_make_forward.py

# Authors: Matti Hämäläinen <msh@nmr.mgh.harvard.edu>
#          Alexandre Gramfort <alexandre.gramfort@inria.fr>
#          Martin Luessi <mluessi@nmr.mgh.harvard.edu>
#          Eric Larson <larson.eric.d@gmail.com>
#
# License: BSD-3-Clause

# The computations in this code were primarily derived from Matti Hämäläinen's
# C code.

from copy import deepcopy
from contextlib import contextmanager
from pathlib import Path
import os
import os.path as op

import numpy as np

from ._compute_forward import _compute_forwards
from ..io import read_info, _loc_to_coil_trans, _loc_to_eeg_loc, Info
from ..io.compensator import get_current_comp, make_compensator
from ..io.pick import _has_kit_refs, pick_types, pick_info
from ..io.constants import FIFF, FWD
from ..transforms import (_ensure_trans, transform_surface_to, apply_trans,
                          _get_trans, _print_coord_trans, _coord_frame_name,
                          Transform, invert_transform)
from ..utils import logger, verbose, warn, _pl, _validate_type, _check_fname
from ..source_space import (_ensure_src, _filter_source_spaces,
                            _make_discrete_source_space, _complete_vol_src)
from ..source_estimate import VolSourceEstimate
from ..surface import _normalize_vectors, _CheckInside
from ..bem import read_bem_solution, _bem_find_surface, ConductorModel

from .forward import (Forward, _merge_fwds, convert_forward_solution,
                      _FWD_ORDER)


_accuracy_dict = dict(normal=FWD.COIL_ACCURACY_NORMAL,
                      accurate=FWD.COIL_ACCURACY_ACCURATE)
_extra_coil_def_fname = None


@verbose
def _read_coil_defs(verbose=None):
    """Read a coil definition file.

    Parameters
    ----------
    %(verbose)s

    Returns
    -------
    res : list of dict
        The coils. It is a dictionary with valid keys:
        'cosmag' | 'coil_class' | 'coord_frame' | 'rmag' | 'type' |
        'chname' | 'accuracy'.
        cosmag contains the direction of the coils and rmag contains the
        position vector.

    Notes
    -----
    The global variable "_extra_coil_def_fname" can be used to prepend
    additional definitions. These are never added to the registry.
    """
    coil_dir = op.join(op.split(__file__)[0], '..', 'data')
    coils = list()
    if _extra_coil_def_fname is not None:
        coils += _read_coil_def_file(_extra_coil_def_fname, use_registry=False)
    coils += _read_coil_def_file(op.join(coil_dir, 'coil_def.dat'))
    return coils


# Typically we only have 1 or 2 coil def files, but they can end up being
# read a lot. Let's keep a list of them and just reuse them:
_coil_registry = {}


def _read_coil_def_file(fname, use_registry=True):
    """Read a coil def file."""
    if not use_registry or fname not in _coil_registry:
        big_val = 0.5
        coils = list()
        with open(fname, 'r') as fid:
            lines = fid.readlines()
        lines = lines[::-1]
        while len(lines) > 0:
            line = lines.pop().strip()
            if line[0] == '#' and len(line) > 0:
                continue
            desc_start = line.find('"')
            desc_end = len(line) - 1
            assert line.strip()[desc_end] == '"'
            desc = line[desc_start:desc_end]
            vals = np.fromstring(line[:desc_start].strip(),
                                 dtype=float, sep=' ')
            assert len(vals) == 6
            npts = int(vals[3])
            coil = dict(coil_type=vals[1], coil_class=vals[0], desc=desc,
                        accuracy=vals[2], size=vals[4], base=vals[5])
            # get parameters of each component
            rmag = list()
            cosmag = list()
            w = list()
            for p in range(npts):
                # get next non-comment line
                line = lines.pop()
                while line[0] == '#':
                    line = lines.pop()
                vals = np.fromstring(line, sep=' ')
                if len(vals) != 7:
                    raise RuntimeError(
                        f'Could not interpret line {p + 1} as 7 points:\n'
                        f'{line}')
                # Read and verify data for each integration point
                w.append(vals[0])
                rmag.append(vals[[1, 2, 3]])
                cosmag.append(vals[[4, 5, 6]])
            w = np.array(w)
            rmag = np.array(rmag)
            cosmag = np.array(cosmag)
            size = np.sqrt(np.sum(cosmag ** 2, axis=1))
            if np.any(np.sqrt(np.sum(rmag ** 2, axis=1)) > big_val):
                raise RuntimeError('Unreasonable integration point')
            if np.any(size <= 0):
                raise RuntimeError('Unreasonable normal')
            cosmag /= size[:, np.newaxis]
            coil.update(dict(w=w, cosmag=cosmag, rmag=rmag))
            coils.append(coil)
        if use_registry:
            _coil_registry[fname] = coils
    if use_registry:
        coils = deepcopy(_coil_registry[fname])
    logger.info('%d coil definition%s read', len(coils), _pl(coils))
    return coils


