.update(sss_info=dict(), sss_cal=dict(), sss_ctc=dict()) else: max_info_dict.update(sss_info=sss_info_dict, sss_cal=sss_cal, sss_ctc=sss_ctc) # Reset 'bads' for any MEG channels since they've been reconstructed _reset_meg_bads(raw.info) # set the reconstruction transform with raw.info._unlock(): raw.info['dev_head_t'] = recon_trans block_id = _generate_meas_id() with raw.info._unlock(): raw.info['proc_history'].insert(0, dict( max_info=max_info_dict, block_id=block_id, date=DATE_NONE, creator='mne-python v%s' % __version__, experimenter='')) def _reset_meg_bads(info): """Reset MEG bads.""" meg_picks = pick_types(info, meg=True, exclude=[]) info['bads'] = [bad for bad in info['bads'] if info['ch_names'].index(bad) not in meg_picks] check_disable = dict(check_finite=False) def _orth_overwrite(A): """Create a slightly more efficient 'orth'.""" # adapted from scipy/linalg/decomp_svd.py u, s = _safe_svd(A, full_matrices=False, **check_disable)[:2] M, N = A.shape eps = np.finfo(float).eps tol = max(M, N) * np.amax(s) * eps num = np.sum(s > tol, dtype=int) return u[:, :num] def _overlap_projector(data_int, data_res, corr): """Calculate projector for removal of subspace intersection in tSSS.""" # corr necessary to deal with noise when finding identical signal # directions in the subspace. See the end of the Results section in # :footcite:`TauluSimola2006` # Note that the procedure here is an updated version of # :footcite:`TauluSimola2006` (and used in MF's tSSS) that uses residuals # instead of internal/external spaces directly. This provides more degrees # of freedom when analyzing for intersections between internal and # external spaces. # Normalize data, then compute orth to get temporal bases. Matrices # must have shape (n_samps x effective_rank) when passed into svd # computation # we use np.linalg.norm instead of sp.linalg.norm here: ~2x faster! from scipy import linalg n = np.linalg.norm(data_int) n = 1. if n == 0 else n # all-zero data should gracefully continue data_int = _orth_overwrite((data_int / n).T) n = np.linalg.norm(data_res) n = 1. if n == 0 else n data_res = _orth_overwrite((data_res / n).T) if data_int.shape[1] == 0 or data_res.shape[1] == 0: return np.empty((data_int.shape[0], 0)) Q_int = linalg.qr(data_int, overwrite_a=True, mode='economic', **check_disable)[0].T Q_res = linalg.qr(data_res, overwrite_a=True, mode='economic', **check_disable)[0] C_mat = np.dot(Q_int, Q_res) del Q_int # Compute angles between subspace and which bases to keep S_intersect, Vh_intersect = _safe_svd(C_mat, full_matrices=False, **check_disable)[1:] del C_mat intersect_mask = (S_intersect >= corr) del S_intersect # Compute projection operator as (I-LL_T) Eq. 12 in # :footcite:`TauluSimola2006` V_principal should be shape # (n_time_pts x n_retained_inds) Vh_intersect = Vh_intersect[intersect_mask].T V_principal = np.dot(Q_res, Vh_intersect) return V_principal def _prep_fine_cal(info, fine_cal): from ._fine_cal import read_fine_calibration _validate_type(fine_cal, (dict, 'path-like')) if not isinstance(fine_cal, dict): extra = op.basename(str(fine_cal)) fine_cal = read_fine_calibration(fine_cal) else: extra = 'dict' logger.info(f' Using fine calibration {extra}') ch_names = _clean_names(info['ch_names'], remove_whitespace=True) info_to_cal = OrderedDict() missing = list() for ci, name in enumerate(fine_cal['ch_names']): if name not in ch_names: missing.append(name) else: oi = ch_names.index(name) info_to_cal[oi] = ci meg_picks = pick_types(info, meg=True, exclude=[]) if len(info_to_cal) != len(meg_picks): raise RuntimeError( 'Not all MEG channels found in fine calibration file, missing:\n%s' % sorted(list({ch_names[pick] for pick in