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_field_interpolation.py
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_field_interpolation.py
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# -*- coding: utf-8 -*-
# Authors: Matti Hämäläinen <msh@nmr.mgh.harvard.edu>
# Alexandre Gramfort <alexandre.gramfort@inria.fr>
# Eric Larson <larsoner@uw.edu>
# The computations in this code were primarily derived from Matti Hämäläinen's
# C code.
from copy import deepcopy
import numpy as np
from scipy import linalg
from ..io.constants import FWD, FIFF
from ..bem import _check_origin
from ..io.pick import pick_types, pick_info
from ..surface import get_head_surf, get_meg_helmet_surf
from ..io.proj import _has_eeg_average_ref_proj, make_projector
from ..transforms import (transform_surface_to, read_trans, _find_trans,
_ensure_trans)
from ._make_forward import _create_meg_coils, _create_eeg_els, _read_coil_defs
from ._lead_dots import (_do_self_dots, _do_surface_dots, _get_legen_table,
_do_cross_dots)
from ..parallel import check_n_jobs
from ..utils import logger, verbose, _check_option, _reg_pinv, _pl
from ..epochs import EpochsArray, BaseEpochs
from ..evoked import Evoked, EvokedArray
def _is_axial_coil(coil):
"""Determine if the coil is axial."""
is_ax = coil['coil_class'] in (
FWD.COILC_MAG, FWD.COILC_AXIAL_GRAD, FWD.COILC_AXIAL_GRAD2)
return is_ax
def _ad_hoc_noise(coils, ch_type='meg'):
"""Create ad-hoc noise covariance."""
# XXX should de-duplicate with make_ad_hoc_cov
v = np.empty(len(coils))
if ch_type == 'meg':
axs = np.array([_is_axial_coil(coil) for coil in coils], dtype=bool)
v[axs] = 4e-28 # 20e-15 ** 2
v[np.logical_not(axs)] = 2.5e-25 # 5e-13 ** 2
else:
v.fill(1e-12) # 1e-6 ** 2
cov = dict(diag=True, data=v, eig=None, eigvec=None)
return cov
def _setup_dots(mode, coils, ch_type):
"""Set up dot products."""
from scipy.interpolate import interp1d
int_rad = 0.06
noise = _ad_hoc_noise(coils, ch_type)
n_coeff, interp = (50, 'nearest') if mode == 'fast' else (100, 'linear')
lut, n_fact = _get_legen_table(ch_type, False, n_coeff, verbose=False)
lut_fun = interp1d(np.linspace(-1, 1, lut.shape[0]), lut, interp, axis=0)
return int_rad, noise, lut_fun, n_fact
def _compute_mapping_matrix(fmd, info):
"""Do the hairy computations."""
logger.info(' Preparing the mapping matrix...')
# assemble a projector and apply it to the data
ch_names = fmd['ch_names']
projs = info.get('projs', list())
proj_op = make_projector(projs, ch_names)[0]
proj_dots = np.dot(proj_op.T, np.dot(fmd['self_dots'], proj_op))
noise_cov = fmd['noise']
# Whiten
if not noise_cov['diag']:
raise NotImplementedError # this shouldn't happen
whitener = np.diag(1.0 / np.sqrt(noise_cov['data'].ravel()))
whitened_dots = np.dot(whitener.T, np.dot(proj_dots, whitener))
# SVD is numerically better than the eigenvalue composition even if
# mat is supposed to be symmetric and positive definite
if fmd.get('pinv_method', 'tsvd') == 'tsvd':
inv, fmd['nest'] = _pinv_trunc(whitened_dots, fmd['miss'])
else:
assert fmd['pinv_method'] == 'tikhonov', fmd['pinv_method']
inv, fmd['nest'] = _pinv_tikhonov(whitened_dots, fmd['miss'])
# Sandwich with the whitener
inv_whitened = np.dot(whitener.T, np.dot(inv, whitener))
# Take into account that the lead fields used to compute
# d->surface_dots were unprojected
inv_whitened_proj = proj_op.T @ inv_whitened
# Finally sandwich in the selection matrix
# This one picks up the correct lead field projection
mapping_mat = np.dot(fmd['surface_dots'], inv_whitened_proj)
# Optionally apply the average electrode reference to the final field map
if fmd['kind'] == 'eeg' and _has_eeg_average_ref_proj(projs):
logger.info(
' The map has an average electrode reference '
f'({mapping_mat.shape[0]} channels)')
mapping_mat -= np.mean(mapping_mat, axis=0)
return mapping_mat
def _pinv_trunc(x, miss):
"""Compute pseudoinverse, truncating at most "miss" fraction of varexp."""