def _create_meg_coil(coilset, ch, acc, do_es):
    """Create a coil definition using templates, transform if necessary."""
    # Also change the coordinate frame if so desired
    if ch['kind'] not in [FIFF.FIFFV_MEG_CH, FIFF.FIFFV_REF_MEG_CH]:
        raise RuntimeError('%s is not a MEG channel' % ch['ch_name'])

    # Simple linear search from the coil definitions
    for coil in coilset:
        if coil['coil_type'] == (ch['coil_type'] & 0xFFFF) and \
                coil['accuracy'] == acc:
            break
    else:
        raise RuntimeError('Desired coil definition not found '
                           '(type = %d acc = %d)' % (ch['coil_type'], acc))

    # Apply a coordinate transformation if so desired
    coil_trans = _loc_to_coil_trans(ch['loc'])

    # Create the result
    res = dict(chname=ch['ch_name'], coil_class=coil['coil_class'],
               accuracy=coil['accuracy'], base=coil['base'], size=coil['size'],
               type=ch['coil_type'], w=coil['w'], desc=coil['desc'],
               coord_frame=FIFF.FIFFV_COORD_DEVICE, rmag_orig=coil['rmag'],
               cosmag_orig=coil['cosmag'], coil_trans_orig=coil_trans,
               r0=coil_trans[:3, 3],
               rmag=apply_trans(coil_trans, coil['rmag']),
               cosmag=apply_trans(coil_trans, coil['cosmag'], False))
    if do_es:
        r0_exey = (np.dot(coil['rmag'][:, :2], coil_trans[:3, :2].T) +
                   coil_trans[:3, 3])
        res.update(ex=coil_trans[:3, 0], ey=coil_trans[:3, 1],
                   ez=coil_trans[:3, 2], r0_exey=r0_exey)
    return res


def _create_eeg_el(ch, t=None):
    """Create an electrode definition, transform coords if necessary."""
    if ch['kind'] != FIFF.FIFFV_EEG_CH:
        raise RuntimeError('%s is not an EEG channel. Cannot create an '
                           'electrode definition.' % ch['ch_name'])
    if t is None:
        t = Transform('head', 'head')  # identity, no change
    if t.from_str != 'head':
        raise RuntimeError('Inappropriate coordinate transformation')

    r0ex = _loc_to_eeg_loc(ch['loc'])
    if r0ex.shape[1] == 1:  # no reference
        w = np.array([1.])
    else:  # has reference
        w = np.array([1., -1.])