meg_picks} - set(fine_cal['ch_names'])))) if len(missing): warn('Found cal channel%s not in data: %s' % (_pl(missing), missing)) return info_to_cal, fine_cal, ch_names def _update_sensor_geometry(info, fine_cal, ignore_ref): """Replace sensor geometry information and reorder cal_chs.""" info_to_cal, fine_cal, ch_names = _prep_fine_cal(info, fine_cal) grad_picks = pick_types(info, meg='grad', exclude=()) mag_picks = pick_types(info, meg='mag', exclude=()) # Determine gradiometer imbalances and magnetometer calibrations grad_imbalances = np.array([fine_cal['imb_cals'][info_to_cal[gi]] for gi in grad_picks]).T if grad_imbalances.shape[0] not in [0, 1, 3]: raise ValueError('Must have 1 (x) or 3 (x, y, z) point-like ' + 'magnetometers. Currently have %i' % grad_imbalances.shape[0]) mag_cals = np.array([fine_cal['imb_cals'][info_to_cal[mi]] for mi in mag_picks]) # Now let's actually construct our point-like adjustment coils for grads grad_coilsets = _get_grad_point_coilsets( info, n_types=len(grad_imbalances), ignore_ref=ignore_ref) calibration = dict(grad_imbalances=grad_imbalances, grad_coilsets=grad_coilsets, mag_cals=mag_cals) # Replace sensor locations (and track differences) for fine calibration ang_shift = list() used = np.zeros(len(info['chs']), bool) cal_corrs = list() cal_chans = list() adjust_logged = False for oi, ci in info_to_cal.items(): assert not used[oi] used[oi] = True info_ch = info['chs'][oi] ch_num = int(fine_cal['ch_names'][ci].lstrip('MEG').lstrip('0')) cal_chans.append([ch_num, info_ch['coil_type']]) # Some .dat files might only rotate EZ, so we must check first that # EX and EY are orthogonal to EZ. If not, we find the rotation between # the original and fine-cal ez, and rotate EX and EY accordingly: ch_coil_rot = _loc_to_coil_trans(info_ch['loc'])[:3, :3] cal_loc = fine_cal['locs'][ci].copy() cal_coil_rot = _loc_to_coil_trans(cal_loc)[:3, :3] if np.max([np.abs(np.dot(cal_coil_rot[:, ii], cal_coil_rot[:, 2])) for ii in range(2)]) > 1e-6: # X or Y not orthogonal if not adjust_logged: logger.info(' Adjusting non-orthogonal EX and EY') adjust_logged = True # find the rotation matrix that goes from one to the other this_trans = _find_vector_rotation( ch_coil_rot[:, 2], cal_coil_rot[:, 2]) cal_loc[3:] = np.dot(this_trans, ch_coil_rot).T.ravel() # calculate shift angle v1 = _loc_to_coil_trans(cal_loc)[:3, :3] _normalize_vectors(v1) v2 = _loc_to_coil_trans(info_ch['loc'])[:3, :3] _normalize_vectors(v2) ang_shift.append(np.sum(v1 * v2, axis=0)) if oi in grad_picks: extra = [1., fine_cal['imb_cals'][ci][0]] else: extra = [fine_cal['imb_cals'][ci][0], 0.] cal_corrs.append(np.concatenate([extra, cal_loc])) # Adjust channel normal orientations with those from fine calibration # Channel positions are not changed info_ch['loc'][3:] = cal_loc[3:] assert (info_ch['coord_frame'] == FIFF.FIFFV_COORD_DEVICE) meg_picks = pick_types(info, meg=True, exclude=()) assert used[meg_picks].all() assert not used[np.setdiff1d(np.arange(len(used)), meg_picks)].any() # This gets written to the Info struct sss_cal = dict(cal_corrs=np.array(cal_corrs), cal_chans=np.array(cal_chans)) # Log quantification of sensor changes # Deal with numerical precision giving absolute vals slightly more than 1. ang_shift = np.array(ang_shift) np.clip(ang_shift, -1., 1., ang_shift) np.rad2deg(np.arccos(ang_shift), ang_shift) # Convert to degrees logger.info(' Adjusted coil positions by (μ ± σ): ' '%0.1f° ± %0.1f° (max: %0.1f°)' % (np.mean(ang_shift), np.std(ang_shift), np.max(np.abs(ang_shift)))) return calibration, sss_cal def _get_grad_point_coilsets(info, n_types, ignore_ref): """Get point-type coilsets for gradiometers.""" _rotations = dict( x=np.array([[0, 0, 1, 0], [0, 1, 0, 0], [1, 0, 0, 