code: # Authors: Alexandre Gramfort <alexandre.gramfort@telecom-paristech.fr>
  #          Matti Hamalainen <msh@nmr.mgh.harvard.edu>
  #          Martin Luessi <mluessi@nmr.mgh.harvard.edu>
  #          Mads Jensen <mje.mads@gmail.com>
  #
  # License: BSD (3-clause)
  
  import copy
  import os.path as op
  import numpy as np
  from scipy import linalg, sparse
  from scipy.sparse import coo_matrix, block_diag as sparse_block_diag
  
  from .filter import resample
  from .fixes import einsum
  from .evoked import _get_peak
  from .surface import read_surface, _get_ico_surface, mesh_edges
  from .source_space import (_ensure_src, _get_morph_src_reordering,
                             _ensure_src_subject, SourceSpaces)
  from .utils import (get_subjects_dir, _check_subject, logger, verbose,
                      _time_mask, warn as warn_, copy_function_doc_to_method_doc)
  from .viz import (plot_source_estimates, plot_vector_source_estimates,
                    plot_volume_source_estimates)
  from .io.base import ToDataFrameMixin, TimeMixin
  from .externals.h5io import read_hdf5, write_hdf5
  
  
  def _read_stc(filename):
      """Aux Function."""
      with open(filename, 'rb') as fid:
          buf = fid.read()
  
      stc = dict()
      offset = 0
      num_bytes = 4
  
      # read tmin in ms
      stc['tmin'] = float(np.frombuffer(buf, dtype=">f4", count=1,
                                        offset=offset))
      stc['tmin'] /= 1000.0
      offset += num_bytes
  
      # read sampling rate in ms
      stc['tstep'] = float(np.frombuffer(buf, dtype=">f4", count=1,
                                         offset=offset))
      stc['tstep'] /= 1000.0
      offset += num_bytes
  
      # read number of vertices/sources
      vertices_n = int(np.frombuffer(buf, dtype=">u4", count=1, offset=offset))
      offset += num_bytes
  
      # read the source vector
      stc['vertices'] = np.frombuffer(buf, dtype=">u4", count=vertices_n,
                                      offset=offset)
      offset += num_bytes * vertices_n
  
      # read the number of timepts
      data_n = int(np.frombuffer(buf, dtype=">u4", count=1, offset=offset))
      offset += num_bytes
  
      if (vertices_n and  # vertices_n can be 0 (empty stc)
              ((len(buf) // 4 - 4 - vertices_n) % (data_n * vertices_n)) != 0):
          raise ValueError('incorrect stc file size')
  
      # read the data matrix
      stc['data'] = np.frombuffer(buf, dtype=">f4", count=vertices_n * data_n,
                                  offset=offset)
      stc['data'] = stc['data'].reshape([data_n, vertices_n]).T
  
      return stc
  
  
  def _write_stc(filename, tmin, tstep, vertices, data):
      """Write an STC file.
  
      Parameters
      ----------
      filename : string
          The name of the STC file.
      tmin : float
          The first time point of the data in seconds.
      tstep : float
          Time between frames in seconds.
      vertices : array of integers
          Vertex indices (0 based).
      data : 2D array
          The data matrix (nvert * ntime).
      """
      fid = open(filename, 'wb')
  
      # write start time in ms
      fid.write(np.array(1000 * tmin, dtype='>f4').tostring())
      # write sampling rate in ms
      fid.write(np.array(1000 * tstep, dtype='>f4').tostring())
      # write number of vertices
      fid.write(np.array(vertices.shape[0], dtype='>u4').tostring())
      # write the vertex indices
      fid.write(np.array(vertices, dtype='>u4').tostring())
  
      # write the number of timepts
      fid.write(np.array(data.shape[1], dtype='>u4').tostring())
      #
      # write the data
      #
      fid.write(np.array(data.T, dtype='>f4').tostring())
  
      # close the file
      fid.close()
  
  
  def _read_3(fid):
      """Read 3 byte integer from file."""
      data = np.fromfile(fid, dtype=np.uint8, count=3).astype(np.int32)
  
      out = np.left_shift(data[0], 16) + np.left_shift(data[1], 8) + data[2]
  
      return out
  
  
  def _read_w(filename):
      """Read a w file.
  
      w files contain activations or source reconstructions for a single time
      point.
  
      Parameters
      ----------
      filename : string
          The name of the w file.
  
      Returns
      -------
      data: dict
          The w structure. It has the following keys:
             vertices       vertex indices (0 based)
             data           The data matrix (nvert long)
      """
      with open(filename, 'rb', buffering=0) as fid:  # buffering=0 for np bug
          # skip first 2 bytes
          fid.read(2)
  
          # read number of vertices/sources (3 byte integer)
          vertices_n = int(_read_3(fid))
  
          vertices = np.zeros((vertices_n), dtype=np.int32)
          data = np.zeros((vertices_n), dtype=np.float32)
  
          # read the vertices and data
          for i in range(vertices_n):
              vertices[i] = _read_3(fid)
              data[i] = np.fromfile(fid, dtype='>f4', count=1)[0]
  
          w = dict()
          w['vertices'] = vertices
          w['data'] = data
  
      return w
  
  
  def _write_3(fid, val):
      """Write 3 byte integer to file."""
      f_bytes = np.zeros((3), dtype=np.uint8)
      f_bytes[0] = (val >> 16) & 255
      f_bytes[1] = (val >> 8) & 255
      f_bytes[2] = val & 255
      fid.write(f_bytes.tostring())
  
  
  def _write_w(filename, vertices, data):
      """Write a w file.
  
      w files contain activations or source reconstructions for a single time
      point.
  
      Parameters
      ----------
      filename: string
          The name of the w file.
      vertices: array of int
          Vertex indices (0 based).
      data: 1D array
          The data array (nvert).
      """
      assert (len(vertices) == len(data))
  
      fid = open(filename, 'wb')
  
      # write 2 zero bytes
      fid.write(np.zeros((2), dtype=np.uint8).tostring())
  
      # write number of vertices/sources (3 byte integer)
      vertices_n = len(vertices)
      _write_3(fid, vertices_n)
  
      # write the vertices and data
      for i in range(vertices_n):
          _write_3(fid, vertices[i])
          # XXX: without float() endianness is wrong, not sure why
          fid.write(np.array(float(data[i]), dtype='>f4').tostring())
  
      # close the file
      fid.close()
  
  
  def read_source_estimate(fname, subject=None):
      """Read a source estimate object.
  
      Parameters
      ----------
      fname : str
          Path to (a) source-estimate file(s).
      subject : str | None
          Name of the subject the source estimate(s) is (are) from.
          It is good practice to set this attribute to avoid combining
          incompatible labels and SourceEstimates (e.g., ones from other
          subjects). Note that due to file specification limitations, the
          subject name isn't saved to or loaded from files written to disk.
  
      Returns
      -------
      stc : SourceEstimate | VectorSourceEstimate | VolSourceEstimate | MixedSourceEstimate
          The source estimate object loaded from file.
  
      Notes
      -----
       - for volume source estimates, ``fname`` should provide the path to a
         single file named '*-vl.stc` or '*-vol.stc'
       - for surface source estimates, ``fname`` should either provide the
         path to the file corresponding to a single hemisphere ('*-lh.stc',
         '*-rh.stc') or only specify the asterisk part in these patterns. In any
         case, the function expects files for both hemisphere with names
         following this pattern.
       - for vector surface source estimates, only HDF5 files are supported.
       - for mixed source estimates, only HDF5 files are supported.
       - for single time point .w files, ``fname`` should follow the same
         pattern as for surface estimates, except that files are named
         '*-lh.w' and '*-rh.w'.
      """  # noqa: E501
      fname_arg = fname
  
      # make sure corresponding file(s) can be found
      ftype = None
      if op.exists(fname):
          if fname.endswith('-vl.stc') or fname.endswith('-vol.stc') or \
                  fname.endswith('-vl.w') or fname.endswith('-vol.w'):
              ftype = 'volume'
          elif fname.endswith('.stc'):
              ftype = 'surface'
              if fname.endswith(('-lh.stc', '-rh.stc')):
                  fname = fname[:-7]
              else:
                  err = ("Invalid .stc filename: %r; needs to end with "
                         "hemisphere tag ('...-lh.stc' or '...-rh.stc')"
                         % fname)
                  raise IOError(err)
          elif fname.endswith('.w'):
              ftype = 'w'
              if fname.endswith(('-lh.w', '-rh.w')):
                  fname = fname[:-5]
              else:
                  err = ("Invalid .w filename: %r; needs to end with "
                         "hemisphere tag ('...-lh.w' or '...-rh.w')"
                         % fname)
                  raise IOError(err)
          elif fname.endswith('.h5'):
              ftype = 'h5'
              fname = fname[:-3]
          else:
              raise RuntimeError('Unknown extension for file %s' % fname_arg)
  
      if ftype is not 'volume':
          stc_exist = [op.exists(f)
                       for f in [fname + '-rh.stc', fname + '-lh.stc']]
          w_exist = [op.exists(f)
                     for f in [fname + '-rh.w', fname + '-lh.w']]
          if all(stc_exist) and (ftype is not 'w'):
              ftype = 'surface'
          elif all(w_exist):
              ftype = 'w'
          elif op.exists(fname + '.h5'):
              ftype = 'h5'
          elif op.exists(fname + '-stc.h5'):
              ftype = 'h5'
              fname += '-stc'
          elif any(stc_exist) or any(w_exist):
              raise IOError("Hemisphere missing for %r" % fname_arg)
          else:
              raise IOError("SourceEstimate File(s) not found for: %r"
                            % fname_arg)
  
      # read the files
      if ftype == 'volume':  # volume source space
          if fname.endswith('.stc'):
              kwargs = _read_stc(fname)
          elif fname.endswith('.w'):
              kwargs = _read_w(fname)
              kwargs['data'] = kwargs['data'][:, np.newaxis]
              kwargs['tmin'] = 0.0
              kwargs['tstep'] = 0.0
          else:
              raise IOError('Volume source estimate must end with .stc or .w')
      elif ftype == 'surface':  # stc file with surface source spaces
          lh = _read_stc(fname + '-lh.stc')
          rh = _read_stc(fname + '-rh.stc')
          assert lh['tmin'] == rh['tmin']
          assert lh['tstep'] == rh['tstep']
          kwargs = lh.copy()
          kwargs['data'] = np.r_[lh['data'], rh['data']]
          kwargs['vertices'] = [lh['vertices'], rh['vertices']]
      elif ftype == 'w':  # w file with surface source spaces
          lh = _read_w(fname + '-lh.w')
          rh = _read_w(fname + '-rh.w')
          kwargs = lh.copy()
          kwargs['data'] = np.atleast_2d(np.r_[lh['data'], rh['data']]).T
          kwargs['vertices'] = [lh['vertices'], rh['vertices']]
          # w files only have a single time point
          kwargs['tmin'] = 0.0
          kwargs['tstep'] = 1.0
      elif ftype == 'h5':
          kwargs = read_hdf5(fname + '.h5', title='mnepython')
          if "src_type" in kwargs:
              ftype = kwargs['src_type']
              del kwargs['src_type']
  
      if ftype != 'volume':
          # Make sure the vertices are ordered
          vertices = kwargs['vertices']
          if any(np.any(np.diff(v.astype(int)) <= 0) for v in vertices):
              sidx = [np.argsort(verts) for verts in vertices]
              vertices = [verts[idx] for verts, idx in zip(vertices, sidx)]
              data = kwargs['data'][np.r_[sidx[0], len(sidx[0]) + sidx[1]]]
              kwargs['vertices'] = vertices
              kwargs['data'] = data
  
      if 'subject' not in kwargs:
          kwargs['subject'] = subject
      if subject is not None and subject != kwargs['subject']:
          raise RuntimeError('provided subject name "%s" does not match '
                             'subject name from the file "%s'
                             % (subject, kwargs['subject']))
  
      if ftype in ('volume', 'discrete'):
          stc = VolSourceEstimate(**kwargs)
      elif ftype == 'mixed':
          stc = MixedSourceEstimate(**kwargs)
      elif ftype == 'h5' and kwargs['data'].ndim == 3:
          stc = VectorSourceEstimate(**kwargs)
      else:
          stc = SourceEstimate(**kwargs)
  
      return stc
  
  
  def _get_src_type(src, vertices, warn_text=None):
      src_type = None
      if src is None:
          if warn_text is None:
              warn_("src should not be None for a robust guess of stc type.")
          else:
              warn_(warn_text)
          if isinstance(vertices, list) and len(vertices) == 2:
              src_type = 'surface'
          elif isinstance(vertices, np.ndarray) or isinstance(vertices, list) \
                  and len(vertices) == 1:
              src_type = 'volume'
          elif isinstance(vertices, list) and len(vertices) > 2:
              src_type = 'mixed'
      else:
          src_type = src.kind
      assert src_type in ('surface', 'volume', 'mixed', 'discrete')
      return src_type
  
  
  def _make_stc(data, vertices, src_type=None, tmin=None, tstep=None,
                subject=None, vector=False, source_nn=None, warn_text=None):
      """Generate a surface, vector-surface, volume or mixed source estimate."""
      if src_type is None:
          # attempt to guess from vertices
          src_type = _get_src_type(src=None, vertices=vertices,
                                   warn_text=warn_text)
  
      if src_type == 'surface':
          # make a surface source estimate
          n_vertices = len(vertices[0]) + len(vertices[1])
          if vector:
              if source_nn is None:
                  raise RuntimeError('No source vectors supplied.')
  