    # Optional coordinate transformation
    r0ex = apply_trans(t['trans'], r0ex.T)

    # The electrode location
    cosmag = r0ex.copy()
    _normalize_vectors(cosmag)
    res = dict(chname=ch['ch_name'], coil_class=FWD.COILC_EEG, w=w,
               accuracy=_accuracy_dict['normal'], type=ch['coil_type'],
               coord_frame=t['to'], rmag=r0ex, cosmag=cosmag)
    return res


def _create_meg_coils(chs, acc, t=None, coilset=None, do_es=False):
    """Create a set of MEG coils in the head coordinate frame."""
    acc = _accuracy_dict[acc] if isinstance(acc, str) else acc
    coilset = _read_coil_defs(verbose=False) if coilset is None else coilset
    coils = [_create_meg_coil(coilset, ch, acc, do_es) for ch in chs]
    _transform_orig_meg_coils(coils, t, do_es=do_es)
    return coils


def _transform_orig_meg_coils(coils, t, do_es=True):
    """Transform original (device) MEG coil positions."""
    if t is None:
        return
    for coil in coils:
        coil_trans = np.dot(t['trans'], coil['coil_trans_orig'])
        coil.update(
            coord_frame=t['to'], r0=coil_trans[:3, 3],
            rmag=apply_trans(coil_trans, coil['rmag_orig']),
            cosmag=apply_trans(coil_trans, coil['cosmag_orig'], False))
        if do_es:
            r0_exey = (np.dot(coil['rmag_orig'][:, :2],
                              coil_trans[:3, :2].T) + coil_trans[:3, 3])
            coil.update(ex=coil_trans[:3, 0], ey=coil_trans[:3, 1],
                        ez=coil_trans[:3, 2], r0_exey=r0_exey)


def _create_eeg_els(chs):
    """Create a set of EEG electrodes in the head coordinate frame."""
    return [_create_eeg_el(ch) for ch in chs]


@verbose
def _setup_bem(bem, bem_extra, neeg, mri_head_t, allow_none=False,
               verbose=None):
    """Set up a BEM for forward computation, making a copy and modifying."""
    if allow_none and bem is None:
        return None
    logger.info('')
    _validate_type(bem, ('path-like', ConductorModel), bem)
    if not isinstance(bem, ConductorModel):
        logger.info('Setting up the BEM model using %s...\n' % bem_extra)
        bem = read_bem_solution(bem)
    else:
        bem = bem.copy()
    if bem['is_sphere']:
        logger.info('Using the sphere model.\n')
        if len(bem['layers']) == 0 and neeg > 0:
            raise RuntimeError('Spherical model has zero shells, cannot use '
                               'with EEG data')
        if bem['coord_frame'] != FIFF.FIFFV_COORD_HEAD:
            raise RuntimeError('Spherical model is not in head coordinates')
    else:
        if bem['surfs'][0]['coord_frame'] != FIFF.FIFFV_COORD_MRI:
            raise RuntimeError(
                'BEM is in %s coordinates, should be in MRI'
                % (_coord_frame_name(bem['surfs'][0]['coord_frame']),))
        if neeg > 0 and len(bem['surfs']) == 1:
            raise RuntimeError('Cannot use a homogeneous (1-layer BEM) model '
                               'for EEG forward calculations, consider '
                               'using a 3-layer BEM instead')
        logger.info('Employing the head->MRI coordinate transform with the '
                    'BEM model.')
        # fwd_bem_set_head_mri_t: Set the coordinate transformation
        bem['head_mri_t'] = _ensure_trans(mri_head_t, 'head', 'mri')
        logger.info('BEM model %s is now set up' % op.split(bem_extra)[1])
        logger.info('')
    return bem


@verbose
def _prep_meg_channels(info, accuracy='accurate', exclude=(), *,
                       ignore_ref=False, head_frame=True, do_es=False,
                       verbose=None):
    """Prepare MEG coil definitions for forward calculation."""
    # Find MEG channels
    ref_meg = True if not ignore_ref else False
    picks = pick_types(info, meg=True, ref_meg=ref_meg, exclude=exclude)

    # Make sure MEG coils exist
    if len(picks) <= 0:
        raise RuntimeError('Could not find any MEG channels')
    info_meg = pick_info(info, picks)
    del picks