0], [0, 0, 0, 1.]]), y=np.array([[1, 0, 0, 0], [0, 0, 1, 0], [0, 1, 0, 0], [0, 0, 0, 1.]]), z=np.eye(4)) grad_coilsets = list() grad_picks = pick_types(info, meg='grad', exclude=[]) if len(grad_picks) == 0: return grad_coilsets grad_info = pick_info(_simplify_info(info), grad_picks) # Coil_type values for x, y, z point magnetometers # Note: 1D correction files only have x-direction corrections for ch in grad_info['chs']: ch['coil_type'] = FIFF.FIFFV_COIL_POINT_MAGNETOMETER orig_locs = [ch['loc'].copy() for ch in grad_info['chs']] for rot in 'xyz'[:n_types]: # Rotate the Z magnetometer orientation to the destination orientation for ci, ch in enumerate(grad_info['chs']): ch['loc'][3:] = _coil_trans_to_loc(np.dot( _loc_to_coil_trans(orig_locs[ci]), _rotations[rot]))[3:] grad_coilsets.append(_prep_mf_coils(grad_info, ignore_ref)) return grad_coilsets def _sss_basis_point(exp, trans, cal, ignore_ref=False, mag_scale=100.): """Compute multipolar moments for point-like mags (in fine cal).""" # Loop over all coordinate directions desired and create point mags S_tot = 0. # These are magnetometers, so use a uniform coil_scale of 100. this_cs = np.array([mag_scale], float) for imb, coils in zip(cal['grad_imbalances'], cal['grad_coilsets']): S_add = _trans_sss_basis(exp, coils, trans, this_cs) # Scale spaces by gradiometer imbalance S_add *= imb[:, np.newaxis] S_tot += S_add # Return point-like mag bases return S_tot def _regularize_out(int_order, ext_order, mag_or_fine, extended_remove): """Regularize out components based on norm.""" n_in = _get_n_moments(int_order) remove_homog = ext_order > 0 and not mag_or_fine.any() return list(range(n_in, n_in + 3 * remove_homog)) + extended_remove def _regularize_in(int_order, ext_order, S_decomp, mag_or_fine, extended_remove): """Regularize basis set using idealized SNR measure.""" n_in, n_out = _get_n_moments([int_order, ext_order]) # The "signal" terms depend only on the inner expansion order # (i.e., not sensor geometry or head position / expansion origin) a_lm_sq, rho_i = _compute_sphere_activation_in( np.arange(int_order + 1)) degrees, orders = _get_degrees_orders(int_order) a_lm_sq = a_lm_sq[degrees] I_tots = np.zeros(n_in) # we might not traverse all, so use np.zeros in_keepers = list(range(n_in)) out_removes = _regularize_out(int_order, ext_order, mag_or_fine, extended_remove) out_keepers = list(np.setdiff1d(np.arange(n_in, S_decomp.shape[1]), out_removes)) remove_order = [] S_decomp = S_decomp.copy() use_norm = np.sqrt(np.sum(S_decomp * S_decomp, axis=0)) S_decomp /= use_norm eigs = np.zeros((n_in, 2)) # plot = False # for debugging # if plot: # import matplotlib.pyplot as plt # fig, axs = plt.subplots(3, figsize=[6, 12]) # plot_ord = np.empty(n_in, int) # plot_ord.fill(-1) # count = 0 # # Reorder plot to match MF # for degree in range(1, int_order + 1): # for order in range(0, degree + 1): # assert plot_ord[count] == -1 # plot_ord[count] = _deg_ord_idx(degree, order) # count += 1 # if order > 0: # assert plot_ord[count] == -1 # plot_ord[count] = _deg_ord_idx(degree, -order) # count += 1 # assert count == n_in # assert (plot_ord >= 0).all() # assert len(np.unique(plot_ord)) == n_in noise_lev = 5e-13 # noise level in T/m noise_lev *= noise_lev # effectively what would happen by earlier multiply for ii in range(n_in): this_S = S_decomp.take(in_keepers + out_keepers, axis=1) u, s, v = _safe_svd(this_S, full_matrices=False, **check_disable) del this_S eigs[ii] = s[[0, -1]] v = v.T[:len(in_keepers)] v /= use_norm[in_keepers][:, np.newaxis] eta_lm_sq = np.dot(v * 1. / s, u.T) del u, s, v eta_lm_sq *= eta_lm_sq eta_lm_sq = eta_lm_sq.sum(axis=1) eta_lm_sq *= noise_lev # Mysterious scale factors to match MF, likely