/
dipole.py
1528 lines (1348 loc) · 56.3 KB
/
dipole.py
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# -*- coding: utf-8 -*-
"""Single-dipole functions and classes."""
# Authors: Alexandre Gramfort <alexandre.gramfort@inria.fr>
# Eric Larson <larson.eric.d@gmail.com>
#
# License: Simplified BSD
from copy import deepcopy
import functools
from functools import partial
import re
import numpy as np
from .cov import compute_whitener, _ensure_cov
from .io.constants import FIFF
from .io.pick import pick_types
from .io.proj import make_projector, _needs_eeg_average_ref_proj
from .bem import _fit_sphere
from .evoked import _read_evoked, _aspect_rev, _write_evokeds
from .fixes import pinvh
from ._freesurfer import read_freesurfer_lut, _get_aseg
from .transforms import _print_coord_trans, _coord_frame_name, apply_trans
from .viz.evoked import _plot_evoked
from ._freesurfer import head_to_mni, head_to_mri
from .forward._make_forward import (_get_trans, _setup_bem,
_prep_meg_channels, _prep_eeg_channels)
from .forward._compute_forward import (_compute_forwards_meeg,
_prep_field_computation)
from .surface import (transform_surface_to, _compute_nearest,
_points_outside_surface)
from .bem import _bem_find_surface, _bem_surf_name
from .source_space import _make_volume_source_space, SourceSpaces
from .parallel import parallel_func
from .utils import (logger, verbose, _time_mask, warn, _check_fname,
check_fname, _pl, fill_doc, _check_option,
_svd_lwork, _repeated_svd, _get_blas_funcs, _validate_type,
copy_function_doc_to_method_doc, TimeMixin)
from .viz import plot_dipole_locations
@fill_doc
class Dipole(TimeMixin):
u"""Dipole class for sequential dipole fits.
.. note:: This class should usually not be instantiated directly,
instead :func:`mne.read_dipole` should be used.
Used to store positions, orientations, amplitudes, times, goodness of fit
of dipoles, typically obtained with Neuromag/xfit, mne_dipole_fit
or certain inverse solvers. Note that dipole position vectors are given in
the head coordinate frame.
Parameters
----------
times : array, shape (n_dipoles,)
The time instants at which each dipole was fitted (sec).
pos : array, shape (n_dipoles, 3)
The dipoles positions (m) in head coordinates.
amplitude : array, shape (n_dipoles,)
The amplitude of the dipoles (Am).
ori : array, shape (n_dipoles, 3)
The dipole orientations (normalized to unit length).
gof : array, shape (n_dipoles,)
The goodness of fit.
name : str | None
Name of the dipole.
conf : dict
Confidence limits in dipole orientation for "vol" in m^3 (volume),
"depth" in m (along the depth axis), "long" in m (longitudinal axis),
"trans" in m (transverse axis), "qlong" in Am, and "qtrans" in Am
(currents). The current confidence limit in the depth direction is
assumed to be zero (although it can be non-zero when a BEM is used).
.. versionadded:: 0.15
khi2 : array, shape (n_dipoles,)
The χ^2 values for the fits.
.. versionadded:: 0.15
nfree : array, shape (n_dipoles,)
The number of free parameters for each fit.
.. versionadded:: 0.15
%(verbose)s
See Also
--------
fit_dipole
DipoleFixed
read_dipole
Notes
-----
This class is for sequential dipole fits, where the position
changes as a function of time. For fixed dipole fits, where the
position is fixed as a function of time, use :class:`mne.DipoleFixed`.
"""
@verbose
def __init__(self, times, pos, amplitude, ori, gof,
name=None, conf=None, khi2=None, nfree=None,
*, verbose=None): # noqa: D102
self._set_times(np.array(times))
self.pos = np.array(pos)
self.amplitude = np.array(amplitude)
self.ori = np.array(ori)
self.gof = np.array(gof)
self.name = name
self.conf = dict()
if conf is not None:
for key, value in conf.items():
self.conf[key] = np.array(value)
self.khi2 = np.array(khi2) if khi2 is not None else None
self.nfree = np.array(nfree) if nfree is not None else None
def __repr__(self): # noqa: D105
s = "n_times : %s" % len(self.times)
s += ", tmin : %0.3f" % np.min(self.times)
s += ", tmax : %0.3f" % np.max(self.times)
return "<Dipole | %s>" % s
@verbose
def save(self, fname, overwrite=False, *, verbose=None):
"""Save dipole in a .dip or .bdip file.