    # Get channel info and names for MEG channels
    logger.info(f'Read {len(info_meg["chs"])} MEG channels from info')

    # Get MEG compensation channels
    compensator = post_picks = None
    ch_names = info_meg['ch_names']
    if not ignore_ref:
        ref_picks = pick_types(info, meg=False, ref_meg=True, exclude=exclude)
        ncomp = len(ref_picks)
        if (ncomp > 0):
            logger.info(f'Read {ncomp} MEG compensation channels from info')
            # We need to check to make sure these are NOT KIT refs
            if _has_kit_refs(info, ref_picks):
                raise NotImplementedError(
                    'Cannot create forward solution with KIT reference '
                    'channels. Consider using "ignore_ref=True" in '
                    'calculation')
            logger.info(
                f'{len(info["comps"])} compensation data sets in info')
            # Compose a compensation data set if necessary
            # adapted from mne_make_ctf_comp() from mne_ctf_comp.c
            logger.info('Setting up compensation data...')
            comp_num = get_current_comp(info)
            if comp_num is None or comp_num == 0:
                logger.info('    No compensation set. Nothing more to do.')
            else:
                compensator = make_compensator(
                    info_meg, 0, comp_num, exclude_comp_chs=False)
                logger.info(
                    f'    Desired compensation data ({comp_num}) found.')
                logger.info('    All compensation channels found.')
                logger.info('    Preselector created.')
                logger.info('    Compensation data matrix created.')
                logger.info('    Postselector created.')
            post_picks = pick_types(
                info_meg, meg=True, ref_meg=False, exclude=exclude)
            ch_names = [ch_names[pick] for pick in post_picks]

    # Create coil descriptions with transformation to head or device frame
    templates = _read_coil_defs()

    if head_frame:
        _print_coord_trans(info['dev_head_t'])
        transform = info['dev_head_t']
    else:
        transform = None

    megcoils = _create_meg_coils(
        info_meg['chs'], accuracy, transform, templates, do_es=do_es)

    # Check that coordinate frame is correct and log it
    if head_frame:
        assert megcoils[0]['coord_frame'] == FIFF.FIFFV_COORD_HEAD
        logger.info('MEG coil definitions created in head coordinates.')
    else:
        assert megcoils[0]['coord_frame'] == FIFF.FIFFV_COORD_DEVICE
        logger.info('MEG coil definitions created in device coordinate.')

    return dict(
        defs=megcoils, ch_names=ch_names, compensator=compensator,
        info=info_meg, post_picks=post_picks)


@verbose
def _prep_eeg_channels(info, exclude=(), verbose=None):
    """Prepare EEG electrode definitions for forward calculation."""
    info_extra = 'info'

    # Find EEG electrodes
    picks = pick_types(info, meg=False, eeg=True, ref_meg=False,
                       exclude=exclude)

    # Make sure EEG electrodes exist
    neeg = len(picks)
    if neeg <= 0:
        raise RuntimeError('Could not find any EEG channels')

    # Get channel info and names for EEG channels
    eegchs = pick_info(info, picks)['chs']
    eegnames = [info['ch_names'][p] for p in picks]
    logger.info('Read %3d EEG channels from %s' % (len(picks), info_extra))

    # Create EEG electrode descriptions
    eegels = _create_eeg_els(eegchs)
    logger.info('Head coordinate coil definitions created.')

    return dict(defs=eegels, ch_names=eegnames)


@verbose
def _prepare_for_forward(src, mri_head_t, info, bem, mindist, n_jobs,
                         bem_extra='', trans='', info_extra='',
                         meg=True, eeg=True, ignore_ref=False,
                         allow_bem_none=False, verbose=None):
    """Prepare for forward computation.