due to differences # in the basis normalizations... eta_lm_sq[orders[in_keepers] == 0] *= 2 eta_lm_sq *= 0.0025 snr = a_lm_sq[in_keepers] / eta_lm_sq I_tots[ii] = 0.5 * np.log2(snr + 1.).sum() remove_order.append(in_keepers[np.argmin(snr)]) in_keepers.pop(in_keepers.index(remove_order[-1])) # heuristic to quit if we're past the peak to save cycles if ii > 10 and (I_tots[ii - 1:ii + 1] < 0.95 * I_tots.max()).all(): break # if plot and ii == 0: # axs[0].semilogy(snr[plot_ord[in_keepers]], color='k') # if plot: # axs[0].set(ylabel='SNR', ylim=[0.1, 500], xlabel='Component') # axs[1].plot(I_tots) # axs[1].set(ylabel='Information', xlabel='Iteration') # axs[2].plot(eigs[:, 0] / eigs[:, 1]) # axs[2].set(ylabel='Condition', xlabel='Iteration') # Pick the components that give at least 98% of max info # This is done because the curves can be quite flat, and we err on the # side of including rather than excluding components max_info = np.max(I_tots) lim_idx = np.where(I_tots >= 0.98 * max_info)[0][0] in_removes = remove_order[:lim_idx] for ii, ri in enumerate(in_removes): logger.debug(' Condition %0.3f/%0.3f = %03.1f, ' 'Removing in component %s: l=%s, m=%+0.0f' % (tuple(eigs[ii]) + (eigs[ii, 0] / eigs[ii, 1], ri, degrees[ri], orders[ri]))) logger.debug(' Resulting information: %0.1f bits/sample ' '(%0.1f%% of peak %0.1f)' % (I_tots[lim_idx], 100 * I_tots[lim_idx] / max_info, max_info)) return in_removes, out_removes def _compute_sphere_activation_in(degrees): u"""Compute the "in" power from random currents in a sphere. Parameters ---------- degrees : ndarray The degrees to evaluate. Returns ------- a_power : ndarray The a_lm associated for the associated degrees (see :footcite:`KnuutilaEtAl1993`). rho_i : float The current density. References ---------- .. footbibliography:: """ r_in = 0.080 # radius of the randomly-activated sphere # set the observation point r=r_s, az=el=0, so we can just look at m=0 term # compute the resulting current density rho_i # This is the "surface" version of the equation: # b_r_in = 100e-15 # fixed radial field amplitude at distance r_s = 100 fT # r_s = 0.13 # 5 cm from the surface # rho_degrees = np.arange(1, 100) # in_sum = (rho_degrees * (rho_degrees + 1.) / # ((2. * rho_degrees + 1.)) * # (r_in / r_s) ** (2 * rho_degrees + 2)).sum() * 4. * np.pi # rho_i = b_r_in * 1e7 / np.sqrt(in_sum) # rho_i = 5.21334885574e-07 # value for r_s = 0.125 rho_i = 5.91107375632e-07 # deterministic from above, so just store it a_power = _sq(rho_i) * (degrees * r_in ** (2 * degrees + 4) / (_sq(2. * degrees + 1.) * (degrees + 1.))) return a_power, rho_i def _trans_sss_basis(exp, all_coils, trans=None, coil_scale=100.): """Compute SSS basis (optionally) using a dev<->head trans.""" if trans is not None: if not isinstance(trans, Transform): trans = Transform('meg', 'head', trans) assert not np.isnan(trans['trans']).any() all_coils = (apply_trans(trans, all_coils[0]), apply_trans(trans, all_coils[1], move=False), ) + all_coils[2:] if not isinstance(coil_scale, np.ndarray): # Scale all magnetometers (with `coil_class` == 1.0) by `mag_scale` cs = coil_scale coil_scale = np.ones((all_coils[3], 1)) coil_scale[all_coils[4]] = cs S_tot = _sss_basis(exp, all_coils) S_tot *= coil_scale return S_tot # intentionally omitted: st_duration, st_correlation, destination, st_fixed, # st_only @verbose def find_bad_channels_maxwell( raw, limit=7., duration=5., min_count=5, return_scores=False, origin='auto', int_order=8, ext_order=3, calibration=None, cross_talk=None, coord_frame='head', regularize='in', ignore_ref=False, bad_condition='error', head_pos=None, mag_scale=100., skip_by_annotation=('edge', 'bad_acq_skip'), h_freq=40.0, extended_proj=(), verbose=None): r"""Find