u, s, v = linalg.svd(x, full_matrices=False)
# Eigenvalue truncation
varexp = np.cumsum(s)
varexp /= varexp[-1]
n = np.where(varexp >= (1.0 - miss))[0][0] + 1
logger.info(' Truncating at %d/%d components to omit less than %g '
'(%0.2g)' % (n, len(s), miss, 1. - varexp[n - 1]))
s = 1. / s[:n]
inv = ((u[:, :n] * s) @ v[:n]).T
return inv, n
def _pinv_tikhonov(x, reg):
# _reg_pinv requires square Hermitian, which we have here
inv, _, n = _reg_pinv(x, reg=reg, rank=None)
logger.info(f' Truncating at {n}/{len(x)} components and regularizing '
f'with α={reg:0.1e}')
return inv, n
def _map_meg_or_eeg_channels(info_from, info_to, mode, origin, miss=None):
"""Find mapping from one set of channels to another.
Parameters
----------
info_from : instance of Info
The measurement data to interpolate from.
info_to : instance of Info
The measurement info to interpolate to.
mode : str
Either `'accurate'` or `'fast'`, determines the quality of the
Legendre polynomial expansion used. `'fast'` should be sufficient
for most applications.
origin : array-like, shape (3,) | str
Origin of the sphere in the head coordinate frame and in meters.
Can be ``'auto'``, which means a head-digitization-based origin
fit. Default is ``(0., 0., 0.04)``.
Returns
-------
mapping : array, shape (n_to, n_from)
A mapping matrix.
"""
# no need to apply trans because both from and to coils are in device
# coordinates
info_kinds = set(ch['kind'] for ch in info_to['chs'])
info_kinds |= set(ch['kind'] for ch in info_from['chs'])
if FIFF.FIFFV_REF_MEG_CH in info_kinds: # refs same as MEG
info_kinds |= set([FIFF.FIFFV_MEG_CH])
info_kinds -= set([FIFF.FIFFV_REF_MEG_CH])
info_kinds = sorted(info_kinds)
# This should be guaranteed by the callers
assert (len(info_kinds) == 1 and info_kinds[0] in (
FIFF.FIFFV_MEG_CH, FIFF.FIFFV_EEG_CH))
kind = 'eeg' if info_kinds[0] == FIFF.FIFFV_EEG_CH else 'meg'
#
# Step 1. Prepare the coil definitions
#
if kind == 'meg':
templates = _read_coil_defs(verbose=False)
coils_from = _create_meg_coils(info_from['chs'], 'normal',
info_from['dev_head_t'], templates)
coils_to = _create_meg_coils(info_to['chs'], 'normal',
info_to['dev_head_t'], templates)
pinv_method = 'tsvd'
miss = 1e-4
else:
coils_from = _create_eeg_els(info_from['chs'])
coils_to = _create_eeg_els(info_to['chs'])
pinv_method = 'tikhonov'
miss = 1e-1
if _has_eeg_average_ref_proj(info_from['projs']) and \
not _has_eeg_average_ref_proj(info_to['projs']):
raise RuntimeError(
'info_to must have an average EEG reference projector if '
'info_from has one')
origin = _check_origin(origin, info_from)
#
# Step 2. Calculate the dot products
#
int_rad, noise, lut_fun, n_fact = _setup_dots(mode, coils_from, kind)
logger.info(f' Computing dot products for {len(coils_from)} '
f'{kind.upper()} channel{_pl(coils_from)}...')
self_dots = _do_self_dots(int_rad, False, coils_from, origin, kind,
lut_fun, n_fact, n_jobs=1)
logger.info(f' Computing cross products for {len(coils_from)} → '
f'{len(coils_to)} {kind.upper()} channel{_pl(coils_to)}...')
cross_dots = _do_cross_dots(int_rad, False, coils_from, coils_to,
origin, kind, lut_fun, n_fact).T
ch_names = [c['ch_name'] for c in info_from['chs']]
fmd = dict(kind=kind, ch_names=ch_names,
origin=origin, noise=noise, self_dots=self_dots,
surface_dots=cross_dots, int_rad=int_rad, miss=miss,
pinv_method=pinv_method)
#
# Step 3. Compute the mapping matrix
#
mapping = _compute_mapping_matrix(fmd, info_from)
return mapping
def _as_meg_type_inst(inst, ch_type='grad', mode='fast'):
"""Compute virtual evoked using interpolated fields in mag/grad channels.
Parameters
----------
inst : instance of mne.Evoked or mne.Epochs
The evoked or epochs object.
ch_type : str
The destination channel type. It can be 'mag' or 'grad'.
mode : str
Either `'accurate'` or `'fast'`, determines the quality of the
Legendre polynomial expansion used. `'fast'` should be sufficient
for most applications.