    The sensors dict contains keys for each sensor type, e.g. 'meg', 'eeg'.
    The vale for each of these is a dict that comes from _prep_meg_channels or
    _prep_eeg_channels. Each dict contains:

    - defs : a list of dicts (one per channel) with 'rmag', 'cosmag', etc.
    - ch_names: a list of str channel names corresponding to the defs
    - compensator (optional): the ndarray compensation matrix to apply
    - post_picks (optional): the ndarray of indices to pick after applying the
      compensator
    """
    # Read the source locations
    logger.info('')
    # let's make a copy in case we modify something
    src = _ensure_src(src).copy()
    nsource = sum(s['nuse'] for s in src)
    if nsource == 0:
        raise RuntimeError('No sources are active in these source spaces. '
                           '"do_all" option should be used.')
    logger.info('Read %d source spaces a total of %d active source locations'
                % (len(src), nsource))
    # Delete some keys to clean up the source space:
    for key in ['working_dir', 'command_line']:
        if key in src.info:
            del src.info[key]

    # Read the MRI -> head coordinate transformation
    logger.info('')
    _print_coord_trans(mri_head_t)

    # make a new dict with the relevant information
    arg_list = [info_extra, trans, src, bem_extra, meg, eeg, mindist,
                n_jobs, verbose]
    cmd = 'make_forward_solution(%s)' % (', '.join([str(a) for a in arg_list]))
    mri_id = dict(machid=np.zeros(2, np.int32), version=0, secs=0, usecs=0)

    info_trans = str(trans) if isinstance(trans, Path) else trans
    info = Info(chs=info['chs'], comps=info['comps'],
                dev_head_t=info['dev_head_t'], mri_file=info_trans,
                mri_id=mri_id,
                meas_file=info_extra, meas_id=None, working_dir=os.getcwd(),
                command_line=cmd, bads=info['bads'], mri_head_t=mri_head_t)
    info._update_redundant()
    info._check_consistency()
    logger.info('')

    sensors = dict()
    if meg and len(pick_types(info, meg=True, ref_meg=False, exclude=[])) > 0:
        sensors['meg'] = _prep_meg_channels(info, ignore_ref=ignore_ref)
    if eeg and len(pick_types(info, eeg=True, exclude=[])) > 0:
        sensors['eeg'] = _prep_eeg_channels(info)

    # Check that some channels were found
    if len(sensors) == 0:
        raise RuntimeError('No MEG or EEG channels found.')

    # pick out final info
    info = pick_info(info, pick_types(info, meg=meg, eeg=eeg, ref_meg=False,
                                      exclude=[]))

    # Transform the source spaces into the appropriate coordinates
    # (will either be HEAD or MRI)
    for s in src:
        transform_surface_to(s, 'head', mri_head_t)
    logger.info('Source spaces are now in %s coordinates.'
                % _coord_frame_name(s['coord_frame']))

    # Prepare the BEM model
    eegnames = sensors.get('eeg', dict()).get('ch_names', [])
    bem = _setup_bem(bem, bem_extra, len(eegnames), mri_head_t,
                     allow_none=allow_bem_none)
    del eegnames

    # Circumvent numerical problems by excluding points too close to the skull,
    # and check that sensors are not inside any BEM surface
    if bem is not None:
        if not bem['is_sphere']:
            check_surface = 'inner skull surface'
            inner_skull = _bem_find_surface(bem, 'inner_skull')
            check_inside = _filter_source_spaces(
                inner_skull, mindist, mri_head_t, src, n_jobs)
            logger.info('')
            if len(bem['surfs']) == 3:
                check_surface = 'scalp surface'
                check_inside = _CheckInside(_bem_find_surface(bem, 'head'))
        else:
            check_surface = 'outermost sphere shell'
            if len(bem['layers']) == 0:
                def check_inside(x):
                    return np.zeros(len(x), bool)
            else:
                def check_inside(x):
                    return (np.linalg.norm(x - bem['r0'], axis=1) <
                            bem['layers'][-1]['rad'])
        if 'meg' in sensors:
            meg_loc = apply_trans(
                invert_transform(mri_head_t),
                np.array([coil['r0'] for coil in sensors['meg']['defs']]))
            n_inside = check_inside(meg_loc).sum()
            if n_inside:
                raise RuntimeError(
                    f'Found {n_inside} MEG sensor{_pl(n_inside)} inside the '
                    f'{check_surface}, perhaps coordinate frames and/or '
                    'coregistration must be incorrect')

    rr = np.concatenate([s['rr'][s['vertno']] for s in src])
    if len(rr) < 1:
        raise RuntimeError('No points left in source space after excluding '
                           'points close to inner skull.')