bad channels using Maxwell filtering. Parameters ---------- raw : instance of Raw Raw data to process. limit : float Detection limit for noisy segments (default is 7.). Smaller values will find more bad channels at increased risk of including good ones. This value can be interpreted as the standard score of differences between the original and Maxwell-filtered data. See the ``Notes`` section for details. .. note:: This setting only concerns *noisy* channel detection. The limit for *flat* channel detection currently cannot be controlled by the user. Flat channel detection is always run before noisy channel detection. duration : float Duration of the segments into which to slice the data for processing, in seconds. Default is 5. min_count : int Minimum number of times a channel must show up as bad in a chunk. Default is 5. return_scores : bool If ``True``, return a dictionary with scoring information for each evaluated segment of the data. Default is ``False``. .. warning:: This feature is experimental and may change in a future version of MNE-Python without prior notice. Please report any problems and enhancement proposals to the developers. .. versionadded:: 0.21 %(origin_maxwell)s %(int_order_maxwell)s %(ext_order_maxwell)s %(calibration_maxwell_cal)s %(cross_talk_maxwell)s %(coord_frame_maxwell)s %(regularize_maxwell_reg)s %(ignore_ref_maxwell)s %(bad_condition_maxwell_cond)s %(head_pos_maxwell)s %(mag_scale_maxwell)s %(skip_by_annotation_maxwell)s h_freq : float | None The cutoff frequency (in Hz) of the low-pass filter that will be applied before processing the data. This defaults to ``40.``, which should provide similar results to MaxFilter. If you do not wish to apply a filter, set this to ``None``. %(extended_proj_maxwell)s %(verbose)s Returns ------- noisy_chs : list List of bad MEG channels that were automatically detected as being noisy among the good MEG channels. flat_chs : list List of MEG channels that were detected as being flat in at least ``min_count`` segments. scores : dict A dictionary with information produced by the scoring algorithms. Only returned when ``return_scores`` is ``True``. It contains the following keys: - ``ch_names`` : ndarray, shape (n_meg,) The names of the MEG channels. Their order corresponds to the order of rows in the ``scores`` and ``limits`` arrays. - ``ch_types`` : ndarray, shape (n_meg,) The types of the MEG channels in ``ch_names`` (``'mag'``, ``'grad'``). - ``bins`` : ndarray, shape (n_windows, 2) The inclusive window boundaries (start and stop; in seconds) used to calculate the scores. - ``scores_flat`` : ndarray, shape (n_meg, n_windows) The scores for testing whether MEG channels are flat. These values correspond to the standard deviation of a segment. See the ``Notes`` section for details. - ``limits_flat`` : ndarray, shape (n_meg, 1) The score thresholds (in standard deviation) above which a segment was classified as "flat". - ``scores_noisy`` : ndarray, shape (n_meg, n_windows) The scores for testing whether MEG channels are noisy. These values correspond to the standard score of a segment. See the ``Notes`` section for details. - ``limits_noisy`` : ndarray, shape (n_meg, 1) The score thresholds (in standard scores) above which a segment was classified as "noisy". .. note:: The scores and limits for channels marked as ``bad`` in the input data will be set to ``np.nan``. See Also -------- annotate_amplitude maxwell_filter Notes ----- All arguments after ``raw``, ``limit``, ``duration``, ``min_count``, and ``return_scores`` are the same as :func:`~maxwell_filter`, except that the following are not allowed in this function because they are unused: ``st_duration``, ``st_correlation``, ``destination``, ``st_fixed``, and ``st_only``. This algorithm, for a given chunk of data: 1. Runs SSS on the data, without removing external components. 