              # Rotate data to absolute XYZ coordinates
              data_rot = np.zeros((n_vertices, 3, data.shape[1]))
              if data.shape[0] == 3 * n_vertices:
                  source_nn = source_nn.reshape(n_vertices, 3, 3)
                  data = data.reshape(n_vertices, 3, -1)
              else:
                  raise RuntimeError('Shape of data array does not match the '
                                     'number of vertices.')
              for i, d, n in zip(range(data.shape[0]), data, source_nn):
                  data_rot[i] = np.dot(n.T, d)
              data = data_rot
              stc = VectorSourceEstimate(data, vertices=vertices, tmin=tmin,
                                         tstep=tstep, subject=subject)
          else:
              stc = SourceEstimate(data, vertices=vertices, tmin=tmin,
                                   tstep=tstep, subject=subject)
      elif src_type in ('volume', 'discrete'):
          if vector:
              data = data.reshape((-1, 3, data.shape[-1]))
          stc = VolSourceEstimate(data, vertices=vertices, tmin=tmin,
                                  tstep=tstep, subject=subject)
      elif src_type == 'mixed':
          # make a mixed source estimate
          stc = MixedSourceEstimate(data, vertices=vertices, tmin=tmin,
                                    tstep=tstep, subject=subject)
      else:
          raise ValueError('vertices has to be either a list with one or more '
                           'arrays or an array')
      return stc
  
  
  def _verify_source_estimate_compat(a, b):
      """Make sure two SourceEstimates are compatible for arith. operations."""
      compat = False
      if type(a) != type(b):
          raise ValueError('Cannot combine %s and %s.' % (type(a), type(b)))
      if len(a.vertices) == len(b.vertices):
          if all(np.array_equal(av, vv)
                 for av, vv in zip(a.vertices, b.vertices)):
              compat = True
      if not compat:
          raise ValueError('Cannot combine source estimates that do not have '
                           'the same vertices. Consider using stc.expand().')
      if a.subject != b.subject:
          raise ValueError('source estimates do not have the same subject '
                           'names, %r and %r' % (a.subject, b.subject))
  
  
  class _BaseSourceEstimate(ToDataFrameMixin, TimeMixin):
      """Abstract base class for source estimates.
  
      Parameters
      ----------
      data : array of shape (n_dipoles, n_times) | 2-tuple (kernel, sens_data)
          The data in source space. The data can either be a single array or
          a tuple with two arrays: "kernel" shape (n_vertices, n_sensors) and
          "sens_data" shape (n_sensors, n_times). In this case, the source
          space data corresponds to "numpy.dot(kernel, sens_data)".
      vertices : array | list of two arrays
          Vertex numbers corresponding to the data.
      tmin : float
          Time point of the first sample in data.
      tstep : float
          Time step between successive samples in data.
      subject : str | None
          The subject name. While not necessary, it is safer to set the
          subject parameter to avoid analysis errors.
      verbose : bool, str, int, or None
          If not None, override default verbose level (see :func:`mne.verbose`
          and :ref:`Logging documentation <tut_logging>` for more).
  
      Attributes
      ----------
      subject : str | None
          The subject name.
      times : array of shape (n_times,)
          The time vector.
      vertices : array or list of arrays of shape (n_dipoles,)
          The indices of the dipoles in the different source spaces. Can
          be an array if there is only one source space (e.g., for volumes).
      data : array of shape (n_dipoles, n_times)
          The data in source space.
      shape : tuple
          The shape of the data. A tuple of int (n_dipoles, n_times).
      """
  
      @verbose
      def __init__(self, data, vertices=None, tmin=None, tstep=None,
                   subject=None, verbose=None):  # noqa: D102
          kernel, sens_data = None, None
          if isinstance(data, tuple):
              if len(data) != 2:
                  raise ValueError('If data is a tuple it has to be length 2')
              kernel, sens_data = data
              data = None
              if kernel.shape[1] != sens_data.shape[0]:
                  raise ValueError('kernel and sens_data have invalid '
                                   'dimensions')
  
          if isinstance(vertices, list):
              vertices = [np.asarray(v, int) for v in vertices]
              if any(np.any(np.diff(v.astype(int)) <= 0) for v in vertices):
                  raise ValueError('Vertices must be ordered in increasing '
                                   'order.')
  
              n_src = sum([len(v) for v in vertices])
  
              if len(vertices) == 1:
                  vertices = vertices[0]
          elif isinstance(vertices, np.ndarray):
              n_src = len(vertices)
          else:
              raise ValueError('Vertices must be a list or numpy array')
  
          # safeguard the user against doing something silly
          if data is not None and data.shape[0] != n_src:
              raise ValueError('Number of vertices (%i) and stc.shape[0] (%i) '
                               'must match' % (n_src, data.shape[0]))
  
          self._data = data
          self._tmin = tmin
          self._tstep = tstep
          self.vertices = vertices
          self.verbose = verbose
          self._kernel = kernel
          self._sens_data = sens_data
          self._kernel_removed = False
          self._times = None
          self._update_times()
          self.subject = _check_subject(None, subject, False)
  
      @property
      def sfreq(self):
          """Sample rate of the data."""
          return 1. / self.tstep
  
      def _remove_kernel_sens_data_(self):
          """Remove kernel and sensor space data and compute self._data."""
          if self._kernel is not None or self._sens_data is not None:
              self._kernel_removed = True
              self._data = np.dot(self._kernel, self._sens_data)
              self._kernel = None
              self._sens_data = None
  
      def crop(self, tmin=None, tmax=None):
          """Restrict SourceEstimate to a time interval.
  
          Parameters
          ----------
          tmin : float | None
              The first time point in seconds. If None the first present is used.
          tmax : float | None
              The last time point in seconds. If None the last present is used.
          """
          mask = _time_mask(self.times, tmin, tmax, sfreq=self.sfreq)
          self.tmin = self.times[np.where(mask)[0][0]]
          if self._kernel is not None and self._sens_data is not None:
              self._sens_data = self._sens_data[..., mask]
          else:
              self.data = self.data[..., mask]
  
          return self  # return self for chaining methods
  
      @verbose
      def resample(self, sfreq, npad='auto', window='boxcar', n_jobs=1,
                   verbose=None):
          """Resample data.
  
          Parameters
          ----------
          sfreq : float
              New sample rate to use.
          npad : int | str
              Amount to pad the start and end of the data.
              Can also be "auto" to use a padding that will result in
              a power-of-two size (can be much faster).
          window : string or tuple
              Window to use in resampling. See scipy.signal.resample.
          n_jobs : int
              Number of jobs to run in parallel.
          verbose : bool, str, int, or None
              If not None, override default verbose level (see
              :func:`mne.verbose` and :ref:`Logging documentation <tut_logging>`
              for more). Defaults to self.verbose.
  
          Notes
          -----
          For some data, it may be more accurate to use npad=0 to reduce
          artifacts. This is dataset dependent -- check your data!
  
          Note that the sample rate of the original data is inferred from tstep.
          """
          # resampling in sensor instead of source space gives a somewhat
          # different result, so we don't allow it
          self._remove_kernel_sens_data_()
  
          o_sfreq = 1.0 / self.tstep
          self.data = resample(self.data, sfreq, o_sfreq, npad, n_jobs=n_jobs)
  
          # adjust indirectly affected variables
          self.tstep = 1.0 / sfreq
          return self
  
      @property
      def data(self):
          """Numpy array of source estimate data."""
          if self._data is None:
              # compute the solution the first time the data is accessed and
              # remove the kernel and sensor data
              self._remove_kernel_sens_data_()
          return self._data
  
      @data.setter
      def data(self, value):
          value = np.asarray(value)
          if self._data is not None and value.ndim != self._data.ndim:
              raise ValueError('Data array should have %d dimensions.' %
                               self._data.ndim)
  
          # vertices can be a single number, so cast to ndarray
          if isinstance(self.vertices, list):
              n_verts = sum([len(v) for v in self.vertices])
          elif isinstance(self.vertices, np.ndarray):
              n_verts = len(self.vertices)
          else:
              raise ValueError('Vertices must be a list or numpy array')
  
          if value.shape[0] != n_verts:
              raise ValueError('The first dimension of the data array must '
                               'match the number of vertices (%d != %d)' %
                               (value.shape[0], n_verts))
  
          self._data = value
          self._update_times()
  
      @property
      def shape(self):
          """Shape of the data."""
          if self._data is not None:
              return self._data.shape
          return (self._kernel.shape[0], self._sens_data.shape[1])
  
      @property
      def tmin(self):
          """The first timestamp."""
          return self._tmin
  
      @tmin.setter
      def tmin(self, value):
          self._tmin = float(value)
          self._update_times()
  
      @property
      def tstep(self):
          """The change in time between two consecutive samples (1 / sfreq)."""
          return self._tstep
  
      @tstep.setter
      def tstep(self, value):
          if value <= 0:
              raise ValueError('.tstep must be greater than 0.')
          self._tstep = float(value)
          self._update_times()
  
      @property
      def times(self):
          """A timestamp for each sample."""
          return self._times
  
      @times.setter
      def times(self, value):
          raise ValueError('You cannot write to the .times attribute directly. '
                           'This property automatically updates whenever '
                           '.tmin, .tstep or .data changes.')
  
      def _update_times(self):
          """Update the times attribute after changing tmin, tmax, or tstep."""
          self._times = self.tmin + (self.tstep * np.arange(self.shape[-1]))
          self._times.flags.writeable = False
  
      def __add__(self, a):
          """Add source estimates."""
          stc = self.copy()
          stc += a
          return stc
  
      def __iadd__(self, a):  # noqa: D105
          self._remove_kernel_sens_data_()
          if isinstance(a, _BaseSourceEstimate):
              _verify_source_estimate_compat(self, a)
              self.data += a.data
          else:
              self.data += a
          return self
  
      def mean(self):
          """Make a summary stc file with mean over time points.
  
          Returns
          -------
          stc : SourceEstimate | VectorSourceEstimate
              The modified stc.
          """
          out = self.sum()
          out /= len(self.times)
          return out
  
      def sum(self):
          """Make a summary stc file with sum over time points.
  
