code: # Authors: Alexandre Gramfort <alexandre.gramfort@inria.fr>
  #          Matti Hamalainen <msh@nmr.mgh.harvard.edu>
  #          Martin Luessi <mluessi@nmr.mgh.harvard.edu>
  #
  # License: BSD (3-clause)
  
  from time import time
  from copy import deepcopy
  import re
  
  import numpy as np
  from scipy import linalg, sparse
  
  import shutil
  import os
  from os import path as op
  import tempfile
  
  from ..io import RawArray, Info
  from ..io.constants import FIFF
  from ..io.open import fiff_open
  from ..io.tree import dir_tree_find
  from ..io.tag import find_tag, read_tag
  from ..io.matrix import (_read_named_matrix, _transpose_named_matrix,
                           write_named_matrix)
  from ..io.meas_info import read_bad_channels, write_info
  from ..io.pick import (pick_channels_forward, pick_info, pick_channels,
                         pick_types)
  from ..io.write import (write_int, start_block, end_block,
                          write_coord_trans, write_ch_info, write_name_list,
                          write_string, start_file, end_file, write_id)
  from ..io.base import BaseRaw
  from ..evoked import Evoked, EvokedArray
  from ..epochs import BaseEpochs
  from ..source_space import (_read_source_spaces_from_tree,
                              find_source_space_hemi, _set_source_space_vertices,
                              _write_source_spaces_to_fid)
  from ..source_estimate import _BaseSourceEstimate
  from ..transforms import (transform_surface_to, invert_transform,
                            write_trans)
  from ..utils import (_check_fname, get_subjects_dir, has_mne_c, warn,
                       run_subprocess, check_fname, logger, verbose, fill_doc,
                       _validate_type, _check_compensation_grade, _check_option)
  from ..label import Label
  from ..fixes import einsum
  
  
  class Forward(dict):
      """Forward class to represent info from forward solution."""
  
      def copy(self):
          """Copy the Forward instance."""
          return Forward(deepcopy(self))
  
      def __repr__(self):
          """Summarize forward info instead of printing all."""
          entr = '<Forward'
  
          nchan = len(pick_types(self['info'], meg=True, eeg=False, exclude=[]))
          entr += ' | ' + 'MEG channels: %d' % nchan
          nchan = len(pick_types(self['info'], meg=False, eeg=True, exclude=[]))
          entr += ' | ' + 'EEG channels: %d' % nchan
  
          src_types = np.array([src['type'] for src in self['src']])
          if (src_types == 'surf').all():
              entr += (' | Source space: Surface with %d vertices'
                       % self['nsource'])
          elif (src_types == 'vol').all():
              entr += (' | Source space: Volume with %d grid points'
                       % self['nsource'])
          elif (src_types == 'discrete').all():
              entr += (' | Source space: Discrete with %d dipoles'
                       % self['nsource'])
          else:
              count_string = ''
              if (src_types == 'surf').any():
                  count_string += '%d surface, ' % (src_types == 'surf').sum()
              if (src_types == 'vol').any():
                  count_string += '%d volume, ' % (src_types == 'vol').sum()
              if (src_types == 'discrete').any():
                  count_string += '%d discrete, ' \
                                  % (src_types == 'discrete').sum()
              count_string = count_string.rstrip(', ')
              entr += (' | Source space: Mixed (%s) with %d vertices'
                       % (count_string, self['nsource']))
  
          if self['source_ori'] == FIFF.FIFFV_MNE_UNKNOWN_ORI:
              entr += (' | Source orientation: Unknown')
          elif self['source_ori'] == FIFF.FIFFV_MNE_FIXED_ORI:
              entr += (' | Source orientation: Fixed')
          elif self['source_ori'] == FIFF.FIFFV_MNE_FREE_ORI:
              entr += (' | Source orientation: Free')
  
          entr += '>'
  
          return entr
  
  
  def _block_diag(A, n):
      """Construct a block diagonal from a packed structure.
  
      You have to try it on a matrix to see what it's doing.
  
      If A is not sparse, then returns a sparse block diagonal "bd",
      diagonalized from the
      elements in "A".
      "A" is ma x na, comprising bdn=(na/"n") blocks of submatrices.
      Each submatrix is ma x "n", and these submatrices are
      placed down the diagonal of the matrix.
  
      If A is already sparse, then the operation is reversed, yielding
      a block
      row matrix, where each set of n columns corresponds to a block element
      from the block diagonal.
  
      Parameters
      ----------
      A : array
          The matrix
      n : int
          The block size
      Returns
      -------
      bd : sparse matrix
          The block diagonal matrix
      """
      if sparse.issparse(A):  # then make block sparse
          raise NotImplementedError('sparse reversal not implemented yet')
      ma, na = A.shape
      bdn = na // int(n)  # number of submatrices
  
      if na % n > 0:
          raise ValueError('Width of matrix must be a multiple of n')
  
      tmp = np.arange(ma * bdn, dtype=np.int).reshape(bdn, ma)
      tmp = np.tile(tmp, (1, n))
      ii = tmp.ravel()
  
      jj = np.arange(na, dtype=np.int)[None, :]
      jj = jj * np.ones(ma, dtype=np.int)[:, None]
      jj = jj.T.ravel()  # column indices foreach sparse bd
  
      bd = sparse.coo_matrix((A.T.ravel(), np.c_[ii, jj].T)).tocsc()
  
      return bd
  
  
  def _inv_block_diag(A, n):
      """Construct an inverse block diagonal from a packed structure.
  
      You have to try it on a matrix to see what it's doing.
  
      "A" is ma x na, comprising bdn=(na/"n") blocks of submatrices.
      Each submatrix is ma x "n", and the inverses of these submatrices
      are placed down the diagonal of the matrix.
  
      Parameters
      ----------
      A : array
          The matrix.
      n : int
          The block size.
  
      Returns
      -------
      bd : sparse matrix
          The block diagonal matrix.
      """
      ma, na = A.shape
      bdn = na // int(n)  # number of submatrices
  
      if na % n > 0:
          raise ValueError('Width of matrix must be a multiple of n')
  
      # modify A in-place to invert each sub-block
      A = A.copy()
      for start in range(0, na, 3):
          # this is a view
          A[:, start:start + 3] = linalg.inv(A[:, start:start + 3])
  
      tmp = np.arange(ma * bdn, dtype=np.int).reshape(bdn, ma)
      tmp = np.tile(tmp, (1, n))
      ii = tmp.ravel()
  
      jj = np.arange(na, dtype=np.int)[None, :]
      jj = jj * np.ones(ma, dtype=np.int)[:, None]
      jj = jj.T.ravel()  # column indices foreach sparse bd
  
      bd = sparse.coo_matrix((A.T.ravel(), np.c_[ii, jj].T)).tocsc()
  
      return bd
  
  
  def _get_tag_int(fid, node, name, id_):
      """Check we have an appropriate tag."""
      tag = find_tag(fid, node, id_)
      if tag is None:
          fid.close()
          raise ValueError(name + ' tag not found')
      return int(tag.data)
  
  
  def _read_one(fid, node):
      """Read all interesting stuff for one forward solution."""
      # This function assumes the fid is open as a context manager
      if node is None:
          return None
  
      one = Forward()
      one['source_ori'] = _get_tag_int(fid, node, 'Source orientation',
                                       FIFF.FIFF_MNE_SOURCE_ORIENTATION)
      one['coord_frame'] = _get_tag_int(fid, node, 'Coordinate frame',
                                        FIFF.FIFF_MNE_COORD_FRAME)
      one['nsource'] = _get_tag_int(fid, node, 'Number of sources',
                                    FIFF.FIFF_MNE_SOURCE_SPACE_NPOINTS)
      one['nchan'] = _get_tag_int(fid, node, 'Number of channels',
                                  FIFF.FIFF_NCHAN)
      try:
          one['sol'] = _read_named_matrix(fid, node,
                                          FIFF.FIFF_MNE_FORWARD_SOLUTION,
                                          transpose=True)
          one['_orig_sol'] = one['sol']['data'].copy()
      except Exception:
          logger.error('Forward solution data not found')
          raise
  
      try:
          fwd_type = FIFF.FIFF_MNE_FORWARD_SOLUTION_GRAD
          one['sol_grad'] = _read_named_matrix(fid, node, fwd_type,
                                               transpose=True)
          one['_orig_sol_grad'] = one['sol_grad']['data'].copy()
      except Exception:
          one['sol_grad'] = None
  
      if one['sol']['data'].shape[0] != one['nchan'] or \
              (one['sol']['data'].shape[1] != one['nsource'] and
               one['sol']['data'].shape[1] != 3 * one['nsource']):
          raise ValueError('Forward solution matrix has wrong dimensions')
  
      if one['sol_grad'] is not None:
          if one['sol_grad']['data'].shape[0] != one['nchan'] or \
                  (one['sol_grad']['data'].shape[1] != 3 * one['nsource'] and
                   one['sol_grad']['data'].shape[1] != 3 * 3 * one['nsource']):
              raise ValueError('Forward solution gradient matrix has '
                               'wrong dimensions')
  
      return one
  
  
  def _read_forward_meas_info(tree, fid):
      """Read light measurement info from forward operator.
  
      Parameters
      ----------
      tree : tree
          FIF tree structure.
      fid : file id
          The file id.
  