2. Excludes channels as *flat* that have had low variability (standard deviation < 0.01 fT or fT/cm in a 30 ms window) in the given or any previous chunk. 3. For each channel :math:`k`, computes the *range* or peak-to-peak :math:`d_k` of the difference between the reconstructed and original data. 4. Computes the average :math:`\mu_d` and standard deviation :math:`\sigma_d` of the differences (after scaling magnetometer data to roughly match the scale of the gradiometer data using ``mag_scale``). 5. Marks channels as bad for the chunk when :math:`d_k > \mu_d + \textrm{limit} \times \sigma_d`. Note that this expression can be easily transformed into :math:`(d_k - \mu_d) / \sigma_d > \textrm{limit}`, which is equivalent to :math:`z(d_k) > \textrm{limit}`, with :math:`z(d_k)` being the standard or z-score of the difference. Data are processed in chunks of the given ``duration``, and channels that are bad for at least ``min_count`` chunks are returned. Channels marked as *flat* in step 2 are excluded from all subsequent steps of noisy channel detection. This algorithm gives results similar to, but not identical with, MaxFilter. Differences arise because MaxFilter processes on a buffer-by-buffer basis (using buffer-size-dependent downsampling logic), uses different filtering characteristics, and possibly other factors. Channels that are near the ``limit`` for a given ``min_count`` are particularly susceptible to being different between the two implementations. .. versionadded:: 0.20 """ if h_freq is not None: if raw.info.get('lowpass') and raw.info['lowpass'] <= h_freq: freq_loc = 'below' if raw.info['lowpass'] < h_freq else 'equal to' msg = (f'The input data has already been low-pass filtered with a ' f'{raw.info["lowpass"]} Hz cutoff frequency, which is ' f'{freq_loc} the requested cutoff of {h_freq} Hz. Not ' f'applying low-pass filter.') logger.info(msg) else: logger.info(f'Applying low-pass filter with {h_freq} Hz cutoff ' f'frequency ...') raw = raw.copy().load_data().filter(l_freq=None, h_freq=h_freq) limit = float(limit) onsets, ends = _annotations_starts_stops( raw, skip_by_annotation, invert=True) del skip_by_annotation # operate on chunks starts = list() stops = list() step = int(round(raw.info['sfreq'] * duration)) for onset, end in zip(onsets, ends): if end - onset >= step: ss = np.arange(onset, end - step + 1, step) starts.extend(ss) ss = ss + step ss[-1] = end stops.extend(ss) min_count = min(_ensure_int(min_count, 'min_count'), len(starts)) logger.info('Scanning for bad channels in %d interval%s (%0.1f sec) ...' % (len(starts), _pl(starts), step / raw.info['sfreq'])) params = _prep_maxwell_filter( raw, skip_by_annotation=[], # already accounted for origin=origin, int_order=int_order, ext_order=ext_order, calibration=calibration, cross_talk=cross_talk, coord_frame=coord_frame, regularize=regularize, ignore_ref=ignore_ref, bad_condition=bad_condition, head_pos=head_pos, mag_scale=mag_scale, extended_proj=extended_proj) del origin, int_order, ext_order, calibration, cross_talk, coord_frame del regularize, ignore_ref, bad_condition, head_pos, mag_scale good_meg_picks = params['meg_picks'][params['good_mask']] assert len(params['meg_picks']) == len(params['coil_scale']) assert len(params['good_mask']) == len(params['meg_picks']) noisy_chs = Counter() flat_chs = Counter() flat_limits = dict(grad=0.01e-13, mag=0.01e-15) these_limits = np.array([ flat_limits['grad'] if pick in params['grad_picks'] else flat_limits['mag'] for pick in good_meg_picks]) flat_step = max(20, int(30 * raw.info['sfreq'] / 