          Returns
          -------
          stc : SourceEstimate | VectorSourceEstimate
              The modified stc.
          """
          data = self.data
          tmax = self.tmin + self.tstep * data.shape[-1]
          tmin = (self.tmin + tmax) / 2.
          tstep = tmax - self.tmin
          sum_stc = self.__class__(self.data.sum(axis=-1, keepdims=True),
                                   vertices=self.vertices, tmin=tmin,
                                   tstep=tstep, subject=self.subject)
          return sum_stc
  
      def __sub__(self, a):
          """Subtract source estimates."""
          stc = self.copy()
          stc -= a
          return stc
  
      def __isub__(self, a):  # noqa: D105
          self._remove_kernel_sens_data_()
          if isinstance(a, _BaseSourceEstimate):
              _verify_source_estimate_compat(self, a)
              self.data -= a.data
          else:
              self.data -= a
          return self
  
      def __truediv__(self, a):  # noqa: D105
          return self.__div__(a)
  
      def __div__(self, a):  # noqa: D105
          """Divide source estimates."""
          stc = self.copy()
          stc /= a
          return stc
  
      def __itruediv__(self, a):  # noqa: D105
          return self.__idiv__(a)
  
      def __idiv__(self, a):  # noqa: D105
          self._remove_kernel_sens_data_()
          if isinstance(a, _BaseSourceEstimate):
              _verify_source_estimate_compat(self, a)
              self.data /= a.data
          else:
              self.data /= a
          return self
  
      def __mul__(self, a):
          """Multiply source estimates."""
          stc = self.copy()
          stc *= a
          return stc
  
      def __imul__(self, a):  # noqa: D105
          self._remove_kernel_sens_data_()
          if isinstance(a, _BaseSourceEstimate):
              _verify_source_estimate_compat(self, a)
              self.data *= a.data
          else:
              self.data *= a
          return self
  
      def __pow__(self, a):  # noqa: D105
          stc = self.copy()
          stc **= a
          return stc
  
      def __ipow__(self, a):  # noqa: D105
          self._remove_kernel_sens_data_()
          self.data **= a
          return self
  
      def __radd__(self, a):  # noqa: D105
          return self + a
  
      def __rsub__(self, a):  # noqa: D105
          return self - a
  
      def __rmul__(self, a):  # noqa: D105
          return self * a
  
      def __rdiv__(self, a):  # noqa: D105
          return self / a
  
      def __neg__(self):  # noqa: D105
          """Negate the source estimate."""
          stc = self.copy()
          stc._remove_kernel_sens_data_()
          stc.data *= -1
          return stc
  
      def __pos__(self):  # noqa: D105
          return self
  
      def __abs__(self):
          """Compute the absolute value of the data.
  
          Returns
          -------
          stc : instance of _BaseSourceEstimate
              A version of the source estimate, where the data attribute is set
              to abs(self.data).
          """
          stc = self.copy()
          stc._remove_kernel_sens_data_()
          stc._data = abs(stc._data)
          return stc
  
      def sqrt(self):
          """Take the square root.
  
          Returns
          -------
          stc : instance of SourceEstimate
              A copy of the SourceEstimate with sqrt(data).
          """
          return self ** (0.5)
  
      def copy(self):
          """Return copy of source estimate instance."""
          return copy.deepcopy(self)
  
      def bin(self, width, tstart=None, tstop=None, func=np.mean):
          """Return a source estimate object with data summarized over time bins.
  
          Time bins of ``width`` seconds. This method is intended for
          visualization only. No filter is applied to the data before binning,
          making the method inappropriate as a tool for downsampling data.
  
          Parameters
          ----------
          width : scalar
              Width of the individual bins in seconds.
          tstart : scalar | None
              Time point where the first bin starts. The default is the first
              time point of the stc.
          tstop : scalar | None
              Last possible time point contained in a bin (if the last bin would
              be shorter than width it is dropped). The default is the last time
              point of the stc.
          func : callable
              Function that is applied to summarize the data. Needs to accept a
              numpy.array as first input and an ``axis`` keyword argument.
  
          Returns
          -------
          stc : SourceEstimate | VectorSourceEstimate
              The binned source estimate.
          """
          if tstart is None:
              tstart = self.tmin
          if tstop is None:
              tstop = self.times[-1]
  
          times = np.arange(tstart, tstop + self.tstep, width)
          nt = len(times) - 1
          data = np.empty(self.shape[:-1] + (nt,), dtype=self.data.dtype)
          for i in range(nt):
              idx = (self.times >= times[i]) & (self.times < times[i + 1])
              data[..., i] = func(self.data[..., idx], axis=-1)
  
          tmin = times[0] + width / 2.
          stc = self.copy()
          stc._data = data
          stc.tmin = tmin
          stc.tstep = width
          return stc
  
      def transform_data(self, func, idx=None, tmin_idx=None, tmax_idx=None):
          """Get data after a linear (time) transform has been applied.
  
          The transform is applied to each source time course independently.
  
  
          Parameters
          ----------
          func : callable
              The transform to be applied, including parameters (see, e.g.,
              :func:`functools.partial`). The first parameter of the function is
              the input data. The first return value is the transformed data,
              remaining outputs are ignored. The first dimension of the
              transformed data has to be the same as the first dimension of the
              input data.
          idx : array | None
              Indicices of source time courses for which to compute transform.
              If None, all time courses are used.
          tmin_idx : int | None
              Index of first time point to include. If None, the index of the
              first time point is used.
          tmax_idx : int | None
              Index of the first time point not to include. If None, time points
              up to (and including) the last time point are included.
  
          Returns
          -------
          data_t : ndarray
              The transformed data.
  
          Notes
          -----
          Applying transforms can be significantly faster if the
          SourceEstimate object was created using "(kernel, sens_data)", for
          the "data" parameter as the transform is applied in sensor space.
          Inverse methods, e.g., "apply_inverse_epochs", or "apply_lcmv_epochs"
          do this automatically (if possible).
          """
          if idx is None:
              # use all time courses by default
              idx = slice(None, None)
  
          if self._kernel is None and self._sens_data is None:
              if self._kernel_removed:
                  warn_('Performance can be improved by not accessing the data '
                        'attribute before calling this method.')
  
              # transform source space data directly
              data_t = func(self.data[idx, ..., tmin_idx:tmax_idx])
  
              if isinstance(data_t, tuple):
                  # use only first return value
                  data_t = data_t[0]
          else:
              # apply transform in sensor space
              sens_data_t = func(self._sens_data[:, tmin_idx:tmax_idx])
  
              if isinstance(sens_data_t, tuple):
                  # use only first return value
                  sens_data_t = sens_data_t[0]
  
              # apply inverse
              data_shape = sens_data_t.shape
              if len(data_shape) > 2:
                  # flatten the last dimensions
                  sens_data_t = sens_data_t.reshape(data_shape[0],
                                                    np.prod(data_shape[1:]))
  
              data_t = np.dot(self._kernel[idx, :], sens_data_t)
  
              # restore original shape if necessary
              if len(data_shape) > 2:
                  data_t = data_t.reshape(data_t.shape[0], *data_shape[1:])
  
          return data_t
  
      def transform(self, func, idx=None, tmin=None, tmax=None, copy=False):
          """Apply linear transform.
  
          The transform is applied to each source time course independently.
  
          Parameters
          ----------
          func : callable
              The transform to be applied, including parameters (see, e.g.,
              :func:`functools.partial`). The first parameter of the function is
              the input data. The first two dimensions of the transformed data
              should be (i) vertices and (ii) time.  Transforms which yield 3D
              output (e.g. time-frequency transforms) are valid, so long as the
              first two dimensions are vertices and time.  In this case, the
              copy parameter (see below) must be True and a list of
              SourceEstimates, rather than a single instance of SourceEstimate,
              will be returned, one for each index of the 3rd dimension of the
              transformed data.  In the case of transforms yielding 2D output
              (e.g. filtering), the user has the option of modifying the input
              inplace (copy = False) or returning a new instance of
              SourceEstimate (copy = True) with the transformed data.
          idx : array | None
              Indices of source time courses for which to compute transform.
              If None, all time courses are used.
          tmin : float | int | None
              First time point to include (ms). If None, self.tmin is used.
          tmax : float | int | None
              Last time point to include (ms). If None, self.tmax is used.
          copy : bool
              If True, return a new instance of SourceEstimate instead of
              modifying the input inplace.
  
          Returns
          -------
          stcs : SourceEstimate | VectorSourceEstimate | list
              The transformed stc or, in the case of transforms which yield
              N-dimensional output (where N > 2), a list of stcs. For a list,
              copy must be True.
  
          Notes
          -----
          Applying transforms can be significantly faster if the
          SourceEstimate object was created using "(kernel, sens_data)", for
          the "data" parameter as the transform is applied in sensor space.
          Inverse methods, e.g., "apply_inverse_epochs", or "apply_lcmv_epochs"
          do this automatically (if possible).
          """
          # min and max data indices to include
          times = 1000. * self.times
          t_idx = np.where(_time_mask(times, tmin, tmax, sfreq=self.sfreq))[0]
          if tmin is None:
              tmin_idx = None
          else:
              tmin_idx = t_idx[0]
  
          if tmax is None:
              tmax_idx = None
          else:
              # +1, because upper boundary needs to include the last sample
              tmax_idx = t_idx[-1] + 1
  
          data_t = self.transform_data(func, idx=idx, tmin_idx=tmin_idx,
                                       tmax_idx=tmax_idx)
  
          # account for change in n_vertices
          if idx is not None:
              idx_lh = idx[idx < len(self.lh_vertno)]
              idx_rh = idx[idx >= len(self.lh_vertno)] - len(self.lh_vertno)
              verts_lh = self.lh_vertno[idx_lh]
              verts_rh = self.rh_vertno[idx_rh]
          else:
              verts_lh = self.lh_vertno
              verts_rh = self.rh_vertno
          verts = [verts_lh, verts_rh]
  
          tmin_idx = 0 if tmin_idx is None else tmin_idx
          tmin = self.times[tmin_idx]
  
          if data_t.ndim > 2:
              # return list of stcs if transformed data has dimensionality > 2
              if copy:
                  stcs = [SourceEstimate(data_t[:, :, a], verts, tmin,
                                         self.tstep, self.subject)
                          for a in range(data_t.shape[-1])]
              else:
                  raise ValueError('copy must be True if transformed data has '
                                   'more than 2 dimensions')
          else:
              # return new or overwritten stc
              stcs = self if not copy else self.copy()
              stcs.vertices = verts
              stcs.data = data_t
              stcs.tmin = tmin
  
          return stcs
  
  
  def _center_of_mass(vertices, values, hemi, surf, subject, subjects_dir,
                      restrict_vertices):
      """Find the center of mass on a surface."""
      if (values == 0).all() or (values < 0).any():
          raise ValueError('All values must be non-negative and at least one '
                           'must be non-zero, cannot compute COM')
      subjects_dir = get_subjects_dir(subjects_dir, raise_error=True)
      surf = read_surface(op.join(subjects_dir, subject, 'surf',
                                  hemi + '.' + surf))
      if restrict_vertices is True:
          restrict_vertices = vertices
      elif restrict_vertices is False:
          restrict_vertices = np.arange(surf[0].shape[0])
      elif isinstance(restrict_vertices, SourceSpaces):
          idx = 1 if restrict_vertices.kind == 'surface' and hemi == 'rh' else 0
          restrict_vertices = restrict_vertices[idx]['vertno']
      else:
          restrict_vertices = np.array(restrict_vertices, int)
      pos = surf[0][vertices, :].T
      c_o_m = np.sum(pos * values, axis=1) / np.sum(values)
      vertex = np.argmin(np.sqrt(np.mean((surf[0][restrict_vertices, :] -
                                          c_o_m) ** 2, axis=1)))
      vertex = restrict_vertices[vertex]
      return vertex
  
  
  class _BaseSurfaceSourceEstimate(_BaseSourceEstimate):
      """Abstract base class for surface source estimates.
  
