/
dipole.py
1488 lines (1312 loc) · 55.5 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
from functools import partial
import re
import numpy as np
from scipy import linalg
from .cov import read_cov, compute_whitener
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 .transforms import _print_coord_trans, _coord_frame_name, apply_trans
from .viz.evoked import _plot_evoked
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, _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, ShiftTimeMixin,
_svd_lwork, _repeated_svd, ddot, dgemv, dgemm)
@fill_doc
class Dipole(object):
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.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 = deepcopy(conf) if conf is not None else dict()
self.khi2 = np.array(khi2) if khi2 is not None else None
self.nfree = np.array(nfree) if nfree is not None else None
self.verbose = verbose
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
def save(self, fname, overwrite=False):
"""Save dipole in a .dip or .bdip file.
Parameters
----------
fname : str
The name of the .dip or .bdip file.
overwrite : bool
If True, overwrite the file (if it exists).
.. versionadded:: 0.20
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)
@fill_doc
def crop(self, tmin=None, tmax=None, include_tmax=True):
"""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
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)
for attr in ('times', '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
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=5e-3, color=(1.0, 0.0, 0.0), fig=None,
verbose=None, title=None):
"""Plot dipole locations in 3d.
Parameters
----------
trans : dict
The mri to head trans.
subject : str
The subject name corresponding to FreeSurfer environment
variable SUBJECT.
%(subjects_dir)s
mode : str
Can be ``'arrow'``, ``'sphere'`` or ``'orthoview'``.
.. versionadded:: 0.14.0
coord_frame : str
Coordinate frame to use, 'head' or 'mri'. Defaults to 'mri'.
.. versionadded:: 0.14.0
idx : int | 'gof' | 'amplitude'
Index of the initially plotted dipole. Can also be 'gof' to plot
the dipole with highest goodness of fit value or 'amplitude' to
plot the dipole with the highest amplitude. The dipoles can also be
browsed through using up/down arrow keys or mouse scroll. Defaults
to 'gof'. Only used if mode equals 'orthoview'.
.. versionadded:: 0.14.0
show_all : bool
Whether to always plot all the dipoles. If True (default), the
active dipole is plotted as a red dot and it's location determines
the shown MRI slices. The the non-active dipoles are plotted as
small blue dots. If False, only the active dipole is plotted.
Only used if mode equals 'orthoview'.
.. versionadded:: 0.14.0
ax : instance of matplotlib Axes3D | None
Axes to plot into. If None (default), axes will be created.
Only used if mode equals 'orthoview'.
.. versionadded:: 0.14.0
block : bool
Whether to halt program execution until the figure is closed.
Defaults to False. Only used if mode equals 'orthoview'.
.. versionadded:: 0.14.0
show : bool
Show figure if True. Defaults to True.
Only used if mode equals 'orthoview'.
scale : float
The scale of the dipoles if ``mode`` is 'arrow' or 'sphere'.
color : tuple
The color of the dipoles if ``mode`` is 'arrow' or 'sphere'.
fig : mayavi.mlab.Figure | None
Mayavi Scene in which to plot the alignment.
If ``None``, creates a new 600x600 pixel figure with black
background.
.. versionadded:: 0.14.0
%(verbose_meth)s
%(dipole_locs_fig_title)s
.. versionadded:: 0.21.0
Returns
-------
fig : instance of mayavi.mlab.Figure or matplotlib.figure.Figure
The mayavi figure or matplotlib Figure.
Notes
-----
.. versionadded:: 0.9.0
"""
_check_option('mode', mode, [None, 'arrow', 'sphere', 'orthoview'])
from .viz import plot_dipole_locations
return plot_dipole_locations(
self, trans, subject, subjects_dir, mode, coord_frame, idx,
show_all, ax, block, show, scale=scale, color=color, fig=fig,
title=title)
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(ShiftTimeMixin):
"""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 : instance of Info
The measurement info.
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.times = times
self.data = data
self.verbose = verbose
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_meth)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 : instance of Dipole or DipoleFixed
The dipole.
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 = 0
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=1):
"""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)
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=1, 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'
% (_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
def _dipole_gof(uu, sing, vv, B, B2):
"""Calculate the goodness of fit from the forward SVD."""
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."""
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):
"""Fit a single dipole to the given whitened, projected data."""
from scipy.optimize import fmin_cobyla
parallel, p_fun, _ = 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)
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).
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 = linalg.pinvh(J, rcond=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
# v = 4π/3 √(c^3 λ1 λ2 λ3) with c = 7.81, or:
vol_conf = 4 * np.pi / 3. * np.sqrt(
476.379541 * np.prod(linalg.eigh(C[:3, :3], eigvals_only=True)))
conf = np.concatenate([conf, [vol_conf]])
# Now we reorder and subselect the proper columns:
# vol, depth, long, trans, Qlong, Qtrans (discard Qdepth, assumed zero)
conf = conf[[6, 2, 0, 1, 3, 4]]
return conf
def _surface_constraint(rd, surf, min_dist_to_inner_skull):
"""Surface fitting constraint."""
dist = _compute_nearest(surf['rr'], rd[np.newaxis, :],
return_dists=True)[1][0]
if _points_outside_surface(rd[np.newaxis, :], surf, 1)[0]:
dist *= -1.
# Once we know the dipole is below the inner skull,
# let's check if its distance to the inner skull is at least
# min_dist_to_inner_skull. This can be enforced by adding a
# constrain proportional to its distance.
dist -= min_dist_to_inner_skull
return dist