# -*- coding: utf-8 -*- # Authors: Mark Wronkiewicz # Eric Larson # Jussi Nurminen # License: BSD (3-clause) from functools import partial from math import factorial from os import path as op import numpy as np from scipy import linalg from .. import __version__ from ..annotations import _annotations_starts_stops from ..bem import _check_origin from ..chpi import quat_to_rot, rot_to_quat 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) 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 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 from ..io.pick import pick_types, pick_info from ..utils import verbose, logger, _clean_names, warn, _time_mask, _pl from ..fixes import _get_args, _safe_svd, _get_sph_harm, einsum from ..externals.six import string_types from ..channels.channels import _get_T1T2_mag_inds # Note: Elekta 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(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'), verbose=None): u"""Apply Maxwell filter to data using multipole moments. .. warning:: Automatic bad channel detection is not currently implemented. It is critical to mark bad channels before running Maxwell filtering to prevent artifact spreading. .. warning:: Maxwell filtering in MNE is not designed or certified for clinical use. Parameters ---------- raw : instance of mne.io.Raw Data to be filtered origin : array-like, shape (3,) | str Origin of internal and external multipolar moment space in meters. The default is ``'auto'``, which means a head-digitization-based origin fit when ``coord_frame='head'``, and ``(0., 0., 0.)`` when ``coord_frame='meg'``. int_order : int Order of internal component of spherical expansion. ext_order : int Order of external component of spherical expansion. calibration : str | None Path to the ``'.dat'`` file with fine calibration coefficients. File can have 1D or 3D gradiometer imbalance correction. This file is machine/site-specific. cross_talk : str | None Path to the FIF file with cross-talk correction information. st_duration : float | None If not None, apply spatiotemporal SSS with specified buffer duration (in seconds). Elekta's default is 10.0 seconds in MaxFilter™ v2.2. Spatiotemporal SSS acts as implicitly as a high-pass filter where the cut-off frequency is 1/st_dur 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 : str The coordinate frame that the ``origin`` is specified in, either ``'meg'`` or ``'head'``. For empty-room recordings that do not have a head<->meg transform ``info['dev_head_t']``, the MEG coordinate frame should be used. destination : str | array-like, shape (3,) | None The destination location for the head. Can be ``None``, which will not change the head position, or a string path to a FIF file containing a MEG device<->head transformation, or a 3-element array giving the coordinates to translate to (with no rotations). For example, ``destination=(0, 0, 0.04)`` would translate the bases as ``--trans default`` would in MaxFilter™ (i.e., to the default head location). regularize : str | None Basis regularization type, must be "in" or None. "in" is the same algorithm as the "-regularize in" option in MaxFilter™. ignore_ref : bool If True, do not include reference channels in compensation. This option should be True for KIT files, since Maxwell filtering with reference channels is not currently supported. bad_condition : str How to deal with ill-conditioned SSS matrices. Can be "error" (default), "warning", "info", or "ignore". head_pos : array | None If array, movement compensation will be performed. The array should be of shape (N, 10), holding the position parameters as returned by e.g. `read_head_pos`. .. versionadded:: 0.12 st_fixed : bool If True (default), do tSSS using the median head position during the ``st_duration`` window. This is the default behavior of MaxFilter and has been most extensively tested. .. versionadded:: 0.12 st_only : bool If True, only tSSS (temporal) projection of MEG data will be performed on the output data. The non-tSSS parameters (e.g., ``int_order``, ``calibration``, ``head_pos``, etc.) will still be used to form the SSS bases used to calculate temporal projectors, but the output MEG data will *only* have temporal projections performed. Noise reduction from SSS basis multiplication, cross-talk cancellation, movement compensation, and so forth will not be applied to the data. This is useful, for example, when evoked movement compensation will be performed with :func:`mne.epochs.average_movements`. .. versionadded:: 0.12 mag_scale : float | str The magenetometer scale-factor used to bring the magnetometers to approximately the same order of magnitude as the gradiometers (default 100.), as they have different units (T vs T/m). Can be ``'auto'`` to use the reciprocal of the physical distance between the gradiometer pickup loops (e.g., 0.0168 m yields 59.5 for VectorView). .. versionadded:: 0.13 skip_by_annotation : str | list of str If a string (or list of str), any annotation segment that begins with the given string will not be included in filtering, and segments on either side of the given excluded annotated segment will be filtered separately (i.e., as independent signals). The default (``('edge', 'bad_acq_skip')`` will separately filter any segments that were concatenated by :func:`mne.concatenate_raws` or :meth:`mne.io.Raw.append`, or separated during acquisition. To