      Returns
      -------
      info : instance of Info
          The measurement info.
      """
      # This function assumes fid is being used as a context manager
      info = Info()
  
      # Information from the MRI file
      parent_mri = dir_tree_find(tree, FIFF.FIFFB_MNE_PARENT_MRI_FILE)
      if len(parent_mri) == 0:
          raise ValueError('No parent MEG information found in operator')
      parent_mri = parent_mri[0]
  
      tag = find_tag(fid, parent_mri, FIFF.FIFF_MNE_FILE_NAME)
      info['mri_file'] = tag.data if tag is not None else None
      tag = find_tag(fid, parent_mri, FIFF.FIFF_PARENT_FILE_ID)
      info['mri_id'] = tag.data if tag is not None else None
  
      # Information from the MEG file
      parent_meg = dir_tree_find(tree, FIFF.FIFFB_MNE_PARENT_MEAS_FILE)
      if len(parent_meg) == 0:
          raise ValueError('No parent MEG information found in operator')
      parent_meg = parent_meg[0]
  
      tag = find_tag(fid, parent_meg, FIFF.FIFF_MNE_FILE_NAME)
      info['meas_file'] = tag.data if tag is not None else None
      tag = find_tag(fid, parent_meg, FIFF.FIFF_PARENT_FILE_ID)
      info['meas_id'] = tag.data if tag is not None else None
  
      # Add channel information
      chs = list()
      for k in range(parent_meg['nent']):
          kind = parent_meg['directory'][k].kind
          pos = parent_meg['directory'][k].pos
          if kind == FIFF.FIFF_CH_INFO:
              tag = read_tag(fid, pos)
              chs.append(tag.data)
      info['chs'] = chs
      info._update_redundant()
  
      #   Get the MRI <-> head coordinate transformation
      tag = find_tag(fid, parent_mri, FIFF.FIFF_COORD_TRANS)
      coord_head = FIFF.FIFFV_COORD_HEAD
      coord_mri = FIFF.FIFFV_COORD_MRI
      coord_device = FIFF.FIFFV_COORD_DEVICE
      coord_ctf_head = FIFF.FIFFV_MNE_COORD_CTF_HEAD
      if tag is None:
          raise ValueError('MRI/head coordinate transformation not found')
      cand = tag.data
      if cand['from'] == coord_mri and cand['to'] == coord_head:
          info['mri_head_t'] = cand
      else:
          raise ValueError('MRI/head coordinate transformation not found')
  
      #   Get the MEG device <-> head coordinate transformation
      tag = find_tag(fid, parent_meg, FIFF.FIFF_COORD_TRANS)
      if tag is None:
          raise ValueError('MEG/head coordinate transformation not found')
      cand = tag.data
      if cand['from'] == coord_device and cand['to'] == coord_head:
          info['dev_head_t'] = cand
      elif cand['from'] == coord_ctf_head and cand['to'] == coord_head:
          info['ctf_head_t'] = cand
      else:
          raise ValueError('MEG/head coordinate transformation not found')
  
      info['bads'] = read_bad_channels(fid, parent_meg)
      # clean up our bad list, old versions could have non-existent bads
      info['bads'] = [bad for bad in info['bads'] if bad in info['ch_names']]
  
      # Check if a custom reference has been applied
      tag = find_tag(fid, parent_mri, FIFF.FIFF_MNE_CUSTOM_REF)
      if tag is None:
          tag = find_tag(fid, parent_mri, 236)  # Constant 236 used before v0.11
  
      info['custom_ref_applied'] = bool(tag.data) if tag is not None else False
      info._check_consistency()
      return info
  
  
  def _subject_from_forward(forward):
      """Get subject id from inverse operator."""
      return forward['src']._subject
  
  
  @verbose
  def _merge_meg_eeg_fwds(megfwd, eegfwd, verbose=None):
      """Merge loaded MEG and EEG forward dicts into one dict."""
      if megfwd is not None and eegfwd is not None:
          if (megfwd['sol']['data'].shape[1] != eegfwd['sol']['data'].shape[1] or
                  megfwd['source_ori'] != eegfwd['source_ori'] or
                  megfwd['nsource'] != eegfwd['nsource'] or
                  megfwd['coord_frame'] != eegfwd['coord_frame']):
              raise ValueError('The MEG and EEG forward solutions do not match')
  
          fwd = megfwd
          fwd['sol']['data'] = np.r_[fwd['sol']['data'], eegfwd['sol']['data']]
          fwd['_orig_sol'] = np.r_[fwd['_orig_sol'], eegfwd['_orig_sol']]
          fwd['sol']['nrow'] = fwd['sol']['nrow'] + eegfwd['sol']['nrow']
  
          fwd['sol']['row_names'] = (fwd['sol']['row_names'] +
                                     eegfwd['sol']['row_names'])
          if fwd['sol_grad'] is not None:
              fwd['sol_grad']['data'] = np.r_[fwd['sol_grad']['data'],
                                              eegfwd['sol_grad']['data']]
              fwd['_orig_sol_grad'] = np.r_[fwd['_orig_sol_grad'],
                                            eegfwd['_orig_sol_grad']]
              fwd['sol_grad']['nrow'] = (fwd['sol_grad']['nrow'] +
                                         eegfwd['sol_grad']['nrow'])
              fwd['sol_grad']['row_names'] = (fwd['sol_grad']['row_names'] +
                                              eegfwd['sol_grad']['row_names'])
  
          fwd['nchan'] = fwd['nchan'] + eegfwd['nchan']
          logger.info('    MEG and EEG forward solutions combined')
      elif megfwd is not None:
          fwd = megfwd
      else:
          fwd = eegfwd
      return fwd
  
  
  @verbose
  def read_forward_solution(fname, include=(), exclude=(), verbose=None):
      """Read a forward solution a.k.a. lead field.
  
      Parameters
      ----------
      fname : string
          The file name, which should end with -fwd.fif or -fwd.fif.gz.
      include : list, optional
          List of names of channels to include. If empty all channels
          are included.
      exclude : list, optional
          List of names of channels to exclude. If empty include all
          channels.
      %(verbose)s
  
      Returns
      -------
      fwd : instance of Forward
          The forward solution.
  
      See Also
      --------
      write_forward_solution, make_forward_solution
  
      Notes
      -----
      Forward solutions, which are derived from an original forward solution with
      free orientation, are always stored on disk as forward solution with free
      orientation in X/Y/Z RAS coordinates. To apply any transformation to the
      forward operator (surface orientation, fixed orientation) please apply
      :func:`convert_forward_solution` after reading the forward solution with
      :func:`read_forward_solution`.
  
      Forward solutions, which are derived from an original forward solution with
      fixed orientation, are stored on disk as forward solution with fixed
      surface-based orientations. Please note that the transformation to
      surface-based, fixed orientation cannot be reverted after loading the
      forward solution with :func:`read_forward_solution`.
      """
      check_fname(fname, 'forward', ('-fwd.fif', '-fwd.fif.gz',
                                     '_fwd.fif', '_fwd.fif.gz'))
  
      #   Open the file, create directory
      logger.info('Reading forward solution from %s...' % fname)
      f, tree, _ = fiff_open(fname)
      with f as fid:
          #   Find all forward solutions
          fwds = dir_tree_find(tree, FIFF.FIFFB_MNE_FORWARD_SOLUTION)
          if len(fwds) == 0:
              raise ValueError('No forward solutions in %s' % fname)
  
          #   Parent MRI data
          parent_mri = dir_tree_find(tree, FIFF.FIFFB_MNE_PARENT_MRI_FILE)
          if len(parent_mri) == 0:
              raise ValueError('No parent MRI information in %s' % fname)
          parent_mri = parent_mri[0]
  
          src = _read_source_spaces_from_tree(fid, tree, patch_stats=False)
          for s in src:
              s['id'] = find_source_space_hemi(s)
  
          fwd = None
  
          #   Locate and read the forward solutions
          megnode = None
          eegnode = None
          for k in range(len(fwds)):
              tag = find_tag(fid, fwds[k], FIFF.FIFF_MNE_INCLUDED_METHODS)
              if tag is None:
                  raise ValueError('Methods not listed for one of the forward '
                                   'solutions')
  
              if tag.data == FIFF.FIFFV_MNE_MEG:
                  megnode = fwds[k]
              elif tag.data == FIFF.FIFFV_MNE_EEG:
                  eegnode = fwds[k]
  
          megfwd = _read_one(fid, megnode)
          if megfwd is not None:
              if is_fixed_orient(megfwd):
                  ori = 'fixed'
              else:
                  ori = 'free'
              logger.info('    Read MEG forward solution (%d sources, '
                          '%d channels, %s orientations)'
                          % (megfwd['nsource'], megfwd['nchan'], ori))
  
          eegfwd = _read_one(fid, eegnode)
          if eegfwd is not None:
              if is_fixed_orient(eegfwd):
                  ori = 'fixed'
              else:
                  ori = 'free'
              logger.info('    Read EEG forward solution (%d sources, '
                          '%d channels, %s orientations)'
                          % (eegfwd['nsource'], eegfwd['nchan'], ori))
  
          fwd = _merge_meg_eeg_fwds(megfwd, eegfwd)
  
          #   Get the MRI <-> head coordinate transformation
          tag = find_tag(fid, parent_mri, FIFF.FIFF_COORD_TRANS)
          if tag is None:
              raise ValueError('MRI/head coordinate transformation not found')
          mri_head_t = tag.data
          if (mri_head_t['from'] != FIFF.FIFFV_COORD_MRI or
                  mri_head_t['to'] != FIFF.FIFFV_COORD_HEAD):
              mri_head_t = invert_transform(mri_head_t)
              if (mri_head_t['from'] != FIFF.FIFFV_COORD_MRI or
                      mri_head_t['to'] != FIFF.FIFFV_COORD_HEAD):
                  fid.close()
                  raise ValueError('MRI/head coordinate transformation not '
                                   'found')
          fwd['mri_head_t'] = mri_head_t
  