      Parameters
      ----------
      data : array
          The data in source space.
      vertices : list of two arrays
          Vertex numbers corresponding to the data.
      tmin : scalar
          Time point of the first sample in data.
      tstep : scalar
          Time step between successive samples in data.
      subject : str | None
          The subject name. While not necessary, it is safer to set the
          subject parameter to avoid analysis errors.
      verbose : bool, str, int, or None
          If not None, override default verbose level (see :func:`mne.verbose`
          and :ref:`Logging documentation <tut_logging>` for more).
  
      Attributes
      ----------
      subject : str | None
          The subject name.
      times : array of shape (n_times,)
          The time vector.
      vertices : list of two arrays of shape (n_dipoles,)
          The indices of the dipoles in the left and right source space.
      data : array
          The data in source space.
      shape : tuple
          The shape of the data. A tuple of int (n_dipoles, n_times).
      """
  
      @verbose
      def __init__(self, data, vertices=None, tmin=None, tstep=None,
                   subject=None, verbose=None):  # noqa: D102
  
          if not (isinstance(vertices, list) and len(vertices) == 2):
              raise ValueError('Vertices must be a list containing two '
                               'numpy arrays, got type %s (%s)'
                               % (type(vertices), vertices))
  
          _BaseSourceEstimate.__init__(self, data, vertices=vertices, tmin=tmin,
                                       tstep=tstep, subject=subject,
                                       verbose=verbose)
  
      def __repr__(self):  # noqa: D105
          if isinstance(self.vertices, list):
              nv = sum([len(v) for v in self.vertices])
          else:
              nv = self.vertices.size
          s = "%d vertices" % nv
          if self.subject is not None:
              s += ", subject : %s" % self.subject
          s += ", tmin : %s (ms)" % (1e3 * self.tmin)
          s += ", tmax : %s (ms)" % (1e3 * self.times[-1])
          s += ", tstep : %s (ms)" % (1e3 * self.tstep)
          s += ", data shape : %s" % (self.shape,)
          return "<%s  |  %s>" % (type(self).__name__, s)
  
      @property
      def lh_data(self):
          """Left hemisphere data."""
          return self.data[:len(self.lh_vertno)]
  
      @property
      def rh_data(self):
          """Right hemisphere data."""
          return self.data[len(self.lh_vertno):]
  
      @property
      def lh_vertno(self):
          """Left hemisphere vertno."""
          return self.vertices[0]
  
      @property
      def rh_vertno(self):
          """Right hemisphere vertno."""
          return self.vertices[1]
  
      def _hemilabel_stc(self, label):
          if label.hemi == 'lh':
              stc_vertices = self.vertices[0]
          else:
              stc_vertices = self.vertices[1]
  
          # find index of the Label's vertices
          idx = np.nonzero(np.in1d(stc_vertices, label.vertices))[0]
  
          # find output vertices
          vertices = stc_vertices[idx]
  
          # find data
          if label.hemi == 'rh':
              values = self.data[idx + len(self.vertices[0])]
          else:
              values = self.data[idx]
  
          return vertices, values
  
      def in_label(self, label):
          """Get a source estimate object restricted to a label.
  
          SourceEstimate contains the time course of
          activation of all sources inside the label.
  
          Parameters
          ----------
          label : Label | BiHemiLabel
              The label (as created for example by mne.read_label). If the label
              does not match any sources in the SourceEstimate, a ValueError is
              raised.
  
          Returns
          -------
          stc : SourceEstimate | VectorSourceEstimate
              The source estimate restricted to the given label.
          """
          # make sure label and stc are compatible
          if label.subject is not None and self.subject is not None \
                  and label.subject != self.subject:
              raise RuntimeError('label and stc must have same subject names, '
                                 'currently "%s" and "%s"' % (label.subject,
                                                              self.subject))
  
          if label.hemi == 'both':
              lh_vert, lh_val = self._hemilabel_stc(label.lh)
              rh_vert, rh_val = self._hemilabel_stc(label.rh)
              vertices = [lh_vert, rh_vert]
              values = np.vstack((lh_val, rh_val))
          elif label.hemi == 'lh':
              lh_vert, values = self._hemilabel_stc(label)
              vertices = [lh_vert, np.array([], int)]
          elif label.hemi == 'rh':
              rh_vert, values = self._hemilabel_stc(label)
              vertices = [np.array([], int), rh_vert]
          else:
              raise TypeError("Expected  Label or BiHemiLabel; got %r" % label)
  
          if sum([len(v) for v in vertices]) == 0:
              raise ValueError('No vertices match the label in the stc file')
  
          label_stc = self.__class__(values, vertices=vertices, tmin=self.tmin,
                                     tstep=self.tstep, subject=self.subject)
          return label_stc
  
      def expand(self, vertices):
          """Expand SourceEstimate to include more vertices.
  
          This will add rows to stc.data (zero-filled) and modify stc.vertices
          to include all vertices in stc.vertices and the input vertices.
  
          Parameters
          ----------
          vertices : list of array
              New vertices to add. Can also contain old values.
  
          Returns
          -------
          stc : SourceEstimate | VectorSourceEstimate
              The modified stc (note: method operates inplace).
          """
          if not isinstance(vertices, list):
              raise TypeError('vertices must be a list')
          if not len(self.vertices) == len(vertices):
              raise ValueError('vertices must have the same length as '
                               'stc.vertices')
  
          # can no longer use kernel and sensor data
          self._remove_kernel_sens_data_()
  
          inserters = list()
          offsets = [0]
          for vi, (v_old, v_new) in enumerate(zip(self.vertices, vertices)):
              v_new = np.setdiff1d(v_new, v_old)
              inds = np.searchsorted(v_old, v_new)
              # newer numpy might overwrite inds after np.insert, copy here
              inserters += [inds.copy()]
              offsets += [len(v_old)]
              self.vertices[vi] = np.insert(v_old, inds, v_new)
          inds = [ii + offset for ii, offset in zip(inserters, offsets[:-1])]
          inds = np.concatenate(inds)
          new_data = np.zeros((len(inds),) + self.data.shape[1:])
          self.data = np.insert(self.data, inds, new_data, axis=0)
          return self
  
      @verbose
      def to_original_src(self, src_orig, subject_orig=None,
                          subjects_dir=None, verbose=None):
          """Get a source estimate from morphed source to the original subject.
  
          Parameters
          ----------
          src_orig : instance of SourceSpaces
              The original source spaces that were morphed to the current
              subject.
          subject_orig : str | None
              The original subject. For most source spaces this shouldn't need
              to be provided, since it is stored in the source space itself.
          subjects_dir : string, or None
              Path to SUBJECTS_DIR if it is not set in the environment.
          verbose : bool, str, int, or None
              If not None, override default verbose level (see
              :func:`mne.verbose` and :ref:`Logging documentation <tut_logging>`
              for more).
  
          Returns
          -------
          stc : SourceEstimate | VectorSourceEstimate
              The transformed source estimate.
  
          See Also
          --------
          morph_source_spaces
  
          Notes
          -----
          .. versionadded:: 0.10.0
          """
          if self.subject is None:
              raise ValueError('stc.subject must be set')
          src_orig = _ensure_src(src_orig, kind='surf')
          subject_orig = _ensure_src_subject(src_orig, subject_orig)
          data_idx, vertices = _get_morph_src_reordering(
              self.vertices, src_orig, subject_orig, self.subject, subjects_dir)
          return self.__class__(self._data[data_idx], vertices,
                                self.tmin, self.tstep, subject_orig)
  
  
  class SourceEstimate(_BaseSurfaceSourceEstimate):
      """Container for surface source estimates.
  
      Parameters
      ----------
      data : array of shape (n_dipoles, n_times) | 2-tuple (kernel, sens_data)
          The data in source space. The data can either be a single array or
          a tuple with two arrays: "kernel" shape (n_vertices, n_sensors) and
          "sens_data" shape (n_sensors, n_times). In this case, the source
          space data corresponds to "numpy.dot(kernel, sens_data)".
      vertices : list of two arrays
          Vertex numbers corresponding to the data.
      tmin : scalar
          Time point of the first sample in data.
      tstep : scalar
          Time step between successive samples in data.
      subject : str | None
          The subject name. While not necessary, it is safer to set the
          subject parameter to avoid analysis errors.
      verbose : bool, str, int, or None
          If not None, override default verbose level (see :func:`mne.verbose`
          and :ref:`Logging documentation <tut_logging>` for more).
  
      Attributes
      ----------
      subject : str | None
          The subject name.
      times : array of shape (n_times,)
          The time vector.
      vertices : list of two arrays of shape (n_dipoles,)
          The indices of the dipoles in the left and right source space.
      data : array of shape (n_dipoles, n_times)
          The data in source space.
      shape : tuple
          The shape of the data. A tuple of int (n_dipoles, n_times).
  
      See Also
      --------
      VectorSourceEstimate : A container for vector source estimates.
      VolSourceEstimate : A container for volume source estimates.
      MixedSourceEstimate : A container for mixed surface + volume source
                            estimates.
      """
  
      @verbose
      def save(self, fname, ftype='stc', verbose=None):
          """Save the source estimates to a file.
  
          Parameters
          ----------
          fname : string
              The stem of the file name. The file names used for surface source
              spaces are obtained by adding "-lh.stc" and "-rh.stc" (or "-lh.w"
              and "-rh.w") to the stem provided, for the left and the right
              hemisphere, respectively.
          ftype : string
              File format to use. Allowed values are "stc" (default), "w",
              and "h5". The "w" format only supports a single time point.
          verbose : bool, str, int, or None
              If not None, override default verbose level (see
              :func:`mne.verbose` and :ref:`Logging documentation <tut_logging>`
              for more). Defaults to self.verbose.
          """
          if ftype not in ('stc', 'w', 'h5'):
              raise ValueError('ftype must be "stc", "w", or "h5", not "%s"'
                               % ftype)
  
          lh_data = self.data[:len(self.lh_vertno)]
          rh_data = self.data[-len(self.rh_vertno):]
  
          if ftype == 'stc':
              logger.info('Writing STC to disk...')
              _write_stc(fname + '-lh.stc', tmin=self.tmin, tstep=self.tstep,
                         vertices=self.lh_vertno, data=lh_data)
              _write_stc(fname + '-rh.stc', tmin=self.tmin, tstep=self.tstep,
                         vertices=self.rh_vertno, data=rh_data)
  
          elif ftype == 'w':
              if self.shape[1] != 1:
                  raise ValueError('w files can only contain a single time '
                                   'point')
              logger.info('Writing STC to disk (w format)...')
              _write_w(fname + '-lh.w', vertices=self.lh_vertno,
                       data=lh_data[:, 0])
              _write_w(fname + '-rh.w', vertices=self.rh_vertno,
                       data=rh_data[:, 0])
  
          elif ftype == 'h5':
              if not fname.endswith('.h5'):
                  fname += '-stc.h5'
              write_hdf5(fname,
                         dict(vertices=self.vertices, data=self.data,
                              tmin=self.tmin, tstep=self.tstep,
                              subject=self.subject), title='mnepython',
                         overwrite=True)
          logger.info('[done]')
  
      @copy_function_doc_to_method_doc(plot_source_estimates)
      def plot(self, subject=None, surface='inflated', hemi='lh',
               colormap='auto', time_label='auto', smoothing_steps=10,
               transparent=True, alpha=1.0, time_viewer=False, subjects_dir=None,
               figure=None, views='lat', colorbar=True, clim='auto',
               cortex="classic", size=800, background="black",
               foreground="white", initial_time=None, time_unit='s',
               backend='auto', spacing='oct6', title=None, verbose=None):
          brain = plot_source_estimates(
              self, subject, surface=surface, hemi=hemi, colormap=colormap,
              time_label=time_label, smoothing_steps=smoothing_steps,
              transparent=transparent, alpha=alpha, time_viewer=time_viewer,
              subjects_dir=subjects_dir, figure=figure, views=views,
              colorbar=colorbar, clim=clim, cortex=cortex, size=size,
              background=background, foreground=foreground,
              initial_time=initial_time, time_unit=time_unit, backend=backend,
              spacing=spacing, title=title, verbose=verbose)
          return brain
  
      @verbose
      def extract_label_time_course(self, labels, src, mode='mean_flip',
                                    allow_empty=False, verbose=None):
          """Extract label time courses for lists of labels.
  