1000.)) all_flats = set() # Prepare variables to return if `return_scores=True`. bins = np.empty((len(starts), 2)) # To store start, stop of each segment # We create ndarrays with one row per channel, regardless of channel type # and whether the channel has been marked as "bad" in info or not. This # makes indexing in the loop easier. We only filter this down to the subset # of MEG channels after all processing is done. ch_names = np.array(raw.ch_names) ch_types = np.array(raw.get_channel_types()) scores_flat = np.full((len(ch_names), len(starts)), np.nan) scores_noisy = np.full_like(scores_flat, fill_value=np.nan) thresh_flat = np.full((len(ch_names), 1), np.nan) thresh_noisy = np.full_like(thresh_flat, fill_value=np.nan) for si, (start, stop) in enumerate(zip(starts, stops)): n_iter = 0 orig_data = raw.get_data(None, start, stop, verbose=False) chunk_raw = RawArray( orig_data, params['info'], first_samp=raw.first_samp + start, copy='data', verbose=False) t = chunk_raw.times[[0, -1]] + start / raw.info['sfreq'] logger.info(' Interval %3d: %8.3f - %8.3f' % ((si + 1,) + tuple(t[[0, -1]]))) # Flat pass: SD < 0.01 fT/cm or 0.01 fT for at 30 ms (or 20 samples) n = stop - start flat_stop = n - (n % flat_step) data = chunk_raw.get_data(good_meg_picks, 0, flat_stop) data.shape = (data.shape[0], -1, flat_step) delta = np.std(data, axis=-1).min(-1) # min std across segments # We may want to return this later if `return_scores=True`. bins[si, :] = t[0], t[-1] scores_flat[good_meg_picks, si] = delta thresh_flat[good_meg_picks] = these_limits.reshape(-1, 1) chunk_flats = delta < these_limits chunk_flats = np.where(chunk_flats)[0] chunk_flats = [raw.ch_names[good_meg_picks[chunk_flat]] for chunk_flat in chunk_flats] flat_chs.update(chunk_flats) all_flats |= set(chunk_flats) chunk_flats = sorted(all_flats) these_picks = [pick for pick in good_meg_picks if raw.ch_names[pick] not in chunk_flats] if len(these_picks) == 0: logger.info(f' Flat ({len(chunk_flats):2d}): ') warn('All-flat segment detected, all channels will be marked as ' f'flat and processing will stop (t={t[0]:0.3f}). ' 'Consider using annotate_amplitude before calling this ' 'function with skip_by_annotation="bad_flat" (or similar) to ' 'properly process all segments.') break # no reason to continue # Bad pass chunk_noisy = list() params['st_duration'] = int(round( chunk_raw.times[-1] * raw.info['sfreq'])) for n_iter in range(1, 101): # iteratively exclude the worst ones assert set(raw.info['bads']) & set(chunk_noisy) == set() params['good_mask'][:] = [ chunk_raw.ch_names[pick] not in raw.info['bads'] + chunk_noisy + chunk_flats for pick in params['meg_picks']] chunk_raw._data[:] = orig_data delta = chunk_raw.get_data(these_picks) with use_log_level(False): _run_maxwell_filter( chunk_raw, reconstruct='orig', copy=False, **params) if n_iter == 1 and len(chunk_flats): logger.info(' Flat (%2d): %s' % (len(chunk_flats), ' '.join(chunk_flats))) delta -= chunk_raw.get_data(these_picks) # p2p range_ = np.ptp(delta, axis=-1) cs_picks = np.searchsorted(params['meg_picks'], these_picks) range_ *= params['coil_scale'][cs_picks, 0] mean, std = np.mean(range_), np.std(range_) # z score z = (range_ - mean) / std idx = np.argmax(z) max_ = z[idx] # We may want to return this later if `return_scores=True`. scores_noisy[these_picks, si] = z thresh_noisy[these_picks] = limit if max_ < limit: break name = raw.ch_names[these_picks[idx]] logger.debug(' Bad: %s %0.1f' % (name, max_)) these_picks.pop(idx) chunk_noisy.append(name) noisy_chs.update(chunk_noisy) noisy_chs = sorted((b for b, c in noisy_chs.items() if c >= min_count), key=lambda x: raw.ch_names.index(x)) flat_chs = sorted((f for f, c in