          #
          # get parent MEG info
          #
          fwd['info'] = _read_forward_meas_info(tree, fid)
  
          # MNE environment
          parent_env = dir_tree_find(tree, FIFF.FIFFB_MNE_ENV)
          if len(parent_env) > 0:
              parent_env = parent_env[0]
              tag = find_tag(fid, parent_env, FIFF.FIFF_MNE_ENV_WORKING_DIR)
              if tag is not None:
                  fwd['info']['working_dir'] = tag.data
              tag = find_tag(fid, parent_env, FIFF.FIFF_MNE_ENV_COMMAND_LINE)
              if tag is not None:
                  fwd['info']['command_line'] = tag.data
  
      #   Transform the source spaces to the correct coordinate frame
      #   if necessary
  
      # Make sure forward solution is in either the MRI or HEAD coordinate frame
      if fwd['coord_frame'] not in (FIFF.FIFFV_COORD_MRI, FIFF.FIFFV_COORD_HEAD):
          raise ValueError('Only forward solutions computed in MRI or head '
                           'coordinates are acceptable')
  
      # Transform each source space to the HEAD or MRI coordinate frame,
      # depending on the coordinate frame of the forward solution
      # NOTE: the function transform_surface_to will also work on discrete and
      # volume sources
      nuse = 0
      for s in src:
          try:
              s = transform_surface_to(s, fwd['coord_frame'], mri_head_t)
          except Exception as inst:
              raise ValueError('Could not transform source space (%s)' % inst)
  
          nuse += s['nuse']
  
      # Make sure the number of sources match after transformation
      if nuse != fwd['nsource']:
          raise ValueError('Source spaces do not match the forward solution.')
  
      logger.info('    Source spaces transformed to the forward solution '
                  'coordinate frame')
      fwd['src'] = src
  
      #   Handle the source locations and orientations
      fwd['source_rr'] = np.concatenate([ss['rr'][ss['vertno'], :]
                                         for ss in src], axis=0)
  
      #   Store original source orientations
      fwd['_orig_source_ori'] = fwd['source_ori']
  
      #   Deal with include and exclude
      pick_channels_forward(fwd, include=include, exclude=exclude, copy=False)
  
      if is_fixed_orient(fwd, orig=True):
          fwd['source_nn'] = np.concatenate([_src['nn'][_src['vertno'], :]
                                             for _src in fwd['src']], axis=0)
          fwd['source_ori'] = FIFF.FIFFV_MNE_FIXED_ORI
          fwd['surf_ori'] = True
      else:
          fwd['source_nn'] = np.kron(np.ones((fwd['nsource'], 1)), np.eye(3))
          fwd['source_ori'] = FIFF.FIFFV_MNE_FREE_ORI
          fwd['surf_ori'] = False
      return Forward(fwd)
  
  
  @verbose
  def convert_forward_solution(fwd, surf_ori=False, force_fixed=False,
                               copy=True, use_cps=True, verbose=None):
      """Convert forward solution between different source orientations.
  
      Parameters
      ----------
      fwd : Forward
          The forward solution to modify.
      surf_ori : bool, optional (default False)
          Use surface-based source coordinate system? Note that force_fixed=True
          implies surf_ori=True.
      force_fixed : bool, optional (default False)
          Force fixed source orientation mode?
      copy : bool
          Whether to return a new instance or modify in place.
      use_cps : bool (default True)
          Whether to use cortical patch statistics to define normal
          orientations. Only used when surf_ori and/or force_fixed are True.
      %(verbose)s
  
      Returns
      -------
      fwd : Forward
          The modified forward solution.
      """
      fwd = fwd.copy() if copy else fwd
  
      if force_fixed is True:
          surf_ori = True
  
      if any([src['type'] == 'vol' for src in fwd['src']]) and force_fixed:
          raise ValueError(
              'Forward operator was generated with sources from a '
              'volume source space. Conversion to fixed orientation is not '
              'possible. Consider using a discrete source space if you have '
              'meaningful normal orientations.')
  
      if surf_ori:
          if use_cps:
              if any(s.get('patch_inds') is not None for s in fwd['src']):
                  use_ave_nn = True
                  logger.info('    Average patch normals will be employed in '
                              'the rotation to the local surface coordinates..'
                              '..')
              else:
                  use_ave_nn = False
                  logger.info('    No patch info available. The standard source '
                              'space normals will be employed in the rotation '
                              'to the local surface coordinates....')
          else:
              use_ave_nn = False
  
      # We need to change these entries (only):
      # 1. source_nn
      # 2. sol['data']
      # 3. sol['ncol']
      # 4. sol_grad['data']
      # 5. sol_grad['ncol']
      # 6. source_ori
  
      if is_fixed_orient(fwd, orig=True) or (force_fixed and not use_ave_nn):
          # Fixed
          fwd['source_nn'] = np.concatenate([s['nn'][s['vertno'], :]
                                             for s in fwd['src']], axis=0)
          if not is_fixed_orient(fwd, orig=True):
              logger.info('    Changing to fixed-orientation forward '
                          'solution with surface-based source orientations...')
              fix_rot = _block_diag(fwd['source_nn'].T, 1)
              # newer versions of numpy require explicit casting here, so *= no
              # longer works
              fwd['sol']['data'] = (fwd['_orig_sol'] *
                                    fix_rot).astype('float32')
              fwd['sol']['ncol'] = fwd['nsource']
              if fwd['sol_grad'] is not None:
                  x = sparse.block_diag([fix_rot] * 3)
                  fwd['sol_grad']['data'] = fwd['_orig_sol_grad'] * x  # dot prod
                  fwd['sol_grad']['ncol'] = 3 * fwd['nsource']
          fwd['source_ori'] = FIFF.FIFFV_MNE_FIXED_ORI
          fwd['surf_ori'] = True
  
      elif surf_ori:  # Free, surf-oriented
          #   Rotate the local source coordinate systems
          fwd['source_nn'] = np.kron(np.ones((fwd['nsource'], 1)), np.eye(3))
          logger.info('    Converting to surface-based source orientations...')
          #   Actually determine the source orientations
          pp = 0
          for s in fwd['src']:
              if s['type'] in ['surf', 'discrete']:
                  for p in range(s['nuse']):
                      #  Project out the surface normal and compute SVD
                      if use_ave_nn and s.get('patch_inds') is not None:
                          nn = s['nn'][s['pinfo'][s['patch_inds'][p]], :]
                          nn = np.sum(nn, axis=0)[:, np.newaxis]
                          nn /= linalg.norm(nn)
                      else:
                          nn = s['nn'][s['vertno'][p], :][:, np.newaxis]
                      U, S, _ = linalg.svd(np.eye(3, 3) - nn * nn.T)
                      #  Make sure that ez is in the direction of nn
                      if np.sum(nn.ravel() * U[:, 2].ravel()) < 0:
                          U *= -1.0
                      fwd['source_nn'][pp:pp + 3, :] = U.T
                      pp += 3
              else:
                  pp += 3 * s['nuse']
  
          #   Rotate the solution components as well
          if force_fixed:
              fwd['source_nn'] = fwd['source_nn'][2::3, :]
              fix_rot = _block_diag(fwd['source_nn'].T, 1)
              # newer versions of numpy require explicit casting here, so *= no
              # longer works
              fwd['sol']['data'] = (fwd['_orig_sol'] *
                                    fix_rot).astype('float32')
              fwd['sol']['ncol'] = fwd['nsource']
              if fwd['sol_grad'] is not None:
                  x = sparse.block_diag([fix_rot] * 3)
                  fwd['sol_grad']['data'] = fwd['_orig_sol_grad'] * x  # dot prod
                  fwd['sol_grad']['ncol'] = 3 * fwd['nsource']
              fwd['source_ori'] = FIFF.FIFFV_MNE_FIXED_ORI
              fwd['surf_ori'] = True
          else:
              surf_rot = _block_diag(fwd['source_nn'].T, 3)
              fwd['sol']['data'] = fwd['_orig_sol'] * surf_rot
              fwd['sol']['ncol'] = 3 * fwd['nsource']
              if fwd['sol_grad'] is not None:
                  x = sparse.block_diag([surf_rot] * 3)
                  fwd['sol_grad']['data'] = fwd['_orig_sol_grad'] * x  # dot prod
                  fwd['sol_grad']['ncol'] = 9 * fwd['nsource']
              fwd['source_ori'] = FIFF.FIFFV_MNE_FREE_ORI
              fwd['surf_ori'] = True
  
      else:  # Free, cartesian
          logger.info('    Cartesian source orientations...')
          fwd['source_nn'] = np.kron(np.ones((fwd['nsource'], 1)), np.eye(3))
          fwd['sol']['data'] = fwd['_orig_sol'].copy()
          fwd['sol']['ncol'] = 3 * fwd['nsource']
          if fwd['sol_grad'] is not None:
              fwd['sol_grad']['data'] = fwd['_orig_sol_grad'].copy()
              fwd['sol_grad']['ncol'] = 9 * fwd['nsource']
          fwd['source_ori'] = FIFF.FIFFV_MNE_FREE_ORI
          fwd['surf_ori'] = False
  
      logger.info('    [done]')
  
      return fwd
  
  
  @verbose
  def write_forward_solution(fname, fwd, overwrite=False, verbose=None):
      """Write forward solution to a file.
  