          This function will extract one time course for each label. The way the
          time courses are extracted depends on the mode parameter.
  
          Parameters
          ----------
          labels : Label | BiHemiLabel | list of Label or BiHemiLabel
              The labels for which to extract the time courses.
          src : list
              Source spaces for left and right hemisphere.
          mode : str
              Extraction mode, see explanation below.
          allow_empty : bool
              Instead of emitting an error, return all-zero time course for
              labels that do not have any vertices in the source estimate.
          verbose : bool, str, int, or None
              If not None, override default verbose level (see
              :func:`mne.verbose` and :ref:`Logging documentation <tut_logging>`
              for more).
  
          Returns
          -------
          label_tc : array, shape=(len(labels), n_times)
              Extracted time course for each label.
  
          See Also
          --------
          extract_label_time_course : extract time courses for multiple STCs
  
          Notes
          -----
          Valid values for mode are:
  
          - 'mean'
                Average within each label.
          - 'mean_flip'
                Average within each label with sign flip depending
                on source orientation.
          - 'pca_flip'
                Apply an SVD to the time courses within each label
                and use the scaled and sign-flipped first right-singular vector
                as the label time course. The scaling is performed such that the
                power of the label time course is the same as the average
                per-vertex time course power within the label. The sign of the
                resulting time course is adjusted by multiplying it with
                "sign(dot(u, flip))" where u is the first left-singular vector,
                and flip is a sing-flip vector based on the vertex normals. This
                procedure assures that the phase does not randomly change by 180
                degrees from one stc to the next.
          - 'max'
                Max value within each label.
          """
          label_tc = extract_label_time_course(
              self, labels, src, mode=mode, return_generator=False,
              allow_empty=allow_empty, verbose=verbose)
  
          return label_tc
  
      def get_peak(self, hemi=None, tmin=None, tmax=None, mode='abs',
                   vert_as_index=False, time_as_index=False):
          """Get location and latency of peak amplitude.
  
          Parameters
          ----------
          hemi : {'lh', 'rh', None}
              The hemi to be considered. If None, the entire source space is
              considered.
          tmin : float | None
              The minimum point in time to be considered for peak getting.
          tmax : float | None
              The maximum point in time to be considered for peak getting.
          mode : {'pos', 'neg', 'abs'}
              How to deal with the sign of the data. If 'pos' only positive
              values will be considered. If 'neg' only negative values will
              be considered. If 'abs' absolute values will be considered.
              Defaults to 'abs'.
          vert_as_index : bool
              whether to return the vertex index instead of of its ID.
              Defaults to False.
          time_as_index : bool
              Whether to return the time index instead of the latency.
              Defaults to False.
  
          Returns
          -------
          pos : int
              The vertex exhibiting the maximum response, either ID or index.
          latency : float | int
              The time point of the maximum response, either latency in seconds
              or index.
          """
          data = {'lh': self.lh_data, 'rh': self.rh_data, None: self.data}[hemi]
          vertno = {'lh': self.lh_vertno, 'rh': self.rh_vertno,
                    None: np.concatenate(self.vertices)}[hemi]
  
          vert_idx, time_idx, _ = _get_peak(data, self.times, tmin, tmax, mode)
  
          return (vert_idx if vert_as_index else vertno[vert_idx],
                  time_idx if time_as_index else self.times[time_idx])
  
      def center_of_mass(self, subject=None, hemi=None, restrict_vertices=False,
                         subjects_dir=None, surf='sphere'):
          """Compute the center of mass of activity.
  
          This function computes the spatial center of mass on the surface
          as well as the temporal center of mass as in [1]_.
  
          .. note:: All activity must occur in a single hemisphere, otherwise
                    an error is raised. The "mass" of each point in space for
                    computing the spatial center of mass is computed by summing
                    across time, and vice-versa for each point in time in
                    computing the temporal center of mass. This is useful for
                    quantifying spatio-temporal cluster locations, especially
                    when combined with :func:`mne.vertex_to_mni`.
  
          Parameters
          ----------
          subject : string | None
              The subject the stc is defined for.
          hemi : int, or None
              Calculate the center of mass for the left (0) or right (1)
              hemisphere. If None, one of the hemispheres must be all zeroes,
              and the center of mass will be calculated for the other
              hemisphere (useful for getting COM for clusters).
          restrict_vertices : bool | array of int | instance of SourceSpaces
              If True, returned vertex will be one from stc. Otherwise, it could
              be any vertex from surf. If an array of int, the returned vertex
              will come from that array. If instance of SourceSpaces (as of
              0.13), the returned vertex will be from the given source space.
              For most accuruate estimates, do not restrict vertices.
          subjects_dir : str, or None
              Path to the SUBJECTS_DIR. If None, the path is obtained by using
              the environment variable SUBJECTS_DIR.
          surf : str
              The surface to use for Euclidean distance center of mass
              finding. The default here is "sphere", which finds the center
              of mass on the spherical surface to help avoid potential issues
              with cortical folding.
  
          See Also
          --------
          mne.Label.center_of_mass
          mne.vertex_to_mni
  
          Returns
          -------
          vertex : int
              Vertex of the spatial center of mass for the inferred hemisphere,
              with each vertex weighted by the sum of the stc across time. For a
              boolean stc, then, this would be weighted purely by the duration
              each vertex was active.
          hemi : int
              Hemisphere the vertex was taken from.
          t : float
              Time of the temporal center of mass (weighted by the sum across
              source vertices).
  
          References
          ----------
          .. [1] Larson and Lee, "The cortical dynamics underlying effective
                 switching of auditory spatial attention", NeuroImage 2012.
          """
          if not isinstance(surf, str):
              raise TypeError('surf must be a string, got %s' % (type(surf),))
          subject = _check_subject(self.subject, subject)
          if np.any(self.data < 0):
              raise ValueError('Cannot compute COM with negative values')
          values = np.sum(self.data, axis=1)  # sum across time
          vert_inds = [np.arange(len(self.vertices[0])),
                       np.arange(len(self.vertices[1])) + len(self.vertices[0])]
          if hemi is None:
              hemi = np.where(np.array([np.sum(values[vi])
                                        for vi in vert_inds]))[0]
              if not len(hemi) == 1:
                  raise ValueError('Could not infer hemisphere')
              hemi = hemi[0]
          if hemi not in [0, 1]:
              raise ValueError('hemi must be 0 or 1')
          vertices = self.vertices[hemi]
          values = values[vert_inds[hemi]]  # left or right
          del vert_inds
          vertex = _center_of_mass(
              vertices, values, hemi=['lh', 'rh'][hemi], surf=surf,
              subject=subject, subjects_dir=subjects_dir,
              restrict_vertices=restrict_vertices)
          # do time center of mass by using the values across space
          masses = np.sum(self.data, axis=0).astype(float)
          t_ind = np.sum(masses * np.arange(self.shape[1])) / np.sum(masses)
          t = self.tmin + self.tstep * t_ind
          return vertex, hemi, t
  
  
  class VolSourceEstimate(_BaseSourceEstimate):
      """Container for volume source estimates.
  
      Parameters
      ----------
      data : array of shape (n_dipoles, n_times) | 2-tuple (kernel, sens_data)
          The data in source space. The data can either be a single array or
          a tuple with two arrays: "kernel" shape (n_vertices, n_sensors) and
          "sens_data" shape (n_sensors, n_times). In this case, the source
          space data corresponds to "numpy.dot(kernel, sens_data)".
      vertices : array
          Vertex numbers corresponding to the data.
      tmin : scalar
          Time point of the first sample in data.
      tstep : scalar
          Time step between successive samples in data.
      subject : str | None
          The subject name. While not necessary, it is safer to set the
          subject parameter to avoid analysis errors.
      verbose : bool, str, int, or None
          If not None, override default verbose level (see :func:`mne.verbose`
          and :ref:`Logging documentation <tut_logging>` for more).
  
      Attributes
      ----------
      subject : str | None
          The subject name.
      times : array of shape (n_times,)
          The time vector.
      vertices : array of shape (n_dipoles,)
          The indices of the dipoles in the source space.
      data : array of shape (n_dipoles, n_times)
          The data in source space.
      shape : tuple
          The shape of the data. A tuple of int (n_dipoles, n_times).
  
      Notes
      -----
      .. versionadded:: 0.9.0
  
      See Also
      --------
      SourceEstimate : A container for surface source estimates.
      VectorSourceEstimate : A container for vector source estimates.
      MixedSourceEstimate : A container for mixed surface + volume source
                            estimates.
      """
  
      @verbose
      def __init__(self, data, vertices=None, tmin=None, tstep=None,
                   subject=None, verbose=None):  # noqa: D102
          if not (isinstance(vertices, np.ndarray) or
                  isinstance(vertices, list)):
              raise ValueError('Vertices must be a numpy array or a list of '
                               'arrays')
  
          _BaseSourceEstimate.__init__(self, data, vertices=vertices, tmin=tmin,
                                       tstep=tstep, subject=subject,
                                       verbose=verbose)
  
      @copy_function_doc_to_method_doc(plot_volume_source_estimates)
      def plot(self, src, subject=None, subjects_dir=None, mode='stat_map',
               bg_img=None, colorbar=True, colormap='auto', clim='auto',
               transparent='auto', show=True, verbose=None):
          return plot_volume_source_estimates(
              self, src=src, subject=subject, subjects_dir=subjects_dir,
              mode=mode, bg_img=bg_img, colorbar=colorbar, colormap=colormap,
              clim=clim, transparent=transparent, show=show, verbose=verbose)
  
      @verbose
      def save(self, fname, ftype='stc', verbose=None):
          """Save the source estimates to a file.
  
          Parameters
          ----------
          fname : string
              The stem of the file name. The stem is extended with "-vl.stc"
              or "-vl.w".
          ftype : string
              File format to use. Allowed values are "stc" (default), "w",
              and "h5". The "w" format only supports a single time point.
          verbose : bool, str, int, or None
              If not None, override default verbose level (see
              :func:`mne.verbose` and :ref:`Logging documentation <tut_logging>`
              for more). Defaults to self.verbose.
          """
          if ftype not in ['stc', 'w', 'h5']:
              raise ValueError('ftype must be "stc", "w" or "h5", not "%s"' %
                               ftype)
  
          if ftype == 'stc':
              logger.info('Writing STC to disk...')
              if not (fname.endswith('-vl.stc') or fname.endswith('-vol.stc')):
                  fname += '-vl.stc'
              _write_stc(fname, tmin=self.tmin, tstep=self.tstep,
                         vertices=self.vertices, data=self.data)
          elif ftype == 'w':
              logger.info('Writing STC to disk (w format)...')
              if not (fname.endswith('-vl.w') or fname.endswith('-vol.w')):
                  fname += '-vl.w'
              _write_w(fname, vertices=self.vertices, data=self.data)
          elif ftype == 'h5':
              if not fname.endswith('.h5'):
                  fname += '-stc.h5'
              write_hdf5(fname,
                         dict(vertices=self.vertices, data=self.data,
                              tmin=self.tmin, tstep=self.tstep,
                              subject=self.subject, src_type='volume'),
                         title='mnepython',
                         overwrite=True)
  
          logger.info('[done]')
  
      def save_as_volume(self, fname, src, dest='mri', mri_resolution=False,
                         format='nifti1'):
          """Save a volume source estimate in a NIfTI file.
  