Parameters
----------
fname : str
The name of the .dip or .bdip file.
%(overwrite)s
.. versionadded:: 0.20
%(verbose)s
Notes
-----
.. versionchanged:: 0.20
Support for writing bdip (Xfit binary) files.
"""
# obligatory fields
fname = _check_fname(fname, overwrite=overwrite)
if fname.endswith('.bdip'):
_write_dipole_bdip(fname, self)
else:
_write_dipole_text(fname, self)
@verbose
def crop(self, tmin=None, tmax=None, include_tmax=True, verbose=None):
"""Crop data to a given time interval.
Parameters
----------
tmin : float | None
Start time of selection in seconds.
tmax : float | None
End time of selection in seconds.
%(include_tmax)s
%(verbose)s
Returns
-------
self : instance of Dipole
The cropped instance.
"""
sfreq = None
if len(self.times) > 1:
sfreq = 1. / np.median(np.diff(self.times))
mask = _time_mask(self.times, tmin, tmax, sfreq=sfreq,
include_tmax=include_tmax)
self._set_times(self.times[mask])
for attr in ('pos', 'gof', 'amplitude', 'ori', 'khi2', 'nfree'):
if getattr(self, attr) is not None:
setattr(self, attr, getattr(self, attr)[mask])
for key in self.conf.keys():
self.conf[key] = self.conf[key][mask]
return self
def copy(self):
"""Copy the Dipoles object.
Returns
-------
dip : instance of Dipole
The copied dipole instance.
"""
return deepcopy(self)
@verbose
@copy_function_doc_to_method_doc(plot_dipole_locations)
def plot_locations(self, trans, subject, subjects_dir=None,
mode='orthoview', coord_frame='mri', idx='gof',
show_all=True, ax=None, block=False, show=True,
scale=None, color=None, *, highlight_color='r',
fig=None, title=None, head_source='seghead',
surf='pial', width=None, verbose=None):
return plot_dipole_locations(
self, trans, subject, subjects_dir, mode, coord_frame, idx,
show_all, ax, block, show, scale=scale, color=color,
highlight_color=highlight_color, fig=fig, title=title,
head_source=head_source, surf=surf, width=width)
@verbose
def to_mni(self, subject, trans, subjects_dir=None,
verbose=None):
"""Convert dipole location from head to MNI coordinates.
Parameters
----------
%(subject)s
%(trans_not_none)s
%(subjects_dir)s
%(verbose)s
Returns
-------
pos_mni : array, shape (n_pos, 3)
The MNI coordinates (in mm) of pos.
"""
mri_head_t, trans = _get_trans(trans)
return head_to_mni(self.pos, subject, mri_head_t,
subjects_dir=subjects_dir, verbose=verbose)
@verbose
def to_mri(self, subject, trans, subjects_dir=None,
verbose=None):
"""Convert dipole location from head to MRI surface RAS coordinates.
Parameters
----------
%(subject)s
%(trans_not_none)s
%(subjects_dir)s
%(verbose)s
Returns
-------
pos_mri : array, shape (n_pos, 3)
The Freesurfer surface RAS coordinates (in mm) of pos.
"""
mri_head_t, trans = _get_trans(trans)
return head_to_mri(self.pos, subject, mri_head_t,
subjects_dir=subjects_dir, verbose=verbose)
@verbose
def to_volume_labels(self, trans, subject='fsaverage', aseg='aparc+aseg',
subjects_dir=None, verbose=None):
"""Find an ROI in atlas for the dipole positions.
Parameters
----------
%(trans)s
%(subject)s
%(aseg)s
%(subjects_dir)s
%(verbose)s
Returns
-------
labels : list
List of anatomical region names from anatomical segmentation atlas.
Notes
-----
.. versionadded:: 0.24
"""
aseg_img, aseg_data = _get_aseg(aseg, subject, subjects_dir)
mri_vox_t = np.linalg.inv(aseg_img.header.get_vox2ras_tkr())
# Load freesurface atlas LUT
lut_inv = read_freesurfer_lut()[0]
lut = {v: k for k, v in lut_inv.items()}
# transform to voxel space from head space
pos = self.to_mri(subject, trans, subjects_dir=subjects_dir,
verbose=verbose)
pos = apply_trans(mri_vox_t, pos)
pos = np.rint(pos).astype(int)
# Get voxel value and label from LUT
labels = [lut.get(aseg_data[tuple(coord)], 'Unknown') for coord in pos]
return labels
def plot_amplitudes(self, color='k', show=True):
"""Plot the dipole amplitudes as a function of time.