      Parameters
      ----------
      fname : str
          File name to save the forward solution to. It should end with -fwd.fif
          or -fwd.fif.gz.
      fwd : Forward
          Forward solution.
      overwrite : bool
          If True, overwrite destination file (if it exists).
      %(verbose)s
  
      See Also
      --------
      read_forward_solution
  
      Notes
      -----
      Forward solutions, which are derived from an original forward solution with
      free orientation, are always stored on disk as forward solution with free
      orientation in X/Y/Z RAS coordinates. Transformations (surface orientation,
      fixed orientation) will be reverted. To reapply any transformation to the
      forward operator please apply :func:`convert_forward_solution` after
      reading the forward solution with :func:`read_forward_solution`.
  
      Forward solutions, which are derived from an original forward solution with
      fixed orientation, are stored on disk as forward solution with fixed
      surface-based orientations. Please note that the transformation to
      surface-based, fixed orientation cannot be reverted after loading the
      forward solution with :func:`read_forward_solution`.
      """
      check_fname(fname, 'forward', ('-fwd.fif', '-fwd.fif.gz',
                                     '_fwd.fif', '_fwd.fif.gz'))
  
      # check for file existence
      _check_fname(fname, overwrite)
      fid = start_file(fname)
      start_block(fid, FIFF.FIFFB_MNE)
  
      #
      # MNE env
      #
      start_block(fid, FIFF.FIFFB_MNE_ENV)
      write_id(fid, FIFF.FIFF_BLOCK_ID)
      data = fwd['info'].get('working_dir', None)
      if data is not None:
          write_string(fid, FIFF.FIFF_MNE_ENV_WORKING_DIR, data)
      data = fwd['info'].get('command_line', None)
      if data is not None:
          write_string(fid, FIFF.FIFF_MNE_ENV_COMMAND_LINE, data)
      end_block(fid, FIFF.FIFFB_MNE_ENV)
  
      #
      # Information from the MRI file
      #
      start_block(fid, FIFF.FIFFB_MNE_PARENT_MRI_FILE)
      write_string(fid, FIFF.FIFF_MNE_FILE_NAME, fwd['info']['mri_file'])
      if fwd['info']['mri_id'] is not None:
          write_id(fid, FIFF.FIFF_PARENT_FILE_ID, fwd['info']['mri_id'])
      # store the MRI to HEAD transform in MRI file
      write_coord_trans(fid, fwd['info']['mri_head_t'])
      end_block(fid, FIFF.FIFFB_MNE_PARENT_MRI_FILE)
  
      # write measurement info
      write_forward_meas_info(fid, fwd['info'])
  
      # invert our original source space transform
      src = list()
      for s in fwd['src']:
          s = deepcopy(s)
          try:
              # returns source space to original coordinate frame
              # usually MRI
              s = transform_surface_to(s, fwd['mri_head_t']['from'],
                                       fwd['mri_head_t'])
          except Exception as inst:
              raise ValueError('Could not transform source space (%s)' % inst)
          src.append(s)
  
      #
      # Write the source spaces (again)
      #
      _write_source_spaces_to_fid(fid, src)
      n_vert = sum([ss['nuse'] for ss in src])
      if fwd['_orig_source_ori'] == FIFF.FIFFV_MNE_FIXED_ORI:
          n_col = n_vert
      else:
          n_col = 3 * n_vert
  
      # Undo transformations
      sol = fwd['_orig_sol'].copy()
      if fwd['sol_grad'] is not None:
          sol_grad = fwd['_orig_sol_grad'].copy()
      else:
          sol_grad = None
  
      if fwd['surf_ori'] is True:
          if fwd['_orig_source_ori'] == FIFF.FIFFV_MNE_FIXED_ORI:
              warn('The forward solution, which is stored on disk now, is based '
                   'on a forward solution with fixed orientation. Please note '
                   'that the transformation to surface-based, fixed orientation '
                   'cannot be reverted after loading the forward solution with '
                   'read_forward_solution.', RuntimeWarning)
          else:
              warn('This forward solution is based on a forward solution with '
                   'free orientation. The original forward solution is stored '
                   'on disk in X/Y/Z RAS coordinates. Any transformation '
                   '(surface orientation or fixed orientation) will be '
                   'reverted. To reapply any transformation to the forward '
                   'operator please apply convert_forward_solution after '
                   'reading the forward solution with read_forward_solution.',
                   RuntimeWarning)
  
      #
      # MEG forward solution
      #
      picks_meg = pick_types(fwd['info'], meg=True, eeg=False, ref_meg=False,
                             exclude=[])
      picks_eeg = pick_types(fwd['info'], meg=False, eeg=True, ref_meg=False,
                             exclude=[])
      n_meg = len(picks_meg)
      n_eeg = len(picks_eeg)
      row_names_meg = [fwd['sol']['row_names'][p] for p in picks_meg]
      row_names_eeg = [fwd['sol']['row_names'][p] for p in picks_eeg]
  
      if n_meg > 0:
          meg_solution = dict(data=sol[picks_meg], nrow=n_meg, ncol=n_col,
                              row_names=row_names_meg, col_names=[])
          _transpose_named_matrix(meg_solution)
          start_block(fid, FIFF.FIFFB_MNE_FORWARD_SOLUTION)
          write_int(fid, FIFF.FIFF_MNE_INCLUDED_METHODS, FIFF.FIFFV_MNE_MEG)
          write_int(fid, FIFF.FIFF_MNE_COORD_FRAME, fwd['coord_frame'])
          write_int(fid, FIFF.FIFF_MNE_SOURCE_ORIENTATION,
                    fwd['_orig_source_ori'])
          write_int(fid, FIFF.FIFF_MNE_SOURCE_SPACE_NPOINTS, n_vert)
          write_int(fid, FIFF.FIFF_NCHAN, n_meg)
          write_named_matrix(fid, FIFF.FIFF_MNE_FORWARD_SOLUTION, meg_solution)
          if sol_grad is not None:
              meg_solution_grad = dict(data=sol_grad[picks_meg],
                                       nrow=n_meg, ncol=n_col * 3,
                                       row_names=row_names_meg, col_names=[])
              _transpose_named_matrix(meg_solution_grad)
              write_named_matrix(fid, FIFF.FIFF_MNE_FORWARD_SOLUTION_GRAD,
                                 meg_solution_grad)
          end_block(fid, FIFF.FIFFB_MNE_FORWARD_SOLUTION)
  
      #
      #  EEG forward solution
      #
      if n_eeg > 0:
          eeg_solution = dict(data=sol[picks_eeg], nrow=n_eeg, ncol=n_col,
                              row_names=row_names_eeg, col_names=[])
          _transpose_named_matrix(eeg_solution)
          start_block(fid, FIFF.FIFFB_MNE_FORWARD_SOLUTION)
          write_int(fid, FIFF.FIFF_MNE_INCLUDED_METHODS, FIFF.FIFFV_MNE_EEG)
          write_int(fid, FIFF.FIFF_MNE_COORD_FRAME, fwd['coord_frame'])
          write_int(fid, FIFF.FIFF_MNE_SOURCE_ORIENTATION,
                    fwd['_orig_source_ori'])
          write_int(fid, FIFF.FIFF_NCHAN, n_eeg)
          write_int(fid, FIFF.FIFF_MNE_SOURCE_SPACE_NPOINTS, n_vert)
          write_named_matrix(fid, FIFF.FIFF_MNE_FORWARD_SOLUTION, eeg_solution)
          if sol_grad is not None:
              eeg_solution_grad = dict(data=sol_grad[picks_eeg],
                                       nrow=n_eeg, ncol=n_col * 3,
                                       row_names=row_names_eeg, col_names=[])
              _transpose_named_matrix(eeg_solution_grad)
              write_named_matrix(fid, FIFF.FIFF_MNE_FORWARD_SOLUTION_GRAD,
                                 eeg_solution_grad)
          end_block(fid, FIFF.FIFFB_MNE_FORWARD_SOLUTION)
  
      end_block(fid, FIFF.FIFFB_MNE)
      end_file(fid)
  
  
  def is_fixed_orient(forward, orig=False):
      """Check if the forward operator is fixed orientation.
  
      Parameters
      ----------
      forward : instance of Forward
          The forward.
      orig : bool
          If True, consider the original source orientation.
          If False (default), consider the current source orientation.
  
      Returns
      -------
      fixed_ori : bool
          Whether or not it is fixed orientation.
      """
      if orig:  # if we want to know about the original version
          fixed_ori = (forward['_orig_source_ori'] == FIFF.FIFFV_MNE_FIXED_ORI)
      else:  # most of the time we want to know about the current version
          fixed_ori = (forward['source_ori'] == FIFF.FIFFV_MNE_FIXED_ORI)
      return fixed_ori
  
  
  def write_forward_meas_info(fid, info):
      """Write measurement info stored in forward solution.
  