          Parameters
          ----------
          fname : string
              The name of the generated nifti file.
          src : list
              The list of source spaces (should all be of type volume).
          dest : 'mri' | 'surf'
              If 'mri' the volume is defined in the coordinate system of
              the original T1 image. If 'surf' the coordinate system
              of the FreeSurfer surface is used (Surface RAS).
          mri_resolution: bool
              It True the image is saved in MRI resolution.
              WARNING: if you have many time points the file produced can be
              huge.
          format : str
              Either 'nifti1' (default) or 'nifti2'.
  
              .. versionadded:: 0.17
  
  
          Returns
          -------
          img : instance Nifti1Image
              The image object.
  
          Notes
          -----
          .. versionadded:: 0.9.0
          """
          import nibabel as nib
          img = self.as_volume(src, dest=dest, mri_resolution=mri_resolution,
                               format=format)
          nib.save(img, fname)
  
      def as_volume(self, src, dest='mri', mri_resolution=False,
                    format='nifti1'):
          """Export volume source estimate as a nifti object.
  
          Parameters
          ----------
          src : list
              The list of source spaces (should all be of type volume).
          dest : 'mri' | 'surf'
              If 'mri' the volume is defined in the coordinate system of
              the original T1 image. If 'surf' the coordinate system
              of the FreeSurfer surface is used (Surface RAS).
          mri_resolution: bool
              It True the image is saved in MRI resolution.
              WARNING: if you have many time points the file produced can be
              huge.
          format : str
              Either 'nifti1' (default) or 'nifti2'.
  
          Returns
          -------
          img : instance Nifti1Image
              The image object.
  
          Notes
          -----
          .. versionadded:: 0.9.0
          """
          from .morph import _interpolate_data
          return _interpolate_data(self, src, mri_resolution=mri_resolution,
                                   mri_space=True, output=format)
  
      def __repr__(self):  # noqa: D105
          if isinstance(self.vertices, list):
              nv = sum([len(v) for v in self.vertices])
          else:
              nv = self.vertices.size
          s = "%d vertices" % nv
          if self.subject is not None:
              s += ", subject : %s" % self.subject
          s += ", tmin : %s (ms)" % (1e3 * self.tmin)
          s += ", tmax : %s (ms)" % (1e3 * self.times[-1])
          s += ", tstep : %s (ms)" % (1e3 * self.tstep)
          s += ", data size : %s" % ' x '.join(map(str, self.shape))
          return "<VolSourceEstimate  |  %s>" % s
  
      def get_peak(self, tmin=None, tmax=None, mode='abs',
                   vert_as_index=False, time_as_index=False):
          """Get location and latency of peak amplitude.
  
          Parameters
          ----------
          tmin : float | None
              The minimum point in time to be considered for peak getting.
          tmax : float | None
              The maximum point in time to be considered for peak getting.
          mode : {'pos', 'neg', 'abs'}
              How to deal with the sign of the data. If 'pos' only positive
              values will be considered. If 'neg' only negative values will
              be considered. If 'abs' absolute values will be considered.
              Defaults to 'abs'.
          vert_as_index : bool
              whether to return the vertex index instead of of its ID.
              Defaults to False.
          time_as_index : bool
              Whether to return the time index instead of the latency.
              Defaults to False.
  
          Returns
          -------
          pos : int
              The vertex exhibiting the maximum response, either ID or index.
          latency : float
              The latency in seconds.
          """
          vert_idx, time_idx, _ = _get_peak(self.data, self.times, tmin, tmax,
                                            mode)
  
          return (vert_idx if vert_as_index else self.vertices[vert_idx],
                  time_idx if time_as_index else self.times[time_idx])
  
  
  class VectorSourceEstimate(_BaseSurfaceSourceEstimate):
      """Container for vector surface source estimates.
  
      For each vertex, the magnitude of the current is defined in the X, Y and Z
      directions.
  
      Parameters
      ----------
      data : array of shape (n_dipoles, 3, n_times)
          The data in source space. Each dipole contains three vectors that
          denote the dipole strength in X, Y and Z directions over time.
      vertices : array | list of two arrays
          Vertex numbers corresponding to the data.
      tmin : float
          Time point of the first sample in data.
      tstep : float
          Time step between successive samples in data.
      subject : str | None
          The subject name. While not necessary, it is safer to set the
          subject parameter to avoid analysis errors.
      verbose : bool, str, int, or None
          If not None, override default verbose level (see mne.verbose).
  
      Attributes
      ----------
      subject : str | None
          The subject name.
      times : array of shape (n_times,)
          The time vector.
      shape : tuple
          The shape of the data. A tuple of int (n_dipoles, n_times).
  
      Notes
      -----
      .. versionadded:: 0.15
  
      See Also
      --------
      SourceEstimate : A container for surface source estimates.
      VolSourceEstimate : A container for volume source estimates.
      MixedSourceEstimate : A container for mixed surface + volume source
                            estimates.
      """
  
      @verbose
      def save(self, fname, ftype='h5', verbose=None):
          """Save the full source estimate to an HDF5 file.
  
          Parameters
          ----------
          fname : string
              The file name to write the source estimate to, should end in
              '-stc.h5'.
          ftype : string
              File format to use. Currently, the only allowed values is "h5".
          verbose : bool, str, int, or None
              If not None, override default verbose level (see mne.verbose).
              Defaults to self.verbose.
          """
          if ftype != 'h5':
              raise ValueError('VectorSourceEstimate objects can only be '
                               'written as HDF5 files.')
  
          if not fname.endswith('.h5'):
              fname += '-stc.h5'
  
          write_hdf5(fname,
                     dict(vertices=self.vertices, data=self.data, tmin=self.tmin,
                          tstep=self.tstep, subject=self.subject),
                     title='mnepython', overwrite=True)
  
      def magnitude(self):
          """Compute magnitude of activity without directionality.
  
          Returns
          -------
          stc : instance of SourceEstimate
              The source estimate without directionality information.
          """
          data_mag = np.linalg.norm(self.data, axis=1)
          return SourceEstimate(data_mag, self.vertices, self.tmin, self.tstep,
                                self.subject, self.verbose)
  
      def normal(self, src):
          """Compute activity orthogonal to the cortex.
  
          Parameters
          ----------
          src : instance of SourceSpaces
              The source space for which this source estimate is specified.
  
          Returns
          -------
          stc : instance of SourceEstimate
              The source estimate only retaining the activity orthogonal to the
              cortex.
          """
          normals = np.vstack([s['nn'][v] for s, v in zip(src, self.vertices)])
          data_norm = einsum('ijk,ij->ik', self.data, normals)
          return SourceEstimate(data_norm, self.vertices, self.tmin, self.tstep,
                                self.subject, self.verbose)
  
      @copy_function_doc_to_method_doc(plot_vector_source_estimates)
      def plot(self, subject=None, hemi='lh', colormap='hot', time_label='auto',
               smoothing_steps=10, transparent=True, brain_alpha=0.4,
               overlay_alpha=None, vector_alpha=1.0, scale_factor=None,
               time_viewer=False, subjects_dir=None, figure=None, views='lat',
               colorbar=True, clim='auto', cortex='classic', size=800,
               background='black', foreground='white', initial_time=None,
               time_unit='s'):
  
          return plot_vector_source_estimates(
              self, subject=subject, hemi=hemi, colormap=colormap,
              time_label=time_label, smoothing_steps=smoothing_steps,
              transparent=transparent, brain_alpha=brain_alpha,
              overlay_alpha=overlay_alpha, vector_alpha=vector_alpha,
              scale_factor=scale_factor, time_viewer=time_viewer,
              subjects_dir=subjects_dir, figure=figure, views=views,
              colorbar=colorbar, clim=clim, cortex=cortex, size=size,
              background=background, foreground=foreground,
              initial_time=initial_time, time_unit=time_unit
          )
  
      def __abs__(self):
          """Compute the absolute value of each component.
  
          Returns
          -------
          stc_abs : VectorSourceEstimate
              A vector source estimate where the data attribute is set to
              abs(self.data).
  
          See Also
          --------
          VectorSourceEstimate.magnitude
          """
          return super(VectorSourceEstimate, self).__abs__()
  
  
  class MixedSourceEstimate(_BaseSourceEstimate):
      """Container for mixed surface and volume source estimates.
  
      Parameters
      ----------
      data : array of shape (n_dipoles, n_times) | 2-tuple (kernel, sens_data)
          The data in source space. The data can either be a single array or
          a tuple with two arrays: "kernel" shape (n_vertices, n_sensors) and
          "sens_data" shape (n_sensors, n_times). In this case, the source
          space data corresponds to "numpy.dot(kernel, sens_data)".
      vertices : list of arrays
          Vertex numbers corresponding to the data.
      tmin : scalar
          Time point of the first sample in data.
      tstep : scalar
          Time step between successive samples in data.
      subject : str | None
          The subject name. While not necessary, it is safer to set the
          subject parameter to avoid analysis errors.
      verbose : bool, str, int, or None
          If not None, override default verbose level (see :func:`mne.verbose`
          and :ref:`Logging documentation <tut_logging>` for more).
  
      Attributes
      ----------
      subject : str | None
          The subject name.
      times : array of shape (n_times,)
          The time vector.
      vertices : list of arrays of shape (n_dipoles,)
          The indices of the dipoles in each source space.
      data : array of shape (n_dipoles, n_times)
          The data in source space.
      shape : tuple
          The shape of the data. A tuple of int (n_dipoles, n_times).
  
      Notes
      -----
      .. versionadded:: 0.9.0
  
      See Also
      --------
      SourceEstimate : A container for surface source estimates.
      VectorSourceEstimate : A container for vector source estimates.
      VolSourceEstimate : A container for volume source estimates.
      """
  
      @verbose
      def __init__(self, data, vertices=None, tmin=None, tstep=None,
                   subject=None, verbose=None):  # noqa: D102
          if not isinstance(vertices, list) or len(vertices) < 2:
              raise ValueError('Vertices must be a list of numpy arrays with '
                               'one array per source space.')
  
          _BaseSourceEstimate.__init__(self, data, vertices=vertices, tmin=tmin,
                                       tstep=tstep, subject=subject,
                                       verbose=verbose)
  
      def plot_surface(self, src, subject=None, surface='inflated', hemi='lh',
                       colormap='auto', time_label='time=%02.f ms',
                       smoothing_steps=10,
                       transparent=None, alpha=1.0, time_viewer=False,
                       config_opts=None, subjects_dir=None, figure=None,
                       views='lat', colorbar=True, clim='auto'):
          """Plot surface source estimates with PySurfer.
  
          Note: PySurfer currently needs the SUBJECTS_DIR environment variable,
          which will automatically be set by this function. Plotting multiple
          SourceEstimates with different values for subjects_dir will cause
          PySurfer to use the wrong FreeSurfer surfaces when using methods of
          the returned Brain object. It is therefore recommended to set the
          SUBJECTS_DIR environment variable or always use the same value for
          subjects_dir (within the same Python session).
  