    # deal with free orientations:
    source_nn = np.tile(np.eye(3), (len(rr), 1))
    update_kwargs = dict(nchan=len(info['ch_names']), nsource=len(rr),
                         info=info, src=src, source_nn=source_nn,
                         source_rr=rr, surf_ori=False, mri_head_t=mri_head_t)
    return sensors, rr, info, update_kwargs, bem


@verbose
def make_forward_solution(info, trans, src, bem, meg=True, eeg=True, *,
                          mindist=0.0, ignore_ref=False, n_jobs=None,
                          verbose=None):
    """Calculate a forward solution for a subject.

    Parameters
    ----------
    %(info_str)s
    %(trans)s

        .. versionchanged:: 0.19
            Support for 'fsaverage' argument.
    src : path-like | instance of SourceSpaces
        If string, should be a source space filename. Can also be an
        instance of loaded or generated SourceSpaces.
    bem : path-like | dict
        Filename of the BEM (e.g., "sample-5120-5120-5120-bem-sol.fif") to
        use, or a loaded sphere model (dict).
    meg : bool
        If True (Default), include MEG computations.
    eeg : bool
        If True (Default), include EEG computations.
    mindist : float
        Minimum distance of sources from inner skull surface (in mm).
    ignore_ref : bool
        If True, do not include reference channels in compensation. This
        option should be True for KIT files, since forward computation
        with reference channels is not currently supported.
    %(n_jobs)s
    %(verbose)s

    Returns
    -------
    fwd : instance of Forward
        The forward solution.

    See Also
    --------
    convert_forward_solution

    Notes
    -----
    The ``--grad`` option from MNE-C (to compute gradients) is not implemented
    here.

    To create a fixed-orientation forward solution, use this function
    followed by :func:`mne.convert_forward_solution`.

    .. note::
        If the BEM solution was computed with :doc:`OpenMEEG <openmeeg:index>`
        in :func:`mne.make_bem_solution`, then OpenMEEG will automatically
        be used to compute the forward solution.

    .. versionchanged:: 1.2
       Added support for OpenMEEG-based forward solution calculations.
    """
    # Currently not (sup)ported:
    # 1. --grad option (gradients of the field, not used much)
    # 2. --fixed option (can be computed post-hoc)
    # 3. --mricoord option (probably not necessary)

    # read the transformation from MRI to HEAD coordinates
    # (could also be HEAD to MRI)
    mri_head_t, trans = _get_trans(trans)
    if isinstance(bem, ConductorModel):
        bem_extra = 'instance of ConductorModel'
    else:
        bem_extra = bem
    _validate_type(info, ('path-like', Info), 'info')
    if not isinstance(info, Info):
        info_extra = op.split(info)[1]
        info = _check_fname(info, must_exist=True, overwrite='read',
                            name='info')
        info = read_info(info, verbose=False)
    else:
        info_extra = 'instance of Info'

    # Report the setup
    logger.info('Source space          : %s' % src)
    logger.info('MRI -> head transform : %s' % trans)
    logger.info('Measurement data      : %s' % info_extra)
    if isinstance(bem, ConductorModel) and bem['is_sphere']:
        logger.info('Sphere model      : origin at %s mm'
                    % (bem['r0'],))
        logger.info('Standard field computations')
    else:
        logger.info('Conductor model   : %s' % bem_extra)
        logger.info('Accurate field computations')
    logger.info('Do computations in %s coordinates',
                _coord_frame_name(FIFF.FIFFV_COORD_HEAD))
    logger.info('Free source orientations')