      Parameters
      ----------
      fid : file id
          The file id
      info : instance of Info
          The measurement info.
      """
      info._check_consistency()
      #
      # Information from the MEG file
      #
      start_block(fid, FIFF.FIFFB_MNE_PARENT_MEAS_FILE)
      write_string(fid, FIFF.FIFF_MNE_FILE_NAME, info['meas_file'])
      if info['meas_id'] is not None:
          write_id(fid, FIFF.FIFF_PARENT_BLOCK_ID, info['meas_id'])
      # get transformation from CTF and DEVICE to HEAD coordinate frame
      meg_head_t = info.get('dev_head_t', info.get('ctf_head_t'))
      if meg_head_t is None:
          fid.close()
          raise ValueError('Head<-->sensor transform not found')
      write_coord_trans(fid, meg_head_t)
  
      if 'chs' in info:
          #  Channel information
          write_int(fid, FIFF.FIFF_NCHAN, len(info['chs']))
          for k, c in enumerate(info['chs']):
              #   Scan numbers may have been messed up
              c = deepcopy(c)
              c['scanno'] = k + 1
              write_ch_info(fid, c)
      if 'bads' in info and len(info['bads']) > 0:
          #   Bad channels
          start_block(fid, FIFF.FIFFB_MNE_BAD_CHANNELS)
          write_name_list(fid, FIFF.FIFF_MNE_CH_NAME_LIST, info['bads'])
          end_block(fid, FIFF.FIFFB_MNE_BAD_CHANNELS)
  
      end_block(fid, FIFF.FIFFB_MNE_PARENT_MEAS_FILE)
  
  
  def _select_orient_forward(forward, info, noise_cov=None, copy=True):
      """Prepare forward solution for inverse solvers."""
      # fwd['sol']['row_names'] may be different order from fwd['info']['chs']
      fwd_sol_ch_names = forward['sol']['row_names']
      all_ch_names = set(fwd_sol_ch_names)
      all_bads = set(info['bads'])
      if noise_cov is not None:
          all_ch_names &= set(noise_cov['names'])
          all_bads |= set(noise_cov['bads'])
      else:
          noise_cov = dict(bads=info['bads'])
      ch_names = [c['ch_name'] for c in info['chs']
                  if c['ch_name'] not in all_bads and
                  c['ch_name'] in all_ch_names]
  
      if not len(info['bads']) == len(noise_cov['bads']) or \
              not all(b in noise_cov['bads'] for b in info['bads']):
          logger.info('info["bads"] and noise_cov["bads"] do not match, '
                      'excluding bad channels from both')
  
      # check the compensation grade
      _check_compensation_grade(forward['info'], info, 'forward')
  
      n_chan = len(ch_names)
      logger.info("Computing inverse operator with %d channels." % n_chan)
      forward = pick_channels_forward(forward, ch_names, ordered=True,
                                      copy=copy)
      info_idx = [info['ch_names'].index(name) for name in ch_names]
      info_picked = pick_info(info, info_idx)
      forward['info']._check_consistency()
      info_picked._check_consistency()
      return forward, info_picked
  
  
  @verbose
  def compute_orient_prior(forward, loose=0.2, verbose=None):
      """Compute orientation prior.
  
      Parameters
      ----------
      forward : instance of Forward
          Forward operator.
      loose : float
          The loose orientation parameter (between 0 and 1).
      %(verbose)s
  
      Returns
      -------
      orient_prior : ndarray, shape (n_vertices,)
          Orientation priors.
  
      See Also
      --------
      compute_depth_prior
      """
      is_fixed_ori = is_fixed_orient(forward)
      n_sources = forward['sol']['data'].shape[1]
      loose = float(loose)
      if not (0 <= loose <= 1):
          raise ValueError('loose value should be between 0 and 1, '
                           'got %s.' % (loose,))
      orient_prior = np.ones(n_sources, dtype=np.float)
      if loose > 0.:
          if is_fixed_ori:
              raise ValueError('loose must be 0. with forward operator '
                               'with fixed orientation, got %s' % (loose,))
          if loose < 1:
              if not forward['surf_ori']:
                  raise ValueError('Forward operator is not oriented in surface '
                                   'coordinates. loose parameter should be 1 '
                                   'not %s.' % (loose,))
              logger.info('Applying loose dipole orientations. Loose value '
                          'of %s.' % loose)
              orient_prior[0::3] *= loose
              orient_prior[1::3] *= loose
  
      return orient_prior
  
  
  def _restrict_gain_matrix(G, info):
      """Restrict gain matrix entries for optimal depth weighting."""
      # Figure out which ones have been used
      if len(info['chs']) != G.shape[0]:
          raise ValueError('G.shape[0] (%d) and length of info["chs"] (%d) '
                           'do not match' % (G.shape[0], len(info['chs'])))
      for meg, eeg, kind in (
              ('grad', False, 'planar'),
              ('mag', False, 'magnetometer or axial gradiometer'),
              (False, True, 'EEG')):
          sel = pick_types(info, meg=meg, eeg=eeg, ref_meg=False, exclude=[])
          if len(sel) > 0:
              logger.info('    %d %s channels' % (len(sel), kind))
              break
      else:
          warn('Could not find MEG or EEG channels to limit depth channels')
          sel = slice(None)
      return G[sel]
  
  
  @verbose
  def compute_depth_prior(forward, info, exp=0.8, limit=10.0,
                          limit_depth_chs=False, combine_xyz='spectral',
                          noise_cov=None, rank=None, verbose=None):
      """Compute depth prior for depth weighting.
  
      Parameters
      ----------
      forward : instance of Forward
          The forward solution.
      info : instance of Info
          The measurement info.
      exp : float
          Exponent for the depth weighting, must be between 0 and 1.
      limit : float | None
          The upper bound on depth weighting.
          Can be None to be bounded by the largest finite prior.
      limit_depth_chs : bool | 'whiten'
          How to deal with multiple channel types in depth weighting.
          The default is True, which whitens based on the source sensitivity
          of the highest-SNR channel type. See Notes for details.
  
          .. versionchanged:: 0.18
             Added the "whiten" option.
      combine_xyz : 'spectral' | 'fro'
          When a loose (or free) orientation is used, how the depth weighting
          for each triplet should be calculated.
          If 'spectral', use the squared spectral norm of Gk.
          If 'fro', use the squared Frobenius norm of Gk.
  
          .. versionadded:: 0.18
      noise_cov : instance of Covariance | None
          The noise covariance to use to whiten the gain matrix when
          ``limit_depth_chs='whiten'``.
  
          .. versionadded:: 0.18
      %(rank_None)s
  
          .. versionadded:: 0.18
      %(verbose)s
  
      Returns
      -------
      depth_prior : ndarray, shape (n_vertices,)
          The depth prior.
  
      See Also
      --------
      compute_orient_prior
  
      Notes
      -----
      The defaults used by the minimum norm code and sparse solvers differ.
      In particular, the values for MNE are::
  
          compute_depth_prior(..., limit=10., limit_depth_chs=True,
                              combine_xyz='spectral')
  
      In sparse solvers and LCMV, the values are::
  
          compute_depth_prior(..., limit=None, limit_depth_chs='whiten',
                              combine_xyz='fro')
  
      The ``limit_depth_chs`` argument can take the following values:
  
      * :data:`python:True` (default)
            Use only grad channels in depth weighting (equivalent to MNE C
            minimum-norm code). If grad channels aren't present, only mag
            channels will be used (if no mag, then eeg). This makes the depth
            prior dependent only on the sensor geometry (and relationship
            to the sources).
      * ``'whiten'``
            Compute a whitener and apply it to the gain matirx before computing
            the depth prior. In this case ``noise_cov`` must not be None.
            Whitening the gain matrix makes the depth prior
            depend on both sensor geometry and the data of interest captured
            by the noise covariance (e.g., projections, SNR).
  
            .. versionadded:: 0.18
      * :data:`python:False`
            Use all channels. Not recommended since the depth weighting will be
            biased toward whichever channel type has the largest values in
            SI units (such as EEG being orders of magnitude larger than MEG).
  
      """
      from ..cov import Covariance, compute_whitener
      _validate_type(forward, Forward, 'forward')
      patch_areas = forward.get('patch_areas', None)
      is_fixed_ori = is_fixed_orient(forward)
      G = forward['sol']['data']
      logger.info('Creating the depth weighting matrix...')
      _validate_type(noise_cov, (Covariance, None), 'noise_cov',
                     'Covariance or None')
      _validate_type(limit_depth_chs, (str, bool), 'limit_depth_chs')
      if isinstance(limit_depth_chs, str):
          if limit_depth_chs != 'whiten':
              raise ValueError('limit_depth_chs, if str, must be "whiten", got '
                               '%s' % (limit_depth_chs,))
          if not isinstance(noise_cov, Covariance):
              raise ValueError('With limit_depth_chs="whiten", noise_cov must be'
                               ' a Covariance, got %s' % (type(noise_cov),))
      if combine_xyz is not False:  # private / expert option
          _check_option('combine_xyz', combine_xyz, ('fro', 'spectral'))
  
      # If possible, pick best depth-weighting channels
      if limit_depth_chs is True:
          G = _restrict_gain_matrix(G, info)
      elif limit_depth_chs == 'whiten':
          whitener, _ = compute_whitener(noise_cov, info, pca=True, rank=rank,
                                         verbose=False)
          G = np.dot(whitener, G)
  
      # Compute the gain matrix
      if is_fixed_ori or combine_xyz in ('fro', False):
          d = np.sum(G ** 2, axis=0)
          if not (is_fixed_ori or combine_xyz is False):
              d = d.reshape(-1, 3).sum(axis=1)
          # Spherical leadfield can be zero at the center
          d[d == 0.] = np.min(d[d != 0.])
      else:  # 'spectral'
          # n_pos = G.shape[1] // 3
          # The following is equivalent to this, but 4-10x faster
          # d = np.zeros(n_pos)
          # for k in range(n_pos):
          #     Gk = G[:, 3 * k:3 * (k + 1)]
          #     x = np.dot(Gk.T, Gk)
          #     d[k] = linalg.svdvals(x)[0]
          G.shape = (G.shape[0], -1, 3)
          d = np.linalg.norm(einsum('svj,svk->vjk', G, G),  # vector dot products
                             ord=2, axis=(1, 2))  # ord=2 spectral (largest s.v.)
          G.shape = (G.shape[0], -1)
  