          Parameters
          ----------
          src : SourceSpaces
              The source spaces to plot.
          subject : str | None
              The subject name corresponding to FreeSurfer environment
              variable SUBJECT. If None stc.subject will be used. If that
              is None, the environment will be used.
          surface : str
              The type of surface (inflated, white etc.).
          hemi : str, 'lh' | 'rh' | 'split' | 'both'
              The hemisphere to display. Using 'both' or 'split' requires
              PySurfer version 0.4 or above.
          colormap : str | np.ndarray of float, shape(n_colors, 3 | 4)
              Name of colormap to use. See `plot_source_estimates`.
          time_label : str
              How to print info about the time instant visualized.
          smoothing_steps : int
              The amount of smoothing.
          transparent : bool | None
              If True, use a linear transparency between fmin and fmid.
              None will choose automatically based on colormap type.
          alpha : float
              Alpha value to apply globally to the overlay.
          time_viewer : bool
              Display time viewer GUI.
          config_opts : dict
              Keyword arguments for Brain initialization.
              See pysurfer.viz.Brain.
          subjects_dir : str
              The path to the FreeSurfer subjects reconstructions.
              It corresponds to FreeSurfer environment variable SUBJECTS_DIR.
          figure : instance of mayavi.core.scene.Scene | None
              If None, the last figure will be cleaned and a new figure will
              be created.
          views : str | list
              View to use. See surfer.Brain().
          colorbar : bool
              If True, display colorbar on scene.
          clim : str | dict
              Colorbar properties specification. See `plot_source_estimates`.
  
          Returns
          -------
          brain : Brain
              A instance of surfer.viz.Brain from PySurfer.
          """
          # extract surface source spaces
          surf = _ensure_src(src, kind='surf')
  
          # extract surface source estimate
          data = self.data[:surf[0]['nuse'] + surf[1]['nuse']]
          vertices = [s['vertno'] for s in surf]
  
          stc = SourceEstimate(data, vertices, self.tmin, self.tstep,
                               self.subject, self.verbose)
  
          return plot_source_estimates(stc, subject, surface=surface, hemi=hemi,
                                       colormap=colormap, time_label=time_label,
                                       smoothing_steps=smoothing_steps,
                                       transparent=transparent, alpha=alpha,
                                       time_viewer=time_viewer,
                                       config_opts=config_opts,
                                       subjects_dir=subjects_dir, figure=figure,
                                       views=views, colorbar=colorbar, clim=clim)
  
      @verbose
      def save(self, fname, ftype='h5', verbose=None):
          """Save the source estimates to a file.
  
          Parameters
          ----------
          fname : string
              The stem of the file name. The file names used for surface source
              spaces are obtained by adding "-lh.stc" and "-rh.stc" (or "-lh.w"
              and "-rh.w") to the stem provided, for the left and the right
              hemisphere, respectively.
          ftype : string
              File format to use. Allowed values are "stc" (default), "w",
              and "h5". The "w" format only supports a single time point.
          verbose : bool, str, int, or None
              If not None, override default verbose level (see
              :func:`mne.verbose` and :ref:`Logging documentation <tut_logging>`
              for more). Defaults to self.verbose.
          """
          if ftype != 'h5':
              raise ValueError('MixedSourceEstimate objects can only be '
                               'written as HDF5 files.')
  
          if not fname.endswith('.h5'):
              fname += '-stc.h5'
  
          write_hdf5(fname,
                     dict(vertices=self.vertices, data=self.data,
                          tmin=self.tmin, tstep=self.tstep,
                          subject=self.subject, src_type='mixed'),
                     title='mnepython',
                     overwrite=True)
          logger.info('[done]')
  
  
  ###############################################################################
  # Morphing
  
  
  def _get_vol_mask(src):
      """Get the volume source space mask."""
      assert len(src) == 1  # not a mixed source space
      shape = src[0]['shape'][::-1]
      mask = np.zeros(shape, bool)
      mask.flat[src[0]['vertno']] = True
      return mask
  
  
  def _spatio_temporal_src_connectivity_vol(src, n_times):
      from sklearn.feature_extraction import grid_to_graph
      mask = _get_vol_mask(src)
      edges = grid_to_graph(*mask.shape, mask=mask)
      connectivity = _get_connectivity_from_edges(edges, n_times)
      return connectivity
  
  
  def _spatio_temporal_src_connectivity_surf(src, n_times):
      if src[0]['use_tris'] is None:
          # XXX It would be nice to support non oct source spaces too...
          raise RuntimeError("The source space does not appear to be an ico "
                             "surface. Connectivity cannot be extracted from"
                             " non-ico source spaces.")
      used_verts = [np.unique(s['use_tris']) for s in src]
      offs = np.cumsum([0] + [len(u_v) for u_v in used_verts])[:-1]
      tris = np.concatenate([np.searchsorted(u_v, s['use_tris']) + off
                             for u_v, s, off in zip(used_verts, src, offs)])
      connectivity = spatio_temporal_tris_connectivity(tris, n_times)
  
      # deal with source space only using a subset of vertices
      masks = [np.in1d(u, s['vertno']) for s, u in zip(src, used_verts)]
      if sum(u.size for u in used_verts) != connectivity.shape[0] / n_times:
          raise ValueError('Used vertices do not match connectivity shape')
      if [np.sum(m) for m in masks] != [len(s['vertno']) for s in src]:
          raise ValueError('Vertex mask does not match number of vertices')
      masks = np.concatenate(masks)
      missing = 100 * float(len(masks) - np.sum(masks)) / len(masks)
      if missing:
          warn_('%0.1f%% of original source space vertices have been'
                ' omitted, tri-based connectivity will have holes.\n'
                'Consider using distance-based connectivity or '
                'morphing data to all source space vertices.' % missing)
          masks = np.tile(masks, n_times)
          masks = np.where(masks)[0]
          connectivity = connectivity.tocsr()
          connectivity = connectivity[masks]
          connectivity = connectivity[:, masks]
          # return to original format
          connectivity = connectivity.tocoo()
      return connectivity
  
  
  @verbose
  def spatio_temporal_src_connectivity(src, n_times, dist=None, verbose=None):
      """Compute connectivity for a source space activation over time.
  
      Parameters
      ----------
      src : instance of SourceSpaces
          The source space. It can be a surface source space or a
          volume source space.
      n_times : int
          Number of time instants.
      dist : float, or None
          Maximal geodesic distance (in m) between vertices in the
          source space to consider neighbors. If None, immediate neighbors
          are extracted from an ico surface.
      verbose : bool, str, int, or None
          If not None, override default verbose level (see :func:`mne.verbose`
          and :ref:`Logging documentation <tut_logging>` for more).
  
      Returns
      -------
      connectivity : sparse COO matrix
          The connectivity matrix describing the spatio-temporal
          graph structure. If N is the number of vertices in the
          source space, the N first nodes in the graph are the
          vertices are time 1, the nodes from 2 to 2N are the vertices
          during time 2, etc.
      """
      # XXX we should compute connectivity for each source space and then
      # use scipy.sparse.block_diag to concatenate them
      if src[0]['type'] == 'vol':
          if dist is not None:
              raise ValueError('dist must be None for a volume '
                               'source space. Got %s.' % dist)
  
          connectivity = _spatio_temporal_src_connectivity_vol(src, n_times)
      elif dist is not None:
          # use distances computed and saved in the source space file
          connectivity = spatio_temporal_dist_connectivity(src, n_times, dist)
      else:
          connectivity = _spatio_temporal_src_connectivity_surf(src, n_times)
      return connectivity
  
  
  @verbose
  def grade_to_tris(grade, verbose=None):
      """Get tris defined for a certain grade.
  
      Parameters
      ----------
      grade : int
          Grade of an icosahedral mesh.
      verbose : bool, str, int, or None
          If not None, override default verbose level (see :func:`mne.verbose`
          and :ref:`Logging documentation <tut_logging>` for more).
  
      Returns
      -------
      tris : list
          2-element list containing Nx3 arrays of tris, suitable for use in
          spatio_temporal_tris_connectivity.
      """
      a = _get_ico_tris(grade, None, False)
      tris = np.concatenate((a, a + (np.max(a) + 1)))
      return tris
  
  
  @verbose
  def spatio_temporal_tris_connectivity(tris, n_times, remap_vertices=False,
                                        verbose=None):
      """Compute connectivity from triangles and time instants.
  
      Parameters
      ----------
      tris : array
          N x 3 array defining triangles.
      n_times : int
          Number of time points
      remap_vertices : bool
          Reassign vertex indices based on unique values. Useful
          to process a subset of triangles. Defaults to False.
      verbose : bool, str, int, or None
          If not None, override default verbose level (see :func:`mne.verbose`
          and :ref:`Logging documentation <tut_logging>` for more).
  
      Returns
      -------
      connectivity : sparse COO matrix
          The connectivity matrix describing the spatio-temporal
          graph structure. If N is the number of vertices in the
          source space, the N first nodes in the graph are the
          vertices are time 1, the nodes from 2 to 2N are the vertices
          during time 2, etc.
      """
      if remap_vertices:
          logger.info('Reassigning vertex indices.')
          tris = np.searchsorted(np.unique(tris), tris)
  
      edges = mesh_edges(tris).tocoo()
      return _get_connectivity_from_edges(edges, n_times)
  
  
  @verbose
  def spatio_temporal_dist_connectivity(src, n_times, dist, verbose=None):
      """Compute connectivity from distances in a source space and time instants.
  
      Parameters
      ----------
      src : instance of SourceSpaces
          The source space must have distances between vertices computed, such
          that src['dist'] exists and is useful. This can be obtained using MNE
          with a call to mne_add_patch_info with the --dist option.
      n_times : int
          Number of time points
      dist : float
          Maximal geodesic distance (in m) between vertices in the
          source space to consider neighbors.
      verbose : bool, str, int, or None
          If not None, override default verbose level (see :func:`mne.verbose`
          and :ref:`Logging documentation <tut_logging>` for more).
  
      Returns
      -------
      connectivity : sparse COO matrix
          The connectivity matrix describing the spatio-temporal
          graph structure. If N is the number of vertices in the
          source space, the N first nodes in the graph are the
          vertices are time 1, the nodes from 2 to 2N are the vertices
          during time 2, etc.
      """
      if src[0]['dist'] is None:
          raise RuntimeError('src must have distances included, consider using\n'
                             'mne_add_patch_info with --dist argument')
      edges = sparse_block_diag([s['dist'][s['vertno'], :][:, s['vertno']]
                                 for s in src])
      edges.data[:] = np.less_equal(edges.data, dist)
      # clean it up and put it in coo format
      edges = edges.tocsr()
      edges.eliminate_zeros()
      edges = edges.tocoo()
      return _get_connectivity_from_edges(edges, n_times)
  
  
  @verbose
  def spatial_src_connectivity(src, dist=None, verbose=None):
      """Compute connectivity for a source space activation.
  
      Parameters
      ----------
      src : instance of SourceSpaces
          The source space. It can be a surface source space or a
          volume source space.
      dist : float, or None
          Maximal geodesic distance (in m) between vertices in the
          source space to consider neighbors. If None, immediate neighbors
          are extracted from an ico surface.
      verbose : bool, str, int, or None
          If not None, override default verbose level (see :func:`mne.verbose`
          and :ref:`Logging documentation <tut_logging>` for more).
  
      Returns
      -------
      connectivity : sparse COO matrix
          The connectivity matrix describing the spatial graph structure.
      """
      return spatio_temporal_src_connectivity(src, 1, dist)
  
  
  @verbose
  def spatial_tris_connectivity(tris, remap_vertices=False, verbose=None):
      """Compute connectivity from triangles.
  
      Parameters
      ----------
      tris : array
          N x 3 array defining triangles.
      remap_vertices : bool
          Reassign vertex indices based on unique values. Useful
          to process a subset of triangles. Defaults to False.
      verbose : bool, str, int, or None
          If not None, override default verbose level (see :func:`mne.verbose`
          and :ref:`Logging documentation <tut_logging>` for more).
  
      Returns
      -------
      connectivity : sparse COO matrix
          The connectivity matrix describing the spatial graph structure.
      """
      return spatio_temporal_tris_connectivity(tris, 1, remap_vertices)
  
  
  def spatial_dist_connectivity(src, dist, verbose=None):
      """Compute connectivity from distances in a source space.
  