flat_chs.items() if c >= min_count), key=lambda x: raw.ch_names.index(x)) # Only include MEG channels. ch_names = ch_names[params['meg_picks']] ch_types = ch_types[params['meg_picks']] scores_flat = scores_flat[params['meg_picks']] thresh_flat = thresh_flat[params['meg_picks']] scores_noisy = scores_noisy[params['meg_picks']] thresh_noisy = thresh_noisy[params['meg_picks']] logger.info(' Static bad channels: %s' % (noisy_chs,)) logger.info(' Static flat channels: %s' % (flat_chs,)) logger.info('[done]') if return_scores: scores = dict(ch_names=ch_names, ch_types=ch_types, bins=bins, scores_flat=scores_flat, limits_flat=thresh_flat, scores_noisy=scores_noisy, limits_noisy=thresh_noisy) return noisy_chs, flat_chs, scores else: return noisy_chs, flat_chs def _read_cross_talk(cross_talk, ch_names): sss_ctc = dict() ctc = None if cross_talk is not None: sss_ctc = _read_ctc(cross_talk) ctc_chs = sss_ctc['proj_items_chs'] # checking for extra space ambiguity in channel names # between old and new fif files if ch_names[0] not in ctc_chs: ctc_chs = _clean_names(ctc_chs, remove_whitespace=True) ch_names = _clean_names(ch_names, remove_whitespace=True) missing = sorted(list(set(ch_names) - set(ctc_chs))) if len(missing) != 0: raise RuntimeError('Missing MEG channels in cross-talk matrix:\n%s' % missing) missing = sorted(list(set(ctc_chs) - set(ch_names))) if len(missing) > 0: warn('Not all cross-talk channels in raw:\n%s' % missing) ctc_picks = [ctc_chs.index(name) for name in ch_names] ctc = sss_ctc['decoupler'][ctc_picks][:, ctc_picks] # I have no idea why, but MF transposes this for storage.. sss_ctc['decoupler'] = sss_ctc['decoupler'].T.tocsc() return ctc, sss_ctc @verbose def compute_maxwell_basis(info, origin='auto', int_order=8, ext_order=3, calibration=None, coord_frame='head', regularize='in', ignore_ref=True, bad_condition='error', mag_scale=100., extended_proj=(), verbose=None): r"""Compute the SSS basis for a given measurement info structure. Parameters ---------- %(info_not_none)s %(origin_maxwell)s %(int_order_maxwell)s %(ext_order_maxwell)s %(calibration_maxwell_cal)s %(coord_frame_maxwell)s %(regularize_maxwell_reg)s %(ignore_ref_maxwell)s %(bad_condition_maxwell_cond)s %(mag_scale_maxwell)s %(extended_proj_maxwell)s %(verbose)s Returns ------- S : ndarray, shape (n_meg, n_moments) The basis that can be used to reconstruct the data. pS : ndarray, shape (n_moments, n_good_meg) The (stabilized) pseudoinverse of the S array. reg_moments : ndarray, shape (n_moments,) The moments that were kept after regularization. n_use_in : int The number of kept moments that were in the internal space. Notes ----- This outputs variants of :math:`\mathbf{S}` and :math:`\mathbf{S^\dagger}` from equations 27 and 37 of :footcite:`TauluKajola2005` with the coil scale for magnetometers already factored in so that the resulting denoising transform of the data to obtain :math:`\hat{\phi}_{in}` from equation 38 would be:: phi_in = S[:, :n_use_in] @ pS[:n_use_in] @ data_meg_good .. versionadded:: 0.23 References ---------- .. footbibliography:: """ from ..io import RawArray _validate_type(info, Info, 'info') raw = RawArray(np.zeros((len(info['ch_names']), 1)), info.copy(), verbose=False) logger.info('Computing Maxwell basis') params = _prep_maxwell_filter( raw=raw, origin=origin, int_order=int_order, ext_order=ext_order, calibration=calibration, coord_frame=coord_frame, destination=None, regularize=regularize, ignore_ref=ignore_ref, bad_condition=bad_condition, mag_scale=mag_scale, extended_proj=extended_proj) _, S_decomp_full, pS_decomp, reg_moments, n_use_in = \ params['_get_this_decomp_trans'](info['dev_head_t'], t=0.) return S_decomp_full, pS_decomp, reg_moments, n_use_in