      # XXX Currently the fwd solns never have "patch_areas" defined
      if patch_areas is not None:
          if not is_fixed_ori and combine_xyz is False:
              patch_areas = np.repeat(patch_areas, 3)
          d /= patch_areas ** 2
          logger.info('    Patch areas taken into account in the depth '
                      'weighting')
  
      w = 1.0 / d
      if limit is not None:
          ws = np.sort(w)
          weight_limit = limit ** 2
          if limit_depth_chs is False:
              # match old mne-python behavor
              # we used to do ind = np.argmin(ws), but this is 0 by sort above
              n_limit = 0
              limit = ws[0] * weight_limit
          else:
              # match C code behavior
              limit = ws[-1]
              n_limit = len(d)
              if ws[-1] > weight_limit * ws[0]:
                  ind = np.where(ws > weight_limit * ws[0])[0][0]
                  limit = ws[ind]
                  n_limit = ind
  
          logger.info('    limit = %d/%d = %f'
                      % (n_limit + 1, len(d),
                         np.sqrt(limit / ws[0])))
          scale = 1.0 / limit
          logger.info('    scale = %g exp = %g' % (scale, exp))
          w = np.minimum(w / limit, 1)
      depth_prior = w ** exp
  
      if not (is_fixed_ori or combine_xyz is False):
          depth_prior = np.repeat(depth_prior, 3)
  
      return depth_prior
  
  
  def _stc_src_sel(src, stc, on_missing='raise',
                   extra=', likely due to forward calculations'):
      """Select the vertex indices of a source space using a source estimate."""
      if isinstance(stc, list):
          vertices = stc
      else:
          assert isinstance(stc, _BaseSourceEstimate)
          vertices = stc._vertices_list
      del stc
      if not len(src) == len(vertices):
          raise RuntimeError('Mismatch between number of source spaces (%s) and '
                             'STC vertices (%s)' % (len(src), len(vertices)))
      src_sels, stc_sels, out_vertices = [], [], []
      src_offset = stc_offset = 0
      for s, v in zip(src, vertices):
          joint_sel = np.intersect1d(s['vertno'], v)
          src_sels.append(np.searchsorted(s['vertno'], joint_sel) + src_offset)
          src_offset += len(s['vertno'])
          idx = np.searchsorted(v, joint_sel)
          stc_sels.append(idx + stc_offset)
          stc_offset += len(v)
          out_vertices.append(np.array(v)[idx])
      src_sel = np.concatenate(src_sels)
      stc_sel = np.concatenate(stc_sels)
      assert len(src_sel) == len(stc_sel) == sum(len(v) for v in out_vertices)
  
      n_stc = sum(len(v) for v in vertices)
      n_joint = len(src_sel)
      if n_joint != n_stc:
          msg = ('Only %i of %i SourceEstimate %s found in '
                 'source space%s'
                 % (n_joint, n_stc, 'vertex' if n_stc == 1 else 'vertices',
                    extra))
          if on_missing == 'raise':
              raise RuntimeError(msg)
          elif on_missing == 'warn':
              warn(msg)
          else:
              assert on_missing == 'ignore'
      return src_sel, stc_sel, out_vertices
  
  
  def _fill_measurement_info(info, fwd, sfreq):
      """Fill the measurement info of a Raw or Evoked object."""
      sel = pick_channels(info['ch_names'], fwd['sol']['row_names'])
      info = pick_info(info, sel)
      info['bads'] = []
  
      # this is probably correct based on what's done in meas_info.py...
      info['meas_id'] = fwd['info']['meas_id']
      info['file_id'] = info['meas_id']
  
      now = time()
      sec = np.floor(now)
      usec = 1e6 * (now - sec)
  
      info['meas_date'] = (int(sec), int(usec))
      info['highpass'] = 0.0
      info['lowpass'] = sfreq / 2.0
      info['sfreq'] = sfreq
      info['projs'] = []
  
      return info
  
  
  @verbose
  def _apply_forward(fwd, stc, start=None, stop=None, on_missing='raise',
                     verbose=None):
      """Apply forward model and return data, times, ch_names."""
      if not is_fixed_orient(fwd):
          raise ValueError('Only fixed-orientation forward operators are '
                           'supported.')
  
      if np.all(stc.data > 0):
          warn('Source estimate only contains currents with positive values. '
               'Use pick_ori="normal" when computing the inverse to compute '
               'currents not current magnitudes.')
  
      max_cur = np.max(np.abs(stc.data))
      if max_cur > 1e-7:  # 100 nAm threshold for warning
          warn('The maximum current magnitude is %0.1f nAm, which is very large.'
               ' Are you trying to apply the forward model to noise-normalized '
               '(dSPM, sLORETA, or eLORETA) values? The result will only be '
               'correct if currents (in units of Am) are used.'
               % (1e9 * max_cur))
  
      src_sel, stc_sel, _ = _stc_src_sel(fwd['src'], stc, on_missing=on_missing)
      gain = fwd['sol']['data'][:, src_sel]
      # save some memory if possible
      stc_sel = slice(None) if len(stc_sel) == len(stc.data) else stc_sel
  
      logger.info('Projecting source estimate to sensor space...')
      data = np.dot(gain, stc.data[stc_sel, start:stop])
      logger.info('[done]')
  
      times = deepcopy(stc.times[start:stop])
  
      return data, times
  
  
  @verbose
  def apply_forward(fwd, stc, info, start=None, stop=None, use_cps=True,
                    on_missing='raise', verbose=None):
      """Project source space currents to sensor space using a forward operator.
  
      The sensor space data is computed for all channels present in fwd. Use
      pick_channels_forward or pick_types_forward to restrict the solution to a
      subset of channels.
  
      The function returns an Evoked object, which is constructed from
      evoked_template. The evoked_template should be from the same MEG system on
      which the original data was acquired. An exception will be raised if the
      forward operator contains channels that are not present in the template.
  
  
      Parameters
      ----------
      fwd : Forward
          Forward operator to use.
      stc : SourceEstimate
          The source estimate from which the sensor space data is computed.
      info : instance of Info
          Measurement info to generate the evoked.
      start : int, optional
          Index of first time sample (index not time is seconds).
      stop : int, optional
          Index of first time sample not to include (index not time is seconds).
      use_cps : bool (default True)
          Whether to use cortical patch statistics to define normal
          orientations when converting to fixed orientation (if necessary).
  
          .. versionadded:: 0.15
      %(on_missing)s Default is "raise".
  
          .. versionadded:: 0.18
      %(verbose)s
  
      Returns
      -------
      evoked : Evoked
          Evoked object with computed sensor space data.
  
      See Also
      --------
      apply_forward_raw: Compute sensor space data and return a Raw object.
      """
      # make sure evoked_template contains all channels in fwd
      for ch_name in fwd['sol']['row_names']:
          if ch_name not in info['ch_names']:
              raise ValueError('Channel %s of forward operator not present in '
                               'evoked_template.' % ch_name)
  
      # project the source estimate to the sensor space
      if not is_fixed_orient(fwd):
          fwd = convert_forward_solution(fwd, force_fixed=True, use_cps=use_cps)
      data, times = _apply_forward(fwd, stc, start, stop, on_missing=on_missing)
  
      # fill the measurement info
      sfreq = float(1.0 / stc.tstep)
      info_out = _fill_measurement_info(info, fwd, sfreq)
  
      evoked = EvokedArray(data, info_out, times[0], nave=1)
  
      evoked.times = times
      evoked.first = int(np.round(evoked.times[0] * sfreq))
      evoked.last = evoked.first + evoked.data.shape[1] - 1
  
      return evoked
  
  
  @verbose
  def apply_forward_raw(fwd, stc, info, start=None, stop=None,
                        on_missing='raise', verbose=None):
      """Project source space currents to sensor space using a forward operator.
  
      The sensor space data is computed for all channels present in fwd. Use
      pick_channels_forward or pick_types_forward to restrict the solution to a
      subset of channels.
  
      The function returns a Raw object, which is constructed using provided
      info. The info object should be from the same MEG system on which the
      original data was acquired. An exception will be raised if the forward
      operator contains channels that are not present in the info.
  
      Parameters
      ----------
      fwd : Forward
          Forward operator to use. Has to be fixed-orientation.
      stc : SourceEstimate
          The source estimate from which the sensor space data is computed.
      info : instance of Info
          The measurement info.
      start : int, optional
          Index of first time sample (index not time is seconds).
      stop : int, optional
          Index of first time sample not to include (index not time is seconds).
      %(on_missing)s Default is "raise".
  
          .. versionadded:: 0.18
      %(verbose)s
  
      Returns
      -------
      raw : Raw object
          Raw object with computed sensor space data.
  