      Parameters
      ----------
      src : instance of SourceSpaces
          The source space must have distances between vertices computed, such
          that src['dist'] exists and is useful. This can be obtained using MNE
          with a call to mne_add_patch_info with the --dist option.
      dist : float
          Maximal geodesic distance (in m) between vertices in the
          source space to consider neighbors.
      verbose : bool, str, int, or None
          If not None, override default verbose level (see :func:`mne.verbose`
          and :ref:`Logging documentation <tut_logging>` for more).
  
      Returns
      -------
      connectivity : sparse COO matrix
          The connectivity matrix describing the spatial graph structure.
      """
      return spatio_temporal_dist_connectivity(src, 1, dist)
  
  
  def spatial_inter_hemi_connectivity(src, dist, verbose=None):
      """Get vertices on each hemisphere that are close to the other hemisphere.
  
      Parameters
      ----------
      src : instance of SourceSpaces
          The source space. Must be surface type.
      dist : float
          Maximal Euclidean distance (in m) between vertices in one hemisphere
          compared to the other to consider neighbors.
      verbose : bool, str, int, or None
          If not None, override default verbose level (see :func:`mne.verbose`
          and :ref:`Logging documentation <tut_logging>` for more).
  
      Returns
      -------
      connectivity : sparse COO matrix
          The connectivity matrix describing the spatial graph structure.
          Typically this should be combined (addititively) with another
          existing intra-hemispheric connectivity matrix, e.g. computed
          using geodesic distances.
      """
      from scipy.spatial.distance import cdist
      src = _ensure_src(src, kind='surf')
      conn = cdist(src[0]['rr'][src[0]['vertno']],
                   src[1]['rr'][src[1]['vertno']])
      conn = sparse.csr_matrix(conn <= dist, dtype=int)
      empties = [sparse.csr_matrix((nv, nv), dtype=int) for nv in conn.shape]
      conn = sparse.vstack([sparse.hstack([empties[0], conn]),
                            sparse.hstack([conn.T, empties[1]])])
      return conn
  
  
  @verbose
  def _get_connectivity_from_edges(edges, n_times, verbose=None):
      """Given edges sparse matrix, create connectivity matrix."""
      n_vertices = edges.shape[0]
      logger.info("-- number of connected vertices : %d" % n_vertices)
      nnz = edges.col.size
      aux = n_vertices * np.arange(n_times)[:, None] * np.ones((1, nnz), np.int)
      col = (edges.col[None, :] + aux).ravel()
      row = (edges.row[None, :] + aux).ravel()
      if n_times > 1:  # add temporal edges
          o = (n_vertices * np.arange(n_times - 1)[:, None] +
               np.arange(n_vertices)[None, :]).ravel()
          d = (n_vertices * np.arange(1, n_times)[:, None] +
               np.arange(n_vertices)[None, :]).ravel()
          row = np.concatenate((row, o, d))
          col = np.concatenate((col, d, o))
      data = np.ones(edges.data.size * n_times + 2 * n_vertices * (n_times - 1),
                     dtype=np.int)
      connectivity = coo_matrix((data, (row, col)),
                                shape=(n_times * n_vertices,) * 2)
      return connectivity
  
  
  @verbose
  def _get_ico_tris(grade, verbose=None, return_surf=False):
      """Get triangles for ico surface."""
      ico = _get_ico_surface(grade)
      if not return_surf:
          return ico['tris']
      else:
          return ico
  
  
  def _get_label_flip(labels, label_vertidx, src):
      """Get sign-flip for labels."""
      # do the import here to avoid circular dependency
      from .label import label_sign_flip
      # get the sign-flip vector for every label
      label_flip = list()
      for label, vertidx in zip(labels, label_vertidx):
          if vertidx is not None:
              flip = label_sign_flip(label, src)[:, None]
          else:
              flip = None
          label_flip.append(flip)
  
      return label_flip
  
  
  def _pca_flip(flip, data):
      U, s, V = linalg.svd(data, full_matrices=False)
      # determine sign-flip
      sign = np.sign(np.dot(U[:, 0], flip))
      # use average power in label for scaling
      scale = linalg.norm(s) / np.sqrt(len(data))
      return sign * scale * V[0]
  
  
  _label_funcs = {
      'mean': lambda flip, data: np.mean(data, axis=0),
      'mean_flip': lambda flip, data: np.mean(flip * data, axis=0),
      'max': lambda flip, data: np.max(np.abs(data), axis=0),
      'pca_flip': _pca_flip,
  }
  
  
  @verbose
  def _gen_extract_label_time_course(stcs, labels, src, mode='mean',
                                     allow_empty=False, verbose=None):
      """Generate extract_label_time_course."""
      # if src is a mixed src space, the first 2 src spaces are surf type and
      # the other ones are vol type. For mixed source space n_labels will be the
      # given by the number of ROIs of the cortical parcellation plus the number
      # of vol src space
  
      if mode not in _label_funcs:
          raise ValueError('%s is an invalid mode' % mode)
      func = _label_funcs[mode]
  
      if len(src) > 2:
          if src[0]['type'] != 'surf' or src[1]['type'] != 'surf':
              raise ValueError('The first 2 source spaces have to be surf type')
          if any(np.any(s['type'] != 'vol') for s in src[2:]):
              raise ValueError('source spaces have to be of vol type')
  
          n_aparc = len(labels)
          n_aseg = len(src[2:])
          n_labels = n_aparc + n_aseg
      else:
          n_labels = len(labels)
  
      # get vertices from source space, they have to be the same as in the stcs
      vertno = [s['vertno'] for s in src]
      nvert = [len(vn) for vn in vertno]
  
      # do the initialization
      label_vertidx = list()
      for label in labels:
          if label.hemi == 'both':
              # handle BiHemiLabel
              sub_labels = [label.lh, label.rh]
          else:
              sub_labels = [label]
          this_vertidx = list()
          for slabel in sub_labels:
              if slabel.hemi == 'lh':
                  this_vertno = np.intersect1d(vertno[0], slabel.vertices)
                  vertidx = np.searchsorted(vertno[0], this_vertno)
              elif slabel.hemi == 'rh':
                  this_vertno = np.intersect1d(vertno[1], slabel.vertices)
                  vertidx = nvert[0] + np.searchsorted(vertno[1], this_vertno)
              else:
                  raise ValueError('label %s has invalid hemi' % label.name)
              this_vertidx.append(vertidx)
  
          # convert it to an array
          this_vertidx = np.concatenate(this_vertidx)
          if len(this_vertidx) == 0:
              msg = ('source space does not contain any vertices for label %s'
                     % label.name)
              if not allow_empty:
                  raise ValueError(msg)
              else:
                  warn_(msg + '. Assigning all-zero time series to label.')
              this_vertidx = None  # to later check if label is empty
  
          label_vertidx.append(this_vertidx)
  
      # mode-dependent initialization
      if mode not in ('mean', 'max'):
          # get the sign-flip vector for every label
          src_flip = _get_label_flip(labels, label_vertidx, src[:2])
      else:
          src_flip = [None] * len(labels)
  
      # loop through source estimates and extract time series
      for stc in stcs:
          # make sure the stc is compatible with the source space
          for i in range(len(src)):
              if len(stc.vertices[i]) != nvert[i]:
                  raise ValueError('stc not compatible with source space. '
                                   'stc has %s time series but there are %s '
                                   'vertices in source space'
                                   % (len(stc.vertices[i]), nvert[i]))
  
          if any(np.any(svn != vn) for svn, vn in zip(stc.vertices, vertno)):
              raise ValueError('stc not compatible with source space')
          if sum(nvert) != stc.shape[0]:
              raise ValueError('stc not compatible with source space. '
                               'stc has %s vertices but the source space '
                               'has %s vertices'
                               % (stc.shape[0], sum(nvert)))
  
          logger.info('Extracting time courses for %d labels (mode: %s)'
                      % (n_labels, mode))
  
          # do the extraction
          label_tc = np.zeros((n_labels, stc.data.shape[1]),
                              dtype=stc.data.dtype)
          for i, (vertidx, flip) in enumerate(zip(label_vertidx, src_flip)):
              if vertidx is not None:
                  label_tc[i] = func(flip, stc.data[vertidx, :])
  
          # extract label time series for the vol src space
          if len(src) > 2:
              v1 = nvert[0] + nvert[1]
              for i, nv in enumerate(nvert[2:]):
  
                  v2 = v1 + nv
                  v = range(v1, v2)
                  if nv != 0:
                      label_tc[n_aparc + i] = np.mean(stc.data[v, :], axis=0)
  
                  v1 = v2
  
          # this is a generator!
          yield label_tc
  
  
  @verbose
  def extract_label_time_course(stcs, labels, src, mode='mean_flip',
                                allow_empty=False, return_generator=False,
                                verbose=None):
      """Extract label time course for lists of labels and source estimates.
  
      This function will extract one time course for each label and source
      estimate. The way the time courses are extracted depends on the mode
      parameter.
  
      Valid values for mode are:
  
          - 'mean': Average within each label.
          - 'mean_flip': Average within each label with sign flip depending
            on source orientation.
          - 'pca_flip': Apply an SVD to the time courses within each label
            and use the scaled and sign-flipped first right-singular vector
            as the label time course. The scaling is performed such that the
            power of the label time course is the same as the average
            per-vertex time course power within the label. The sign of the
            resulting time course is adjusted by multiplying it with
            "sign(dot(u, flip))" where u is the first left-singular vector,
            and flip is a sing-flip vector based on the vertex normals. This
            procedure assures that the phase does not randomly change by 180
            degrees from one stc to the next.
          - 'max': Max value within each label.
  
  
      Parameters
      ----------
      stcs : SourceEstimate | list (or generator) of SourceEstimate
          The source estimates from which to extract the time course.
      labels : Label | BiHemiLabel | list of Label or BiHemiLabel
          The labels for which to extract the time course.
      src : list
          Source spaces for left and right hemisphere.
      mode : str
          Extraction mode, see explanation above.
      allow_empty : bool
          Instead of emitting an error, return all-zero time courses for labels
          that do not have any vertices in the source estimate.
      return_generator : bool
          If True, a generator instead of a list is returned.
      verbose : bool, str, int, or None
          If not None, override default verbose level (see :func:`mne.verbose`
          and :ref:`Logging documentation <tut_logging>` for more).
  
      Returns
      -------
      label_tc : array | list (or generator) of array, shape=(len(labels), n_times)
          Extracted time course for each label and source estimate.
      """  # noqa: E501
      # convert inputs to lists
      if isinstance(stcs, SourceEstimate):
          stcs = [stcs]
          return_several = False
          return_generator = False
      else:
          return_several = True
  
      if not isinstance(labels, list):
          labels = [labels]
  
      label_tc = _gen_extract_label_time_course(stcs, labels, src, mode=mode,
                                                allow_empty=allow_empty)
  
      if not return_generator:
          # do the extraction and return a list
          label_tc = list(label_tc)
  
      if not return_several:
          # input was a single SoureEstimate, return single array
          label_tc = label_tc[0]
  
      return label_tc
  
apis: numpy.ones numpy.sum scipy.sparse.block_diag scipy.spatial.distance.cdist numpy.intersect1d numpy.any numpy.argsort numpy.asarray numpy.insert numpy.vstack scipy.linalg.norm numpy.in1d numpy.abs scipy.sparse.hstack numpy.where numpy.unique numpy.mean numpy.tile numpy.fromfile numpy.atleast_2d numpy.zeros numpy.dot numpy.searchsorted numpy.setdiff1d numpy.arange scipy.sparse.coo_matrix numpy.max numpy.prod numpy.linalg.norm numpy.empty numpy.left_shift scipy.sparse.csr_matrix sklearn.feature_extraction.grid_to_graph numpy.less_equal numpy.array_equal numpy.array numpy.concatenate numpy.frombuffer scipy.linalg.svd