Parameters
----------
color : matplotlib color
Color to use for the trace.
show : bool
Show figure if True.
Returns
-------
fig : matplotlib.figure.Figure
The figure object containing the plot.
"""
from .viz import plot_dipole_amplitudes
return plot_dipole_amplitudes([self], [color], show)
def __getitem__(self, item):
"""Get a time slice.
Parameters
----------
item : array-like or slice
The slice of time points to use.
Returns
-------
dip : instance of Dipole
The sliced dipole.
"""
if isinstance(item, int): # make sure attributes stay 2d
item = [item]
selected_times = self.times[item].copy()
selected_pos = self.pos[item, :].copy()
selected_amplitude = self.amplitude[item].copy()
selected_ori = self.ori[item, :].copy()
selected_gof = self.gof[item].copy()
selected_name = self.name
selected_conf = dict()
for key in self.conf.keys():
selected_conf[key] = self.conf[key][item]
selected_khi2 = self.khi2[item] if self.khi2 is not None else None
selected_nfree = self.nfree[item] if self.nfree is not None else None
return Dipole(
selected_times, selected_pos, selected_amplitude, selected_ori,
selected_gof, selected_name, selected_conf, selected_khi2,
selected_nfree)
def __len__(self):
"""Return the number of dipoles.
Returns
-------
len : int
The number of dipoles.
Examples
--------
This can be used as::
>>> len(dipoles) # doctest: +SKIP
10
"""
return self.pos.shape[0]
def _read_dipole_fixed(fname):
"""Read a fixed dipole FIF file."""
logger.info('Reading %s ...' % fname)
info, nave, aspect_kind, comment, times, data, _ = _read_evoked(fname)
return DipoleFixed(info, data, times, nave, aspect_kind, comment=comment)
@fill_doc
class DipoleFixed(TimeMixin):
"""Dipole class for fixed-position dipole fits.
.. note:: This class should usually not be instantiated directly,
instead :func:`mne.read_dipole` should be used.
Parameters
----------
%(info_not_none)s
data : array, shape (n_channels, n_times)
The dipole data.
times : array, shape (n_times,)
The time points.
nave : int
Number of averages.
aspect_kind : int
The kind of data.
comment : str
The dipole comment.
%(verbose)s
See Also
--------
read_dipole
Dipole
fit_dipole
Notes
-----
This class is for fixed-position dipole fits, where the position
(and maybe orientation) is static over time. For sequential dipole fits,
where the position can change a function of time, use :class:`mne.Dipole`.
.. versionadded:: 0.12
"""
@verbose
def __init__(self, info, data, times, nave, aspect_kind,
comment='', *, verbose=None): # noqa: D102
self.info = info
self.nave = nave
self._aspect_kind = aspect_kind
self.kind = _aspect_rev.get(aspect_kind, 'unknown')
self.comment = comment
self._set_times(np.array(times))
self.data = data
self.preload = True
self._update_first_last()
def __repr__(self): # noqa: D105
s = "n_times : %s" % len(self.times)
s += ", tmin : %s" % np.min(self.times)
s += ", tmax : %s" % np.max(self.times)
return "<DipoleFixed | %s>" % s
def copy(self):
"""Copy the DipoleFixed object.
Returns
-------
inst : instance of DipoleFixed
The copy.
Notes
-----
.. versionadded:: 0.16
"""
return deepcopy(self)
@property
def ch_names(self):
"""Channel names."""
return self.info['ch_names']
@verbose
def save(self, fname, verbose=None):
"""Save dipole in a .fif file.
Parameters
----------
fname : str
The name of the .fif file. Must end with ``'.fif'`` or
``'.fif.gz'`` to make it explicit that the file contains
dipole information in FIF format.
%(verbose)s
"""
check_fname(fname, 'DipoleFixed', ('-dip.fif', '-dip.fif.gz',
'_dip.fif', '_dip.fif.gz',),
('.fif', '.fif.gz'))
_write_evokeds(fname, self, check=False)
def plot(self, show=True, time_unit='s'):
"""Plot dipole data.
Parameters
----------
show : bool
Call pyplot.show() at the end or not.
time_unit : str
The units for the time axis, can be "ms" or "s" (default).