Returns
-------
inst : instance of mne.EvokedArray or mne.EpochsArray
The transformed evoked object containing only virtual channels.
"""
_check_option('ch_type', ch_type, ['mag', 'grad'])
# pick the original and destination channels
pick_from = pick_types(inst.info, meg=True, eeg=False,
ref_meg=False)
pick_to = pick_types(inst.info, meg=ch_type, eeg=False,
ref_meg=False)
if len(pick_to) == 0:
raise ValueError('No channels matching the destination channel type'
' found in info. Please pass an evoked containing'
'both the original and destination channels. Only the'
' locations of the destination channels will be used'
' for interpolation.')
info_from = pick_info(inst.info, pick_from)
info_to = pick_info(inst.info, pick_to)
# XXX someday we should probably expose the origin
mapping = _map_meg_or_eeg_channels(
info_from, info_to, origin=(0., 0., 0.04), mode=mode)
# compute data by multiplying by the 'gain matrix' from
# original sensors to virtual sensors
if hasattr(inst, 'get_data'):
data = inst.get_data()
else:
data = inst.data
ndim = data.ndim
if ndim == 2:
data = data[np.newaxis, :, :]
data_ = np.empty((data.shape[0], len(mapping), data.shape[2]),
dtype=data.dtype)
for d, d_ in zip(data, data_):
d_[:] = np.dot(mapping, d[pick_from])
# keep only the destination channel types
info = pick_info(inst.info, sel=pick_to, copy=True)
# change channel names to emphasize they contain interpolated data
for ch in info['chs']:
ch['ch_name'] += '_v'
info._update_redundant()
info._check_consistency()
if isinstance(inst, Evoked):
assert ndim == 2
data_ = data_[0] # undo new axis
inst_ = EvokedArray(data_, info, tmin=inst.times[0],
comment=inst.comment, nave=inst.nave)
else:
assert isinstance(inst, BaseEpochs)
inst_ = EpochsArray(data_, info, tmin=inst.tmin,
events=inst.events,
event_id=inst.event_id,
metadata=inst.metadata)
return inst_
@verbose
def _make_surface_mapping(info, surf, ch_type='meg', trans=None, mode='fast',
n_jobs=1, origin=(0., 0., 0.04), verbose=None):
"""Re-map M/EEG data to a surface.
Parameters
----------
info : instance of Info
Measurement info.
surf : dict
The surface to map the data to. The required fields are `'rr'`,
`'nn'`, and `'coord_frame'`. Must be in head coordinates.
ch_type : str
Must be either `'meg'` or `'eeg'`, determines the type of field.
trans : None | dict
If None, no transformation applied. Should be a Head<->MRI
transformation.
mode : str
Either `'accurate'` or `'fast'`, determines the quality of the
Legendre polynomial expansion used. `'fast'` should be sufficient
for most applications.
%(n_jobs)s
origin : array-like, shape (3,) | str
Origin of the sphere in the head coordinate frame and in meters.
The default is ``'auto'``, which means a head-digitization-based
origin fit.
%(verbose)s
Returns
-------
mapping : array
A n_vertices x n_sensors array that remaps the MEG or EEG data,
as `new_data = np.dot(mapping, data)`.
"""
if not all(key in surf for key in ['rr', 'nn']):
raise KeyError('surf must have both "rr" and "nn"')
if 'coord_frame' not in surf:
raise KeyError('The surface coordinate frame must be specified '
'in surf["coord_frame"]')
_check_option('mode', mode, ['accurate', 'fast'])
# deal with coordinate frames here -- always go to "head" (easiest)
orig_surf = surf
surf = transform_surface_to(deepcopy(surf), 'head', trans)
n_jobs = check_n_jobs(n_jobs)
origin = _check_origin(origin, info)
#
# Step 1. Prepare the coil definitions
# Do the dot products, assume surf in head coords
#
_check_option('ch_type', ch_type, ['meg', 'eeg'])
if ch_type == 'meg':
picks = pick_types(info, meg=True, eeg=False, ref_meg=False)
logger.info('Prepare MEG mapping...')
else:
picks = pick_types(info, meg=False, eeg=True, ref_meg=False)
logger.info('Prepare EEG mapping...')