    # Create MEG coils and EEG electrodes in the head coordinate frame
    sensors, rr, info, update_kwargs, bem = _prepare_for_forward(
        src, mri_head_t, info, bem, mindist, n_jobs, bem_extra, trans,
        info_extra, meg, eeg, ignore_ref)
    del (src, mri_head_t, trans, info_extra, bem_extra, mindist,
         meg, eeg, ignore_ref)

    # Time to do the heavy lifting: MEG first, then EEG
    fwds = _compute_forwards(rr, bem=bem, sensors=sensors, n_jobs=n_jobs)

    # merge forwards
    fwds = {key: _to_forward_dict(fwds[key], sensors[key]['ch_names'])
            for key in _FWD_ORDER if key in fwds}
    fwd = _merge_fwds(fwds, verbose=False)
    del fwds
    logger.info('')

    # Don't transform the source spaces back into MRI coordinates (which is
    # done in the C code) because mne-python assumes forward solution source
    # spaces are in head coords.
    fwd.update(**update_kwargs)
    logger.info('Finished.')
    return fwd


@verbose
def make_forward_dipole(dipole, bem, info, trans=None, n_jobs=None, *,
                        verbose=None):
    """Convert dipole object to source estimate and calculate forward operator.

    The instance of Dipole is converted to a discrete source space,
    which is then combined with a BEM or a sphere model and
    the sensor information in info to form a forward operator.

    The source estimate object (with the forward operator) can be projected to
    sensor-space using :func:`mne.simulation.simulate_evoked`.

    .. note:: If the (unique) time points of the dipole object are unevenly
              spaced, the first output will be a list of single-timepoint
              source estimates.

    Parameters
    ----------
    %(dipole)s
    bem : str | dict
        The BEM filename (str) or a loaded sphere model (dict).
    info : instance of Info
        The measurement information dictionary. It is sensor-information etc.,
        e.g., from a real data file.
    trans : str | None
        The head<->MRI transform filename. Must be provided unless BEM
        is a sphere model.
    %(n_jobs)s
    %(verbose)s

    Returns
    -------
    fwd : instance of Forward
        The forward solution corresponding to the source estimate(s).
    stc : instance of VolSourceEstimate | list of VolSourceEstimate
        The dipoles converted to a discrete set of points and associated
        time courses. If the time points of the dipole are unevenly spaced,
        a list of single-timepoint source estimates are returned.

    See Also
    --------
    mne.simulation.simulate_evoked

    Notes
    -----
    .. versionadded:: 0.12.0
    """
    if isinstance(dipole, list):
        from ..dipole import _concatenate_dipoles  # To avoid circular import
        dipole = _concatenate_dipoles(dipole)

    # Make copies to avoid mangling original dipole
    times = dipole.times.copy()
    pos = dipole.pos.copy()
    amplitude = dipole.amplitude.copy()
    ori = dipole.ori.copy()

    # Convert positions to discrete source space (allows duplicate rr & nn)
    # NB information about dipole orientation enters here, then no more
    sources = dict(rr=pos, nn=ori)
    # Dipole objects must be in the head frame
    src = _complete_vol_src(
        [_make_discrete_source_space(sources, coord_frame='head')])

    # Forward operator created for channels in info (use pick_info to restrict)
    # Use defaults for most params, including min_dist
    fwd = make_forward_solution(info, trans, src, bem, n_jobs=n_jobs,
                                verbose=verbose)
    # Convert from free orientations to fixed (in-place)
    convert_forward_solution(fwd, surf_ori=False, force_fixed=True,
                             copy=False, use_cps=False, verbose=None)