disable, provide an empty list. .. versionadded:: 0.17 verbose : bool, str, int, or None If not None, override default verbose level (see :func:`mne.verbose` and :ref:`Logging documentation ` for more). Returns ------- raw_sss : instance of mne.io.Raw The raw data with Maxwell filtering applied. See Also -------- 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 [1]_ and [2]_. .. note:: This code may use multiple CPU cores, see the :ref:`FAQ ` for more information. Compared to Elekta's MaxFilter™ software, the MNE Maxwell filtering routines currently provide the following features: +-----------------------------------------------------------------------------+-----+-----------+ | Feature | MNE | MaxFilter | +=============================================================================+=====+===========+ | Maxwell filtering software shielding | X | X | +-----------------------------------------------------------------------------+-----+-----------+ | Bad channel reconstruction | X | X | +-----------------------------------------------------------------------------+-----+-----------+ | Cross-talk cancellation | X | X | +-----------------------------------------------------------------------------+-----+-----------+ | Fine calibration correction (1D) | X | X | +-----------------------------------------------------------------------------+-----+-----------+ | Fine calibration correction (3D) | X | | +-----------------------------------------------------------------------------+-----+-----------+ | Spatio-temporal SSS (tSSS) | X | X | +-----------------------------------------------------------------------------+-----+-----------+ | Coordinate frame translation | X | X | +-----------------------------------------------------------------------------+-----+-----------+ | Regularization using information theory | X | X | +-----------------------------------------------------------------------------+-----+-----------+ | Movement compensation (raw) | X | X | +-----------------------------------------------------------------------------+-----+-----------+ | Movement compensation (:func:`epochs `) | X | | +-----------------------------------------------------------------------------+-----+-----------+ | :func:`cHPI subtraction ` | X | X | +-----------------------------------------------------------------------------+-----+-----------+ | Double floating point precision | X | | +-----------------------------------------------------------------------------+-----+-----------+ | Seamless processing of split (``-1.fif``) and concatenated files | X | | +-----------------------------------------------------------------------------+-----+-----------+ | Certified for clinical use | | X | +-----------------------------------------------------------------------------+-----+-----------+ | Automatic bad channel detection | | X | +-----------------------------------------------------------------------------+-----+-----------+ | Head position estimation | | X | +-----------------------------------------------------------------------------+-----+-----------+ Epoch-based movement compensation is described in [1]_. Use of Maxwell filtering routines with non-Elekta systems is currently **experimental**. Worse results for non-Elekta 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 Elekta Oy, Helsinki, Finland. 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 ---------- .. [1] Taulu S. and Kajola M. "Presentation of electromagnetic multichannel data: The signal space separation method," Journal of Applied Physics, vol. 97, pp. 124905 1-10, 2005. http://lib.tkk.fi/Diss/2008/isbn9789512295654/article2.pdf .. [2] Taulu S. and Simola J. "Spatiotemporal signal space separation method for rejecting nearby interference in MEG measurements," Physics in Medicine and Biology, vol. 51, pp. 1759-1768, 2006. http://lib.tkk.fi/Diss/2008/isbn9789512295654/article3.pdf """ # noqa: E501 # 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 if not isinstance(raw, BaseRaw): raise TypeError('raw must be Raw, not %s' % type(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) if coord_frame not in ('head', 'meg'): raise ValueError('coord_frame must be either "head" or "meg", not "%s"' % coord_frame) head_frame = True if coord_frame == 'head' else False recon_trans = _check_destination(destination, raw.info, head_frame) onsets, ends = _annotations_starts_stops( raw, skip_by_annotation, 'skip_by_annotation', invert=True) max_samps = (ends - onsets).max() if st_duration is not None: st_duration = float(st_duration) if not 0. < st_duration * raw.info['sfreq'] <= 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, max_samps / raw.info['sfreq'])) 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.') if not isinstance(bad_condition, string_types) or \ bad_condition not in ['error', 'warning', 'ignore', 'info']: raise ValueError('bad_condition must be "error", "warning", "info", or' ' "ignore", not %s' % bad_condition) 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 logger.info('Maxwell filtering raw data') add_channels = (head_pos[0] is not None) and not st_only raw_sss, pos_picks = _copy_preload_add_channels( raw, add_channels=add_channels) del raw if not st_only: # remove MEG projectors, they won't apply now _remove_meg_projs(raw_sss) info = raw_sss.info meg_picks, mag_picks, grad_picks, good_picks, mag_or_fine = \ _get_mf_picks(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) # # 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 orig_origin, orig_coord_frame = origin, coord_frame del origin, coord_frame origin_head.setflags(write=False) n_in, n_out = _get_n_moments([int_order, ext_order]) # # Cross-talk processing # if cross_talk is not None: sss_ctc = _read_ctc(cross_talk) ctc_chs = sss_ctc['proj_items_chs'] meg_ch_names = [info['ch_names'][p] for p in meg_picks] # checking for extra space ambiguity in channel names # between old and new fif files if meg_ch_names[0] not in ctc_chs: ctc_chs = _clean_names(ctc_chs, remove_whitespace=True) missing = sorted(list(set(meg_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(meg_ch_names))) if len(missing) > 0: warn('Not all cross-talk channels in raw:\n%s' % missing) ctc_picks = [ctc_chs.index(info['ch_names'][c]) for c in meg_picks[good_picks]] assert len(ctc_picks) == len(good_picks) # otherwise we errored 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() else: sss_ctc = dict() # # 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 # 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 = max(int(round(10. * info['sfreq'])), 1) st_correlation = None st_when = 'never' st_duration = min(max_samps, st_duration) del st_fixed # 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) / info['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 / info['sfreq'], st_duration / info['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 # # Do the heavy lifting # # Figure out which transforms we need for each tSSS block # (and transform pos[1] to times) head_pos[1] = raw_sss.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_picks=good_picks, mag_or_fine=mag_or_fine, bad_condition=bad_condition, mag_scale=mag_scale) S_decomp, pS_decomp, reg_moments, n_use_in = _get_this_decomp_trans( info['dev_head_t'], t=0.) reg_moments_0 = reg_moments.copy() # 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)): 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_picks], 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 cross_talk 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, 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: out_meg_data[:, rel_start:rel_stop] = \ np.dot(S_recon.take(reg_moments[:n_use_in], axis=1), mm_in) 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 # Update info if not st_only: info['dev_head_t'] = recon_trans # set the reconstruction transform _update_sss_info(raw_sss, orig_origin, int_order, ext_order, len(good_picks), orig_coord_frame, sss_ctc, sss_cal, max_st, reg_moments_0, st_only) logger.info('[done]') 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, string_types): 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 = set(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, string_types): 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 def _prep_mf_coils(info, ignore_ref=True): """Get all coil integration information loaded and sorted.""" coils, comp_coils = _prep_meg_channels( info, accurate=True, 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 = dict((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 [2]_ 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): """Load data for processing and (maybe) add cHPI pos channels.""" raw = raw.copy() 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') raw._preload_data(out_data[:len(raw.ch_names)], verbose=False) 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 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.""" 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_picks, mag_or_fine, bad_condition, t, mag_scale): """Get a decomposition matrix and pseudoinverse matrices.""" # # Fine calibration processing (point-like magnetometers and calib. coeffs) # S_decomp = _get_s_decomp(exp, all_coils, trans, coil_scale, cal, ignore_ref, grad_picks, mag_picks, good_picks, mag_scale) # # Regularization # S_decomp, pS_decomp, sing, reg_moments, n_use_in = _regularize( regularize, exp, S_decomp, mag_or_fine, t=t) # Pseudo-inverse of total multipolar moment basis set (Part of Eq. 37) cond = sing[0] / sing[-1] logger.debug(' Decomposition matrix condition: %0.1f' % cond) 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_picks].T S_decomp /= coil_scale[good_picks] return S_decomp, pS_decomp, reg_moments, n_use_in def _get_s_decomp(exp, all_coils, trans, coil_scale, cal, ignore_ref, grad_picks, mag_picks, good_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. S_decomp[grad_picks, :] += grad_cals # Scale magnetometers by calibration coefficient S_decomp[mag_picks, :] /= cal['mag_cals'] # We need to be careful about KIT gradiometers S_decomp = S_decomp[good_picks] return S_decomp @verbose def _regularize(regularize, exp, S_decomp, mag_or_fine, 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, n_out = _get_n_moments([int_order, ext_order]) 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) else: in_removes = [] out_removes = _regularize_out(int_order, ext_order, mag_or_fine) reg_in_moments = np.setdiff1d(np.arange(n_in), in_removes) reg_out_moments = np.setdiff1d(np.arange(n_in, n_in + n_out), 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) pS_decomp, sing = _col_norm_pinv(S_decomp.copy()) 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, pS_decomp, sing, reg_moments, n_use_in def _get_mf_picks(info, int_order, ext_order, ignore_ref=False): """Pick