if len(picks) == 0:
raise RuntimeError('cannot map, no channels found')
# XXX this code does not do any checking for compensation channels,
# but it seems like this must be intentional from the ref_meg=False
# (presumably from the C code)
chs = [info['chs'][pick] for pick in picks]
# create coil defs in head coordinates
if ch_type == 'meg':
# Put them in head coordinates
coils = _create_meg_coils(chs, 'normal', info['dev_head_t'])
type_str = 'coils'
miss = 1e-4 # Smoothing criterion for MEG
else: # EEG
coils = _create_eeg_els(chs)
type_str = 'electrodes'
miss = 1e-3 # Smoothing criterion for EEG
#
# Step 2. Calculate the dot products
#
int_rad, noise, lut_fun, n_fact = _setup_dots(mode, coils, ch_type)
logger.info('Computing dot products for %i %s...' % (len(coils), type_str))
self_dots = _do_self_dots(int_rad, False, coils, origin, ch_type,
lut_fun, n_fact, n_jobs)
sel = np.arange(len(surf['rr'])) # eventually we should do sub-selection
logger.info('Computing dot products for %i surface locations...'
% len(sel))
surface_dots = _do_surface_dots(int_rad, False, coils, surf, sel,
origin, ch_type, lut_fun, n_fact,
n_jobs)
#
# Step 4. Return the result
#
ch_names = [c['ch_name'] for c in chs]
fmd = dict(kind=ch_type, surf=surf, ch_names=ch_names, coils=coils,
origin=origin, noise=noise, self_dots=self_dots,
surface_dots=surface_dots, int_rad=int_rad, miss=miss)
logger.info('Field mapping data ready')
fmd['data'] = _compute_mapping_matrix(fmd, info)
# bring the original back, whatever coord frame it was in
fmd['surf'] = orig_surf
# Remove some unnecessary fields
del fmd['self_dots']
del fmd['surface_dots']
del fmd['int_rad']
del fmd['miss']
return fmd
@verbose
def make_field_map(evoked, trans='auto', subject=None, subjects_dir=None,
ch_type=None, mode='fast', meg_surf='helmet',
origin=(0., 0., 0.04), n_jobs=1, verbose=None):
"""Compute surface maps used for field display in 3D.
Parameters
----------
evoked : Evoked | Epochs | Raw
The measurement file. Need to have info attribute.
trans : str | 'auto' | None
The full path to the ``*-trans.fif`` file produced during
coregistration. If present or found using 'auto'
the maps will be in MRI coordinates.
If None, map for EEG data will not be available.
subject : str | None
The subject name corresponding to FreeSurfer environment
variable SUBJECT. If None, map for EEG data will not be available.
subjects_dir : str
The path to the freesurfer subjects reconstructions.
It corresponds to Freesurfer environment variable SUBJECTS_DIR.
ch_type : None | 'eeg' | 'meg'
If None, a map for each available channel type will be returned.
Else only the specified type will be used.
mode : 'accurate' | 'fast'
Either ``'accurate'`` or ``'fast'``, determines the quality of the
Legendre polynomial expansion used. ``'fast'`` should be sufficient
for most applications.
meg_surf : 'helmet' | 'head'
Should be ``'helmet'`` or ``'head'`` to specify in which surface
to compute the MEG field map. The default value is ``'helmet'``.
origin : array-like, shape (3,) | 'auto'
Origin of the sphere in the head coordinate frame and in meters.
Can be ``'auto'``, which means a head-digitization-based origin
fit. Default is ``(0., 0., 0.04)``.
.. versionadded:: 0.11
%(n_jobs)s
%(verbose)s
Returns
-------
surf_maps : list
The surface maps to be used for field plots. The list contains
separate ones for MEG and EEG (if both MEG and EEG are present).
"""
info = evoked.info
if ch_type is None:
types = [t for t in ['eeg', 'meg'] if t in evoked]
else:
_check_option('ch_type', ch_type, ['eeg', 'meg'])
types = [ch_type]
if trans == 'auto':
# let's try to do this in MRI coordinates so they're easy to plot
trans = _find_trans(subject, subjects_dir)
if 'eeg' in types and trans is None:
logger.info('No trans file available. EEG data ignored.')
types.remove('eeg')
if len(types) == 0:
raise RuntimeError('No data available for mapping.')
if trans is not None:
if isinstance(trans, str):
trans = read_trans(trans)
trans = _ensure_trans(trans, 'head', 'mri')
_check_option('meg_surf', meg_surf, ['helmet', 'head'])
surfs = []
for this_type in types:
if this_type == 'meg' and meg_surf == 'helmet':
surf = get_meg_helmet_surf(info, trans)
else:
surf = get_head_surf(subject, subjects_dir=subjects_dir)
surfs.append(surf)
surf_maps = list()
for this_type, this_surf in zip(types, surfs):
this_map = _make_surface_mapping(evoked.info, this_surf, this_type,
trans, n_jobs=n_jobs, origin=origin,
mode=mode)
surf_maps.append(this_map)
return surf_maps