      See Also
      --------
      apply_forward: Compute sensor space data and return an Evoked object.
      """
      # make sure info contains all channels in fwd
      for ch_name in fwd['sol']['row_names']:
          if ch_name not in info['ch_names']:
              raise ValueError('Channel %s of forward operator not present in '
                               'info.' % ch_name)
  
      # project the source estimate to the sensor space
      data, times = _apply_forward(fwd, stc, start, stop, on_missing=on_missing)
  
      sfreq = 1.0 / stc.tstep
      info = _fill_measurement_info(info, fwd, sfreq)
      info['projs'] = []
      # store sensor data in Raw object using the info
      raw = RawArray(data, info)
      raw.preload = True
  
      raw._first_samps = np.array([int(np.round(times[0] * sfreq))])
      raw._last_samps = np.array([raw.first_samp + raw._data.shape[1] - 1])
      raw._projector = None
      raw._update_times()
      return raw
  
  
  @fill_doc
  def restrict_forward_to_stc(fwd, stc, on_missing='ignore'):
      """Restrict forward operator to active sources in a source estimate.
  
      Parameters
      ----------
      fwd : instance of Forward
          Forward operator.
      stc : instance of SourceEstimate
          Source estimate.
      %(on_missing)s Default is "ignore".
  
          .. versionadded:: 0.18
  
      Returns
      -------
      fwd_out : instance of Forward
          Restricted forward operator.
  
      See Also
      --------
      restrict_forward_to_label
      """
      _validate_type(on_missing, str, 'on_missing')
      _check_option('on_missing', on_missing, ('ignore', 'warn', 'raise'))
      src_sel, _, vertices = _stc_src_sel(fwd['src'], stc, on_missing=on_missing)
      del stc
      return _restrict_forward_to_src_sel(fwd, src_sel)
  
  
  def _restrict_forward_to_src_sel(fwd, src_sel):
      fwd_out = deepcopy(fwd)
      # figure out the vertno we are keeping
      idx_sel = np.concatenate([[[si] * len(s['vertno']), s['vertno']]
                                for si, s in enumerate(fwd['src'])], axis=-1)
      assert idx_sel.ndim == 2 and idx_sel.shape[0] == 2
      assert idx_sel.shape[1] == fwd['nsource']
      idx_sel = idx_sel[:, src_sel]
  
      fwd_out['source_rr'] = fwd['source_rr'][src_sel]
      fwd_out['nsource'] = len(src_sel)
  
      if is_fixed_orient(fwd):
          idx = src_sel
          if fwd['sol_grad'] is not None:
              idx_grad = (3 * src_sel[:, None] + np.arange(3)).ravel()
      else:
          idx = (3 * src_sel[:, None] + np.arange(3)).ravel()
          if fwd['sol_grad'] is not None:
              idx_grad = (9 * src_sel[:, None] + np.arange(9)).ravel()
  
      fwd_out['source_nn'] = fwd['source_nn'][idx]
      fwd_out['sol']['data'] = fwd['sol']['data'][:, idx]
      if fwd['sol_grad'] is not None:
          fwd_out['sol_grad']['data'] = fwd['sol_grad']['data'][:, idx_grad]
      fwd_out['sol']['ncol'] = len(idx)
  
      if is_fixed_orient(fwd, orig=True):
          idx = src_sel
          if fwd['sol_grad'] is not None:
              idx_grad = (3 * src_sel[:, None] + np.arange(3)).ravel()
      else:
          idx = (3 * src_sel[:, None] + np.arange(3)).ravel()
          if fwd['sol_grad'] is not None:
              idx_grad = (9 * src_sel[:, None] + np.arange(9)).ravel()
  
      fwd_out['_orig_sol'] = fwd['_orig_sol'][:, idx]
      if fwd['sol_grad'] is not None:
          fwd_out['_orig_sol_grad'] = fwd['_orig_sol_grad'][:, idx_grad]
  
      vertices = [idx_sel[1][idx_sel[0] == si]
                  for si in range(len(fwd_out['src']))]
      _set_source_space_vertices(fwd_out['src'], vertices)
  
      return fwd_out
  
  
  def restrict_forward_to_label(fwd, labels):
      """Restrict forward operator to labels.
  
      Parameters
      ----------
      fwd : Forward
          Forward operator.
      labels : instance of Label | list
          Label object or list of label objects.
  
      Returns
      -------
      fwd_out : dict
          Restricted forward operator.
  
      See Also
      --------
      restrict_forward_to_stc
      """
      vertices = [np.array([], int), np.array([], int)]
  
      if not isinstance(labels, list):
          labels = [labels]
  
      # Get vertices separately of each hemisphere from all label
      for label in labels:
          _validate_type(label, Label, "label", "Label or list")
          i = 0 if label.hemi == 'lh' else 1
          vertices[i] = np.append(vertices[i], label.vertices)
      # Remove duplicates and sort
      vertices = [np.unique(vert_hemi) for vert_hemi in vertices]
  
      fwd_out = deepcopy(fwd)
      fwd_out['source_rr'] = np.zeros((0, 3))
      fwd_out['nsource'] = 0
      fwd_out['source_nn'] = np.zeros((0, 3))
      fwd_out['sol']['data'] = np.zeros((fwd['sol']['data'].shape[0], 0))
      fwd_out['_orig_sol'] = np.zeros((fwd['_orig_sol'].shape[0], 0))
      if fwd['sol_grad'] is not None:
          fwd_out['sol_grad']['data'] = np.zeros(
              (fwd['sol_grad']['data'].shape[0], 0))
          fwd_out['_orig_sol_grad'] = np.zeros(
              (fwd['_orig_sol_grad'].shape[0], 0))
      fwd_out['sol']['ncol'] = 0
      nuse_lh = fwd['src'][0]['nuse']
  
      for i in range(2):
          fwd_out['src'][i]['vertno'] = np.array([], int)
          fwd_out['src'][i]['nuse'] = 0
          fwd_out['src'][i]['inuse'] = fwd['src'][i]['inuse'].copy()
          fwd_out['src'][i]['inuse'].fill(0)
          fwd_out['src'][i]['use_tris'] = np.array([[]], int)
          fwd_out['src'][i]['nuse_tri'] = np.array([0])
  
          # src_sel is idx to cols in fwd that are in any label per hemi
          src_sel = np.intersect1d(fwd['src'][i]['vertno'], vertices[i])
          src_sel = np.searchsorted(fwd['src'][i]['vertno'], src_sel)
  
          # Reconstruct each src
          vertno = fwd['src'][i]['vertno'][src_sel]
          fwd_out['src'][i]['inuse'][vertno] = 1
          fwd_out['src'][i]['nuse'] += len(vertno)
          fwd_out['src'][i]['vertno'] = np.where(fwd_out['src'][i]['inuse'])[0]
  
          # Reconstruct part of fwd that is not sol data
          src_sel += i * nuse_lh  # Add column shift to right hemi
          fwd_out['source_rr'] = np.vstack([fwd_out['source_rr'],
                                            fwd['source_rr'][src_sel]])
          fwd_out['nsource'] += len(src_sel)
  
          if is_fixed_orient(fwd):
              idx = src_sel
              if fwd['sol_grad'] is not None:
                  idx_grad = (3 * src_sel[:, None] + np.arange(3)).ravel()
          else:
              idx = (3 * src_sel[:, None] + np.arange(3)).ravel()
              if fwd['sol_grad'] is not None:
                  idx_grad = (9 * src_sel[:, None] + np.arange(9)).ravel()
  
          fwd_out['source_nn'] = np.vstack(
              [fwd_out['source_nn'], fwd['source_nn'][idx]])
          fwd_out['sol']['data'] = np.hstack(
              [fwd_out['sol']['data'], fwd['sol']['data'][:, idx]])
          if fwd['sol_grad'] is not None:
              fwd_out['sol_grad']['data'] = np.hstack(
                  [fwd_out['sol_grad']['data'],
                   fwd['sol_rad']['data'][:, idx_grad]])
          fwd_out['sol']['ncol'] += len(idx)
  
          if is_fixed_orient(fwd, orig=True):
              idx = src_sel
              if fwd['sol_grad'] is not None:
                  idx_grad = (3 * src_sel[:, None] + np.arange(3)).ravel()
          else:
              idx = (3 * src_sel[:, None] + np.arange(3)).ravel()
              if fwd['sol_grad'] is not None:
                  idx_grad = (9 * src_sel[:, None] + np.arange(9)).ravel()
  
          fwd_out['_orig_sol'] = np.hstack(
              [fwd_out['_orig_sol'], fwd['_orig_sol'][:, idx]])
          if fwd['sol_grad'] is not None:
              fwd_out['_orig_sol_grad'] = np.hstack(
                  [fwd_out['_orig_sol_grad'],
                   fwd['_orig_sol_grad'][:, idx_grad]])
  
      return fwd_out
  
  
  def _do_forward_solution(subject, meas, fname=None, src=None, spacing=None,
                           mindist=None, bem=None, mri=None, trans=None,
                           eeg=True, meg=True, fixed=False, grad=False,
                           mricoord=False, overwrite=False, subjects_dir=None,
                           verbose=None):
      """Calculate a forward solution for a subject using MNE-C routines.
  
      This is kept around for testing purposes.
  
      This function wraps to mne_do_forward_solution, so the mne
      command-line tools must be installed and accessible from Python.
  