.. versionadded:: 0.16
Returns
-------
fig : instance of matplotlib.figure.Figure
The figure containing the time courses.
"""
return _plot_evoked(self, picks=None, exclude=(), unit=True, show=show,
ylim=None, xlim='tight', proj=False, hline=None,
units=None, scalings=None, titles=None, axes=None,
gfp=False, window_title=None, spatial_colors=False,
plot_type="butterfly", selectable=False,
time_unit=time_unit)
# #############################################################################
# IO
@verbose
def read_dipole(fname, verbose=None):
"""Read .dip file from Neuromag/xfit or MNE.
Parameters
----------
fname : str
The name of the .dip or .fif file.
%(verbose)s
Returns
-------
%(dipole)s
See Also
--------
Dipole
DipoleFixed
fit_dipole
Notes
-----
.. versionchanged:: 0.20
Support for reading bdip (Xfit binary) format.
"""
fname = _check_fname(fname, overwrite='read', must_exist=True)
if fname.endswith('.fif') or fname.endswith('.fif.gz'):
return _read_dipole_fixed(fname)
elif fname.endswith('.bdip'):
return _read_dipole_bdip(fname)
else:
return _read_dipole_text(fname)
def _read_dipole_text(fname):
"""Read a dipole text file."""
# Figure out the special fields
need_header = True
def_line = name = None
# There is a bug in older np.loadtxt regarding skipping fields,
# so just read the data ourselves (need to get name and header anyway)
data = list()
with open(fname, 'r') as fid:
for line in fid:
if not (line.startswith('%') or line.startswith('#')):
need_header = False
data.append(line.strip().split())
else:
if need_header:
def_line = line
if line.startswith('##') or line.startswith('%%'):
m = re.search('Name "(.*) dipoles"', line)
if m:
name = m.group(1)
del line
data = np.atleast_2d(np.array(data, float))
if def_line is None:
raise IOError('Dipole text file is missing field definition '
'comment, cannot parse %s' % (fname,))
# actually parse the fields
def_line = def_line.lstrip('%').lstrip('#').strip()
# MNE writes it out differently than Elekta, let's standardize them...
fields = re.sub(r'([X|Y|Z] )\(mm\)', # "X (mm)", etc.
lambda match: match.group(1).strip() + '/mm', def_line)
fields = re.sub(r'\((.*?)\)', # "Q(nAm)", etc.
lambda match: '/' + match.group(1), fields)
fields = re.sub('(begin|end) ', # "begin" and "end" with no units
lambda match: match.group(1) + '/ms', fields)
fields = fields.lower().split()
required_fields = ('begin/ms',
'x/mm', 'y/mm', 'z/mm',
'q/nam', 'qx/nam', 'qy/nam', 'qz/nam',
'g/%')
optional_fields = ('khi^2', 'free', # standard ones
# now the confidence fields (up to 5!)
'vol/mm^3', 'depth/mm', 'long/mm', 'trans/mm',
'qlong/nam', 'qtrans/nam')
conf_scales = [1e-9, 1e-3, 1e-3, 1e-3, 1e-9, 1e-9]
missing_fields = sorted(set(required_fields) - set(fields))
if len(missing_fields) > 0:
raise RuntimeError('Could not find necessary fields in header: %s'
% (missing_fields,))
handled_fields = set(required_fields) | set(optional_fields)
assert len(handled_fields) == len(required_fields) + len(optional_fields)
ignored_fields = sorted(set(fields) -
set(handled_fields) -
{'end/ms'})
if len(ignored_fields) > 0:
warn('Ignoring extra fields in dipole file: %s' % (ignored_fields,))
if len(fields) != data.shape[1]:
raise IOError('More data fields (%s) found than data columns (%s): %s'
% (len(fields), data.shape[1], fields))
logger.info("%d dipole(s) found" % len(data))
if 'end/ms' in fields:
if np.diff(data[:, [fields.index('begin/ms'),
fields.index('end/ms')]], 1, -1).any():
warn('begin and end fields differed, but only begin will be used '
'to store time values')
# Find the correct column in our data array, then scale to proper units
idx = [fields.index(field) for field in required_fields]
assert len(idx) >= 9
times = data[:, idx[0]] / 1000.