types for Maxwell filtering.""" # Check for T1/T2 mag types mag_inds_T1T2 = _get_T1T2_mag_inds(info) if len(mag_inds_T1T2) > 0: warn('%d T1/T2 magnetometer channel types found. If using SSS, it is ' 'advised to replace coil types using "fix_mag_coil_types".' % len(mag_inds_T1T2)) # 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_picks = pick_types(meg_info, meg=True, ref_meg=ref, exclude='bads') n_bases = _get_n_moments([int_order, ext_order]).sum() if n_bases > len(good_picks): raise ValueError('Number of requested bases (%s) exceeds number of ' 'good sensors (%s)' % (str(n_bases), len(good_picks))) recons = [ch for ch in meg_info['bads']] if len(recons) > 0: logger.info(' Bad MEG channels being reconstructed: %s' % recons) else: logger.info(' No bad MEG channels') 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_picks, mag_or_fine def _check_regularize(regularize): """Ensure regularize is valid.""" if not (regularize is None or (isinstance(regularize, string_types) 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.""" int_order, ext_order = exp['int_order'], exp['ext_order'] origin = exp['origin'] # 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 = _get_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 = einsum('ij,ij->i', gr, cosmags) vals = np.bincount(bins, gr, len(coils)) spc[:, _deg_ord_idx(degree, oo)] = -vals else: grads = 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 millimeters 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]) S_tot = np.empty((n_coils, n_in + n_out), np.float64) rmags = rmags - exp['origin'] S_in = S_tot[:, :n_in] S_out = S_tot[:, n_in:] # 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) 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. del rmags # 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) 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 (Elekta 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 * 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 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 * 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 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 = einsum('ij,ij->i', grads, cosmags) return np.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 = 1. 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.""" return np.array([(sin_pol * cos_az * b_r + cos_pol * cos_az * b_pol - sin_az * b_az), (sin_pol * sin_az * b_r + cos_pol * sin_az * b_pol + cos_az * b_az), cos_pol * b_r - sin_pol * b_pol]) 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): """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 and in millimeters 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. """ n_in, n_out = _get_n_moments([int_order, ext_order]) raw.info['maxshield'] = False components = np.zeros(n_in + n_out).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) block_id = _generate_meas_id() 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() # not available on really old versions of SciPy if 'check_finite' in _get_args(linalg.svd): check_disable['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 [2]_ # Note that the procedure here is an updated version of [2]_ (and used in # Elekta'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! 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 [2]_ # 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 _update_sensor_geometry(info, fine_cal, ignore_ref): """Replace sensor geometry information and reorder cal_chs.""" from ._fine_cal import read_fine_calibration logger.info(' Using fine calibration %s' % op.basename(fine_cal)) fine_cal = read_fine_calibration(fine_cal) # filename -> dict ch_names = _clean_names(info['ch_names'], remove_whitespace=True) info_to_cal = dict() 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(set(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)) 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 [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 = np.zeros((len(fine_cal['ch_names']), 3)) 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 ch_names[oi] == fine_cal['ch_names'][ci] 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[ci] = 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) assert used[meg_picks].all() assert not used[np.setdiff1d(np.arange(len(used)), meg_picks)].any() ang_shift = ang_shift[list(info_to_cal.values())] # subselect used ones # 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. 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_info = pick_info( _simplify_info(info), pick_types(info, meg='grad', exclude=[])) # 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): """Regularize out components based on norm.""" n_in = _get_n_moments(int_order) out_removes = list(np.arange(0 if mag_or_fine.any() else 3) + n_in) return list(out_removes) def _regularize_in(int_order, ext_order, S_decomp, mag_or_fine): """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) out_keepers = list(np.setdiff1d(np.arange(n_in, n_in + n_out), 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 Elekta, 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 [1]_). rho_i : float The current density. References ---------- .. [1] A 122-channel whole-cortex SQUID system for measuring the brain’s magnetic fields. Knuutila et al. IEEE Transactions on Magnetics, Vol 29 No 6, Nov 1993. """ 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