      Parameters
      ----------
      subject : str
          Name of the subject.
      meas : Raw | Epochs | Evoked | str
          If Raw or Epochs, a temporary evoked file will be created and
          saved to a temporary directory. If str, then it should be a
          filename to a file with measurement information the mne
          command-line tools can understand (i.e., raw or evoked).
      fname : str | None
          Destination forward solution filename. If None, the solution
          will be created in a temporary directory, loaded, and deleted.
      src : str | None
          Source space name. If None, the MNE default is used.
      spacing : str
          The spacing to use. Can be ``'#'`` for spacing in mm, ``'ico#'`` for a
          recursively subdivided icosahedron, or ``'oct#'`` for a recursively
          subdivided octahedron (e.g., ``spacing='ico4'``). Default is 7 mm.
      mindist : float | str | None
          Minimum distance of sources from inner skull surface (in mm).
          If None, the MNE default value is used. If string, 'all'
          indicates to include all points.
      bem : str | None
          Name of the BEM to use (e.g., "sample-5120-5120-5120"). If None
          (Default), the MNE default will be used.
      mri : str | None
          The name of the trans file in FIF format.
          If None, trans must not be None.
      trans : dict | str | None
          File name of the trans file in text format.
          If None, mri must not be None.
      eeg : bool
          If True (Default), include EEG computations.
      meg : bool
          If True (Default), include MEG computations.
      fixed : bool
          If True, make a fixed-orientation forward solution (Default:
          False). Note that fixed-orientation inverses can still be
          created from free-orientation forward solutions.
      grad : bool
          If True, compute the gradient of the field with respect to the
          dipole coordinates as well (Default: False).
      mricoord : bool
          If True, calculate in MRI coordinates (Default: False).
      overwrite : bool
          If True, the destination file (if it exists) will be overwritten.
          If False (default), an error will be raised if the file exists.
      subjects_dir : None | str
          Override the SUBJECTS_DIR environment variable.
      %(verbose)s
  
      See Also
      --------
      make_forward_solution
  
      Returns
      -------
      fwd : Forward
          The generated forward solution.
      """
      if not has_mne_c():
          raise RuntimeError('mne command line tools could not be found')
  
      # check for file existence
      temp_dir = tempfile.mkdtemp()
      if fname is None:
          fname = op.join(temp_dir, 'temp-fwd.fif')
      _check_fname(fname, overwrite)
      _validate_type(subject, "str", "subject")
  
      # check for meas to exist as string, or try to make evoked
      if isinstance(meas, str):
          if not op.isfile(meas):
              raise IOError('measurement file "%s" could not be found' % meas)
      elif isinstance(meas, (BaseRaw, BaseEpochs, Evoked)):
          meas_file = op.join(temp_dir, 'info.fif')
          write_info(meas_file, meas.info)
          meas = meas_file
      else:
          raise ValueError('meas must be string, Raw, Epochs, or Evoked')
  
      # deal with trans/mri
      if mri is not None and trans is not None:
          raise ValueError('trans and mri cannot both be specified')
      if mri is None and trans is None:
          # MNE allows this to default to a trans/mri in the subject's dir,
          # but let's be safe here and force the user to pass us a trans/mri
          raise ValueError('Either trans or mri must be specified')
  
      if trans is not None:
          _validate_type(trans, "str", "trans")
          if not op.isfile(trans):
              raise IOError('trans file "%s" not found' % trans)
      if mri is not None:
          # deal with trans
          if not isinstance(mri, str):
              if isinstance(mri, dict):
                  mri_data = deepcopy(mri)
                  mri = op.join(temp_dir, 'mri-trans.fif')
                  try:
                      write_trans(mri, mri_data)
                  except Exception:
                      raise IOError('mri was a dict, but could not be '
                                    'written to disk as a transform file')
              else:
                  raise ValueError('trans must be a string or dict (trans)')
          if not op.isfile(mri):
              raise IOError('trans file "%s" could not be found' % trans)
  
      # deal with meg/eeg
      if not meg and not eeg:
          raise ValueError('meg or eeg (or both) must be True')
  
      path, fname = op.split(fname)
      if not op.splitext(fname)[1] == '.fif':
          raise ValueError('Forward name does not end with .fif')
      path = op.abspath(path)
  
      # deal with mindist
      if mindist is not None:
          if isinstance(mindist, str):
              if not mindist.lower() == 'all':
                  raise ValueError('mindist, if string, must be "all"')
              mindist = ['--all']
          else:
              mindist = ['--mindist', '%g' % mindist]
  
      # src, spacing, bem
      for element, name, kind in zip((src, spacing, bem),
                                     ("src", "spacing", "bem"),
                                     ('path-like', 'str', 'path-like')):
          if element is not None:
              _validate_type(element, kind, name, "%s or None" % kind)
  
      # put together the actual call
      cmd = ['mne_do_forward_solution',
             '--subject', subject,
             '--meas', meas,
             '--fwd', fname,
             '--destdir', path]
      if src is not None:
          cmd += ['--src', src]
      if spacing is not None:
          if spacing.isdigit():
              pass  # spacing in mm
          else:
              # allow both "ico4" and "ico-4" style values
              match = re.match(r"(oct|ico)-?(\d+)$", spacing)
              if match is None:
                  raise ValueError("Invalid spacing parameter: %r" % spacing)
              spacing = '-'.join(match.groups())
          cmd += ['--spacing', spacing]
      if mindist is not None:
          cmd += mindist
      if bem is not None:
          cmd += ['--bem', bem]
      if mri is not None:
          cmd += ['--mri', '%s' % mri]
      if trans is not None:
          cmd += ['--trans', '%s' % trans]
      if not meg:
          cmd.append('--eegonly')
      if not eeg:
          cmd.append('--megonly')
      if fixed:
          cmd.append('--fixed')
      if grad:
          cmd.append('--grad')
      if mricoord:
          cmd.append('--mricoord')
      if overwrite:
          cmd.append('--overwrite')
  
      env = os.environ.copy()
      subjects_dir = get_subjects_dir(subjects_dir, raise_error=True)
      env['SUBJECTS_DIR'] = subjects_dir
  
      try:
          logger.info('Running forward solution generation command with '
                      'subjects_dir %s' % subjects_dir)
          run_subprocess(cmd, env=env)
      except Exception:
          raise
      else:
          fwd = read_forward_solution(op.join(path, fname), verbose=False)
      finally:
          shutil.rmtree(temp_dir, ignore_errors=True)
      return fwd
  
  
  @verbose
  def average_forward_solutions(fwds, weights=None):
      """Average forward solutions.
  
      Parameters
      ----------
      fwds : list of Forward
          Forward solutions to average. Each entry (dict) should be a
          forward solution.
      weights : array | None
          Weights to apply to each forward solution in averaging. If None,
          forward solutions will be equally weighted. Weights must be
          non-negative, and will be adjusted to sum to one.
  
      Returns
      -------
      fwd : Forward
          The averaged forward solution.
      """
      # check for fwds being a list
      _validate_type(fwds, list, "fwds")
      if not len(fwds) > 0:
          raise ValueError('fwds must not be empty')
  
      # check weights
      if weights is None:
          weights = np.ones(len(fwds))
      weights = np.asanyarray(weights)  # in case it's a list, convert it
      if not np.all(weights >= 0):
          raise ValueError('weights must be non-negative')
      if not len(weights) == len(fwds):
          raise ValueError('weights must be None or the same length as fwds')
      w_sum = np.sum(weights)
      if not w_sum > 0:
          raise ValueError('weights cannot all be zero')
      weights /= w_sum
  
      # check our forward solutions
      for fwd in fwds:
          # check to make sure it's a forward solution
          _validate_type(fwd, dict, "each entry in fwds", "dict")
          # check to make sure the dict is actually a fwd
          check_keys = ['info', 'sol_grad', 'nchan', 'src', 'source_nn', 'sol',
                        'source_rr', 'source_ori', 'surf_ori', 'coord_frame',
                        'mri_head_t', 'nsource']
          if not all(key in fwd for key in check_keys):
              raise KeyError('forward solution dict does not have all standard '
                             'entries, cannot compute average.')
  
      # check forward solution compatibility
      if any(fwd['sol'][k] != fwds[0]['sol'][k]
             for fwd in fwds[1:] for k in ['nrow', 'ncol']):
          raise ValueError('Forward solutions have incompatible dimensions')
      if any(fwd[k] != fwds[0][k] for fwd in fwds[1:]
             for k in ['source_ori', 'surf_ori', 'coord_frame']):
          raise ValueError('Forward solutions have incompatible orientations')
  
      # actually average them (solutions and gradients)
      fwd_ave = deepcopy(fwds[0])
      fwd_ave['sol']['data'] *= weights[0]
      fwd_ave['_orig_sol'] *= weights[0]
      for fwd, w in zip(fwds[1:], weights[1:]):
          fwd_ave['sol']['data'] += w * fwd['sol']['data']
          fwd_ave['_orig_sol'] += w * fwd['_orig_sol']
      if fwd_ave['sol_grad'] is not None:
          fwd_ave['sol_grad']['data'] *= weights[0]
          fwd_ave['_orig_sol_grad'] *= weights[0]
          for fwd, w in zip(fwds[1:], weights[1:]):
              fwd_ave['sol_grad']['data'] += w * fwd['sol_grad']['data']
              fwd_ave['_orig_sol_grad'] += w * fwd['_orig_sol_grad']
      return fwd_ave
  
apis: numpy.ones numpy.sum scipy.sparse.block_diag numpy.intersect1d numpy.vstack numpy.append scipy.linalg.norm numpy.concatenate numpy.abs numpy.where numpy.round numpy.unique numpy.minimum numpy.sqrt numpy.tile numpy.eye numpy.zeros numpy.searchsorted numpy.repeat numpy.asanyarray scipy.linalg.inv numpy.arange numpy.hstack numpy.all numpy.min numpy.sort scipy.sparse.issparse numpy.floor numpy.array numpy.dot