pos = 1e-3 * data[:, idx[1:4]] # put data in meters
amplitude = data[:, idx[4]]
norm = amplitude.copy()
amplitude /= 1e9
norm[norm == 0] = 1
ori = data[:, idx[5:8]] / norm[:, np.newaxis]
gof = data[:, idx[8]]
# Deal with optional fields
optional = [None] * 2
for fi, field in enumerate(optional_fields[:2]):
if field in fields:
optional[fi] = data[:, fields.index(field)]
khi2, nfree = optional
conf = dict()
for field, scale in zip(optional_fields[2:], conf_scales): # confidence
if field in fields:
conf[field.split('/')[0]] = scale * data[:, fields.index(field)]
return Dipole(times, pos, amplitude, ori, gof, name, conf, khi2, nfree)
def _write_dipole_text(fname, dip):
fmt = ' %7.1f %7.1f %8.2f %8.2f %8.2f %8.3f %8.3f %8.3f %8.3f %6.2f'
header = ('# begin end X (mm) Y (mm) Z (mm)'
' Q(nAm) Qx(nAm) Qy(nAm) Qz(nAm) g/%')
t = dip.times[:, np.newaxis] * 1000.
gof = dip.gof[:, np.newaxis]
amp = 1e9 * dip.amplitude[:, np.newaxis]
out = (t, t, dip.pos / 1e-3, amp, dip.ori * amp, gof)
# optional fields
fmts = dict(khi2=(' khi^2', ' %8.1f', 1.),
nfree=(' free', ' %5d', 1),
vol=(' vol/mm^3', ' %9.3f', 1e9),
depth=(' depth/mm', ' %9.3f', 1e3),
long=(' long/mm', ' %8.3f', 1e3),
trans=(' trans/mm', ' %9.3f', 1e3),
qlong=(' Qlong/nAm', ' %10.3f', 1e9),
qtrans=(' Qtrans/nAm', ' %11.3f', 1e9),
)
for key in ('khi2', 'nfree'):
data = getattr(dip, key)
if data is not None:
header += fmts[key][0]
fmt += fmts[key][1]
out += (data[:, np.newaxis] * fmts[key][2],)
for key in ('vol', 'depth', 'long', 'trans', 'qlong', 'qtrans'):
data = dip.conf.get(key)
if data is not None:
header += fmts[key][0]
fmt += fmts[key][1]
out += (data[:, np.newaxis] * fmts[key][2],)
out = np.concatenate(out, axis=-1)
# NB CoordinateSystem is hard-coded as Head here
with open(fname, 'wb') as fid:
fid.write('# CoordinateSystem "Head"\n'.encode('utf-8'))
fid.write((header + '\n').encode('utf-8'))
np.savetxt(fid, out, fmt=fmt)
if dip.name is not None:
fid.write(('## Name "%s dipoles" Style "Dipoles"'
% dip.name).encode('utf-8'))
_BDIP_ERROR_KEYS = ('depth', 'long', 'trans', 'qlong', 'qtrans')
def _read_dipole_bdip(fname):
name = None
nfree = None
with open(fname, 'rb') as fid:
# Which dipole in a multi-dipole set
times = list()
pos = list()
amplitude = list()
ori = list()
gof = list()
conf = dict(vol=list())
khi2 = list()
has_errors = None
while True:
num = np.frombuffer(fid.read(4), '>i4')
if len(num) == 0:
break
times.append(np.frombuffer(fid.read(4), '>f4')[0])
fid.read(4) # end
fid.read(12) # r0
pos.append(np.frombuffer(fid.read(12), '>f4'))
Q = np.frombuffer(fid.read(12), '>f4')
amplitude.append(np.linalg.norm(Q))
ori.append(Q / amplitude[-1])
gof.append(100 * np.frombuffer(fid.read(4), '>f4')[0])
this_has_errors = bool(np.frombuffer(fid.read(4), '>i4')[0])
if has_errors is None:
has_errors = this_has_errors
for key in _BDIP_ERROR_KEYS:
conf[key] = list()
assert has_errors == this_has_errors
fid.read(4) # Noise level used for error computations
limits = np.frombuffer(fid.read(20), '>f4') # error limits
for key, lim in zip(_BDIP_ERROR_KEYS, limits):
conf[key].append(lim)
fid.read(100) # (5, 5) fully describes the conf. ellipsoid
conf['vol'].append(np.frombuffer(fid.read(4), '>f4')[0])
khi2.append(np.frombuffer(fid.read(4), '>f4')[0])
fid.read(4) # prob
fid.read(4) # total noise estimate
return Dipole(times, pos, amplitude, ori, gof, name, conf, khi2, nfree)
def _write_dipole_bdip(fname, dip):
with open(fname, 'wb+') as fid:
for ti, t in enumerate(dip.times):
fid.write(np.zeros(1, '>i4').tobytes()) # int dipole
fid.write(np.array([t, 0]).astype('>f4').tobytes())
fid.write(np.zeros(3, '>f4').tobytes()) # r0
fid.write(dip.pos[ti].astype('>f4').tobytes()) # pos
Q = dip.amplitude[ti] * dip.ori[ti]
fid.write(Q.astype('>f4').tobytes())
fid.write(np.array(dip.gof[ti] / 100., '>f4').tobytes())
has_errors = int(bool(len(dip.conf)))
fid.write(np.array(has_errors, '>i4').tobytes()) # has_errors
fid.write(np.zeros(1, '>f4').tobytes()) # noise level
for key in _BDIP_ERROR_KEYS:
val = dip.conf[key][ti] if key in dip.conf else 0.