    # Check for omissions due to proximity to inner skull in
    # make_forward_solution, which will result in an exception
    if fwd['src'][0]['nuse'] != len(pos):
        inuse = fwd['src'][0]['inuse'].astype(bool)
        head = ('The following dipoles are outside the inner skull boundary')
        msg = len(head) * '#' + '\n' + head + '\n'
        for (t, pos) in zip(times[np.logical_not(inuse)],
                            pos[np.logical_not(inuse)]):
            msg += '    t={:.0f} ms, pos=({:.0f}, {:.0f}, {:.0f}) mm\n'.\
                format(t * 1000., pos[0] * 1000.,
                       pos[1] * 1000., pos[2] * 1000.)
        msg += len(head) * '#'
        logger.error(msg)
        raise ValueError('One or more dipoles outside the inner skull.')

    # multiple dipoles (rr and nn) per time instant allowed
    # uneven sampling in time returns list
    timepoints = np.unique(times)
    if len(timepoints) > 1:
        tdiff = np.diff(timepoints)
        if not np.allclose(tdiff, tdiff[0]):
            warn('Unique time points of dipoles unevenly spaced: returned '
                 'stc will be a list, one for each time point.')
            tstep = -1.0
        else:
            tstep = tdiff[0]
    elif len(timepoints) == 1:
        tstep = 0.001

    # Build the data matrix, essentially a block-diagonal with
    # n_rows: number of dipoles in total (dipole.amplitudes)
    # n_cols: number of unique time points in dipole.times
    # amplitude with identical value of times go together in one col (others=0)
    data = np.zeros((len(amplitude), len(timepoints)))  # (n_d, n_t)
    row = 0
    for tpind, tp in enumerate(timepoints):
        amp = amplitude[np.in1d(times, tp)]
        data[row:row + len(amp), tpind] = amp
        row += len(amp)

    if tstep > 0:
        stc = VolSourceEstimate(data, vertices=[fwd['src'][0]['vertno']],
                                tmin=timepoints[0],
                                tstep=tstep, subject=None)
    else:  # Must return a list of stc, one for each time point
        stc = []
        for col, tp in enumerate(timepoints):
            stc += [VolSourceEstimate(data[:, col][:, np.newaxis],
                                      vertices=[fwd['src'][0]['vertno']],
                                      tmin=tp, tstep=0.001, subject=None)]
    return fwd, stc


def _to_forward_dict(fwd, names, fwd_grad=None,
                     coord_frame=FIFF.FIFFV_COORD_HEAD,
                     source_ori=FIFF.FIFFV_MNE_FREE_ORI):
    """Convert forward solution matrices to dicts."""
    assert names is not None
    sol = dict(data=fwd.T, nrow=fwd.shape[1], ncol=fwd.shape[0],
               row_names=names, col_names=[])
    fwd = Forward(sol=sol, source_ori=source_ori, nsource=sol['ncol'],
                  coord_frame=coord_frame, sol_grad=None,
                  nchan=sol['nrow'], _orig_source_ori=source_ori,
                  _orig_sol=sol['data'].copy(), _orig_sol_grad=None)
    if fwd_grad is not None:
        sol_grad = dict(data=fwd_grad.T, nrow=fwd_grad.shape[1],
                        ncol=fwd_grad.shape[0], row_names=names,
                        col_names=[])
        fwd.update(dict(sol_grad=sol_grad),
                   _orig_sol_grad=sol_grad['data'].copy())
    return fwd


@contextmanager
def use_coil_def(fname):
    """Use a custom coil definition file.

    Parameters
    ----------
    fname : str
        The filename of the coil definition file.

    Returns
    -------
    context : contextmanager
        The context for using the coil definition.

    Notes
    -----
    This is meant to be used a context manager such as:

    >>> with use_coil_def(my_fname):  # doctest:+SKIP
    ...     make_forward_solution(...)

    This allows using custom coil definitions with functions that require
    forward modeling.
    """
    global _extra_coil_def_fname
    _extra_coil_def_fname = fname
    try:
        yield
    finally:
        _extra_coil_def_fname = None