assert val.shape == ()
fid.write(np.array(val, '>f4').tobytes())
fid.write(np.zeros(25, '>f4').tobytes())
conf = dip.conf['vol'][ti] if 'vol' in dip.conf else 0.
fid.write(np.array(conf, '>f4').tobytes())
khi2 = dip.khi2[ti] if dip.khi2 is not None else 0
fid.write(np.array(khi2, '>f4').tobytes())
fid.write(np.zeros(1, '>f4').tobytes()) # prob
fid.write(np.zeros(1, '>f4').tobytes()) # total noise est
# #############################################################################
# Fitting
def _dipole_forwards(fwd_data, whitener, rr, n_jobs=None):
"""Compute the forward solution and do other nice stuff."""
B = _compute_forwards_meeg(rr, fwd_data, n_jobs, silent=True)
B = np.concatenate(B, axis=1)
assert np.isfinite(B).all()
B_orig = B.copy()
# Apply projection and whiten (cov has projections already)
_, _, dgemm = _get_ddot_dgemv_dgemm()
B = dgemm(1., B, whitener.T)
# column normalization doesn't affect our fitting, so skip for now
# S = np.sum(B * B, axis=1) # across channels
# scales = np.repeat(3. / np.sqrt(np.sum(np.reshape(S, (len(rr), 3)),
# axis=1)), 3)
# B *= scales[:, np.newaxis]
scales = np.ones(3)
return B, B_orig, scales
@verbose
def _make_guesses(surf, grid, exclude, mindist, n_jobs=None, verbose=None):
"""Make a guess space inside a sphere or BEM surface."""
if 'rr' in surf:
logger.info('Guess surface (%s) is in %s coordinates'
% (_bem_surf_name[surf['id']],
_coord_frame_name(surf['coord_frame'])))
else:
logger.info('Making a spherical guess space with radius %7.1f mm...'
% (1000 * surf['R']))
logger.info('Filtering (grid = %6.f mm)...' % (1000 * grid))
src = _make_volume_source_space(surf, grid, exclude, 1000 * mindist,
do_neighbors=False, n_jobs=n_jobs)[0]
assert 'vertno' in src
# simplify the result to make things easier later
src = dict(rr=src['rr'][src['vertno']], nn=src['nn'][src['vertno']],
nuse=src['nuse'], coord_frame=src['coord_frame'],
vertno=np.arange(src['nuse']), type='discrete')
return SourceSpaces([src])
def _fit_eval(rd, B, B2, fwd_svd=None, fwd_data=None, whitener=None,
lwork=None):
"""Calculate the residual sum of squares."""
if fwd_svd is None:
fwd = _dipole_forwards(fwd_data, whitener, rd[np.newaxis, :])[0]
uu, sing, vv = _repeated_svd(fwd, lwork, overwrite_a=True)
else:
uu, sing, vv = fwd_svd
gof = _dipole_gof(uu, sing, vv, B, B2)[0]
# mne-c uses fitness=B2-Bm2, but ours (1-gof) is just a normalized version
return 1. - gof
@functools.lru_cache(None)
def _get_ddot_dgemv_dgemm():
return _get_blas_funcs(np.float64, ('dot', 'gemv', 'gemm'))
def _dipole_gof(uu, sing, vv, B, B2):
"""Calculate the goodness of fit from the forward SVD."""
ddot, dgemv, _ = _get_ddot_dgemv_dgemm()
ncomp = 3 if sing[2] / (sing[0] if sing[0] > 0 else 1.) > 0.2 else 2
one = dgemv(1., vv[:ncomp], B) # np.dot(vv[:ncomp], B)
Bm2 = ddot(one, one) # np.sum(one * one)
gof = Bm2 / B2
return gof, one
def _fit_Q(fwd_data, whitener, B, B2, B_orig, rd, ori=None):
"""Fit the dipole moment once the location is known."""
from scipy import linalg
if 'fwd' in fwd_data:
# should be a single precomputed "guess" (i.e., fixed position)
assert rd is None
fwd = fwd_data['fwd']
assert fwd.shape[0] == 3
fwd_orig = fwd_data['fwd_orig']
assert fwd_orig.shape[0] == 3
scales = fwd_data['scales']
assert scales.shape == (3,)
fwd_svd = fwd_data['fwd_svd'][0]
else:
fwd, fwd_orig, scales = _dipole_forwards(fwd_data, whitener,
rd[np.newaxis, :])
fwd_svd = None
if ori is None:
if fwd_svd is None:
fwd_svd = linalg.svd(fwd, full_matrices=False)
uu, sing, vv = fwd_svd
gof, one = _dipole_gof(uu, sing, vv, B, B2)
ncomp = len(one)
one /= sing[:ncomp]
Q = np.dot(one, uu.T[:ncomp])
else:
fwd = np.dot(ori[np.newaxis], fwd)
sing = np.linalg.norm(fwd)
one = np.dot(fwd / sing, B)
gof = (one * one)[0] / B2
Q = ori * np.sum(one / sing)
ncomp = 3
# Counteract the effect of column normalization
Q *= scales[0]
B_residual_noproj = B_orig - np.dot(fwd_orig.T, Q)
return Q, gof, B_residual_noproj, ncomp
def _fit_dipoles(fun, min_dist_to_inner_skull, data, times, guess_rrs,
guess_data, fwd_data, whitener, ori, n_jobs, rank, rhoend):
"""Fit a single dipole to the given whitened, projected data."""
from scipy.optimize import fmin_cobyla
parallel, p_fun, n_jobs = parallel_func(fun, n_jobs)
# parallel over time points
res = parallel(p_fun(min_dist_to_inner_skull, B, t, guess_rrs,
guess_data, fwd_data, whitener,
fmin_cobyla, ori, rank, rhoend)
for B, t in zip(data.T, times))
pos = np.array([r[0] for r in res])
amp = np.array([r[1] for r in res])
ori = np.array([r[2] for r in res])
gof = np.array([r[3] for r in res]) * 100 # convert to percentage
conf = None
if res[0][4] is not None:
conf = np.array([r[4] for r in res])
keys = ['vol', 'depth', 'long', 'trans', 'qlong', 'qtrans']
conf = {key: conf[:, ki] for ki, key in enumerate(keys)}
khi2 = np.array([r[5] for r in res])
nfree = np.array([r[6] for r in res])
residual_noproj = np.array([r[7] for r in res]).T
return pos, amp, ori, gof, conf, khi2, nfree, residual_noproj
'''Simplex code in case we ever want/need it for testing
def _make_tetra_simplex():
"""Make the initial tetrahedron"""
#
# For this definition of a regular tetrahedron, see
#
# http://mathworld.wolfram.com/Tetrahedron.html
#
x = np.sqrt(3.0) / 3.0
r = np.sqrt(6.0) / 12.0
R = 3 * r
d = x / 2.0
simplex = 1e-2 * np.array([[x, 0.0, -r],
[-d, 0.5, -r],
[-d, -0.5, -r],
[0., 0., R]])
return simplex
def try_(p, y, psum, ndim, fun, ihi, neval, fac):
"""Helper to try a value"""
ptry = np.empty(ndim)
fac1 = (1.0 - fac) / ndim
fac2 = fac1 - fac
ptry = psum * fac1 - p[ihi] * fac2
ytry = fun(ptry)
neval += 1
if ytry < y[ihi]:
y[ihi] = ytry
psum[:] += ptry - p[ihi]
p[ihi] = ptry
return ytry, neval
def _simplex_minimize(p, ftol, stol, fun, max_eval=1000):
"""Minimization with the simplex algorithm
Modified from Numerical recipes"""
y = np.array([fun(s) for s in p])
ndim = p.shape[1]
assert p.shape[0] == ndim + 1
mpts = ndim + 1
neval = 0
psum = p.sum(axis=0)
loop = 1
while(True):
ilo = 1
if y[1] > y[2]:
ihi = 1
inhi = 2
else:
ihi = 2
inhi = 1
for i in range(mpts):
if y[i] < y[ilo]:
ilo = i
if y[i] > y[ihi]:
inhi = ihi
ihi = i
elif y[i] > y[inhi]:
if i != ihi:
inhi = i
rtol = 2 * np.abs(y[ihi] - y[ilo]) / (np.abs(y[ihi]) + np.abs(y[ilo]))
if rtol < ftol:
break
if neval >= max_eval:
raise RuntimeError('Maximum number of evaluations exceeded.')
if stol > 0: # Has the simplex collapsed?
dsum = np.sqrt(np.sum((p[ilo] - p[ihi]) ** 2))
if loop > 5 and dsum < stol:
break
ytry, neval = try_(p, y, psum, ndim, fun, ihi, neval, -1.)
if ytry <= y[ilo]:
ytry, neval = try_(p, y, psum, ndim, fun, ihi, neval, 2.)
elif ytry >= y[inhi]:
ysave = y[ihi]
ytry, neval = try_(p, y, psum, ndim, fun, ihi, neval, 0.5)
if ytry >= ysave:
for i in range(mpts):
if i != ilo:
psum[:] = 0.5 * (p[i] + p[ilo])
p[i] = psum
y[i] = fun(psum)
neval += ndim
psum = p.sum(axis=0)
loop += 1
'''
def _fit_confidence(rd, Q, ori, whitener, fwd_data):
# As describedd in the Xfit manual, confidence intervals can be calculated
# by examining a linearization of model at the best-fitting location,
# i.e. taking the Jacobian and using the whitener:
#
# J = [∂b/∂x ∂b/∂y ∂b/∂z ∂b/∂Qx ∂b/∂Qy ∂b/∂Qz]
# C = (J.T C^-1 J)^-1
#
# And then the confidence interval is the diagonal of C, scaled by 1.96
# (for 95% confidence).
from scipy import linalg
direction = np.empty((3, 3))
# The coordinate system has the x axis aligned with the dipole orientation,
direction[0] = ori
# the z axis through the origin of the sphere model
rvec = rd - fwd_data['inner_skull']['r0']
direction[2] = rvec - ori * np.dot(ori, rvec) # orthogonalize
direction[2] /= np.linalg.norm(direction[2])
# and the y axis perpendical with these forming a right-handed system.
direction[1] = np.cross(direction[2], direction[0])
assert np.allclose(np.dot(direction, direction.T), np.eye(3))
# Get spatial deltas in dipole coordinate directions
deltas = (-1e-4, 1e-4)
J = np.empty((whitener.shape[0], 6))
for ii in range(3):
fwds = []
for delta in deltas:
this_r = rd[np.newaxis] + delta * direction[ii]
fwds.append(
np.dot(Q, _dipole_forwards(fwd_data, whitener, this_r)[0]))
J[:, ii] = np.diff(fwds, axis=0)[0] / np.diff(deltas)[0]
# Get current (Q) deltas in the dipole directions
deltas = np.array([-0.01, 0.01]) * np.linalg.norm(Q)
this_fwd = _dipole_forwards(fwd_data, whitener, rd[np.newaxis])[0]
for ii in range(3):
fwds = []
for delta in deltas:
fwds.append(np.dot(Q + delta * direction[ii], this_fwd))
J[:, ii + 3] = np.diff(fwds, axis=0)[0] / np.diff(deltas)[0]
# J is already whitened, so we don't need to do np.dot(whitener, J).
# However, the units in the Jacobian are potentially quite different,
# so we need to do some normalization during inversion, then revert.
direction_norm = np.linalg.norm(J[:, :3])
Q_norm = np.linalg.norm(J[:, 3:5]) # omit possible zero Z
norm = np.array([direction_norm] * 3 + [Q_norm] * 3)
J /= norm
J = np.dot(J.T, J)
C = pinvh(J, rtol=1e-14)
C /= norm
C /= norm[:, np.newaxis]
conf = 1.96 * np.sqrt(np.diag(C))
# The confidence volume of the dipole location is obtained from by
# taking the eigenvalues of the upper left submatrix and computing