"""Compute Linearly constrained minimum variance (LCMV) beamformer."""

# Authors: Alexandre Gramfort <alexandre.gramfort@inria.fr>
#          Roman Goj <roman.goj@gmail.com>
#          Britta Westner <britta.wstnr@gmail.com>
#
# License: BSD-3-Clause
import numpy as np

from ..rank import compute_rank
from ..io.meas_info import _simplify_info
from ..io.pick import pick_channels_cov, pick_info
from ..forward import _subject_from_forward
from ..minimum_norm.inverse import combine_xyz, _check_reference, _check_depth
from ..source_estimate import _make_stc, _get_src_type
from ..utils import (logger, verbose, _check_channels_spatial_filter,
                     _check_one_ch_type, _check_info_inv)
from ._compute_beamformer import (
    _prepare_beamformer_input, _compute_power,
    _compute_beamformer, _check_src_type, Beamformer, _proj_whiten_data)


@verbose
def make_lcmv(info, forward, data_cov, reg=0.05, noise_cov=None, label=None,
              pick_ori=None, rank='info',
              weight_norm='unit-noise-gain-invariant',
              reduce_rank=False, depth=None, inversion='matrix', verbose=None):
    """Compute LCMV spatial filter.

    Parameters
    ----------
    %(info_not_none)s
        Specifies the channels to include. Bad channels (in ``info['bads']``)
        are not used.
    forward : instance of Forward
        Forward operator.
    data_cov : instance of Covariance
        The data covariance.
    reg : float
        The regularization for the whitened data covariance.
    noise_cov : instance of Covariance
        The noise covariance. If provided, whitening will be done. Providing a
        noise covariance is mandatory if you mix sensor types, e.g.
        gradiometers with magnetometers or EEG with MEG.

        .. note::
            If ``noise_cov`` is ``None`` and ``weight_norm='unit-noise-gain'``,
            the unit noise is assumed to be 1 in SI units, e.g., 1 T for
            magnetometers, 1 V for EEG, so resulting amplitudes will be tiny.
            Consider using :func:`mne.make_ad_hoc_cov` to provide a
            ``noise_cov`` to set noise values that are more reasonable for
            neural data or using ``weight_norm='nai'`` for weight-normalized
            beamformer output that is scaled by a noise estimate.
    label : instance of Label
        Restricts the LCMV solution to a given label.
    %(pick_ori_bf)s

        - ``'vector'``
            Keeps the currents for each direction separate
    %(rank_info)s
    %(weight_norm)s

        Defaults to ``'unit-noise-gain-invariant'``.
    %(reduce_rank)s
    %(depth)s

        .. versionadded:: 0.18
    %(inversion_bf)s

        .. versionadded:: 0.21
    %(verbose)s

    Returns
    -------
    filters : instance of Beamformer
        Dictionary containing filter weights from LCMV beamformer.
        Contains the following keys:

            'kind' : str
                The type of beamformer, in this case 'LCMV'.
            'weights' : array
                The filter weights of the beamformer.
            'data_cov' : instance of Covariance
                The data covariance matrix used to compute the beamformer.
            'noise_cov' : instance of Covariance | None
                The noise covariance matrix used to compute the beamformer.
            'whitener' : None | ndarray, shape (n_channels, n_channels)
                Whitening matrix, provided if whitening was applied to the
                covariance matrix and leadfield during computation of the
                beamformer weights.
            'weight_norm' : str | None
                Type of weight normalization used to compute the filter
                weights.
            'pick-ori' : None | 'max-power' | 'normal' | 'vector'
                The orientation in which the beamformer filters were computed.
            'ch_names' : list of str
                Channels used to compute the beamformer.
            'proj' : array
                Projections used to compute the beamformer.
            'is_ssp' : bool
                If True, projections were applied prior to filter computation.
            'vertices' : list
                Vertices for which the filter weights were computed.
            'is_free_ori' : bool
                If True, the filter was computed with free source orientation.
            'n_sources' : int
                Number of source location for which the filter weight were
                computed.
            'src_type' : str
                Type of source space.
            'source_nn' : ndarray, shape (n_sources, 3)
                For each source location, the surface normal.
            'proj' : ndarray, shape (n_channels, n_channels)
                Projections used to compute the beamformer.
            'subject' : str
                The subject ID.
            'rank' : int
                The rank of the data covariance matrix used to compute the
                beamformer weights.
            'max-power-ori' : ndarray, shape (n_sources, 3) | None
                When pick_ori='max-power', this fields contains the estimated
                direction of maximum power at each source location.
            'inversion' : 'single' | 'matrix'
                Whether the spatial filters were computed for each dipole
                separately or jointly for all dipoles at each vertex using a
                matrix inversion.

    Notes
    -----
    The original reference is :footcite:`VanVeenEtAl1997`.

    To obtain the Sekihara unit-noise-gain vector beamformer, you should use
    ``weight_norm='unit-noise-gain', pick_ori='vector'`` followed by
    :meth:`vec_stc.project('pca', src) <mne.VectorSourceEstimate.project>`.

    .. versionchanged:: 0.21
       The computations were extensively reworked, and the default for
       ``weight_norm`` was set to ``'unit-noise-gain-invariant'``.

    References
    ----------
    .. footbibliography::
    """
    # check number of sensor types present in the data and ensure a noise cov
    info = _simplify_info(info)
    noise_cov, _, allow_mismatch = _check_one_ch_type(
        'lcmv', info, forward, data_cov, noise_cov)
    # XXX we need this extra picking step (can't just rely on minimum norm's
    # because there can be a mismatch. Should probably add an extra arg to
    # _prepare_beamformer_input at some point (later)
    picks = _check_info_inv(info, forward, data_cov, noise_cov)
    info = pick_info(info, picks)
    data_rank = compute_rank(data_cov, rank=rank, info=info)
    noise_rank = compute_rank(noise_cov, rank=rank, info=info)
    for key in data_rank:
        if (key not in noise_rank or data_rank[key] != noise_rank[key]) and \
                not allow_mismatch:
            raise ValueError('%s data rank (%s) did not match the noise '
                             'rank (%s)'
                             % (key, data_rank[key],
                                noise_rank.get(key, None)))
    del noise_rank
    rank = data_rank
    logger.info('Making LCMV beamformer with rank %s' % (rank,))
    del data_rank
    depth = _check_depth(depth, 'depth_sparse')
    if inversion == 'single':
        depth['combine_xyz'] = False

    is_free_ori, info, proj, vertno, G, whitener, nn, orient_std = \
        _prepare_beamformer_input(
            info, forward, label, pick_ori, noise_cov=noise_cov, rank=rank,
            pca=False, **depth)
    ch_names = list(info['ch_names'])

    data_cov = pick_channels_cov(data_cov, include=ch_names)
    Cm = data_cov._get_square()
    if 'estimator' in data_cov:
        del data_cov['estimator']
    rank_int = sum(rank.values())
    del rank

    # compute spatial filter
    n_orient = 3 if is_free_ori else 1
    W, max_power_ori = _compute_beamformer(
        G, Cm, reg, n_orient, weight_norm, pick_ori, reduce_rank, rank_int,
        inversion=inversion, nn=nn, orient_std=orient_std,
        whitener=whitener)

    # get src type to store with filters for _make_stc
    src_type = _get_src_type(forward['src'], vertno)

    # get subject to store with filters
    subject_from = _subject_from_forward(forward)

    # Is the computed beamformer a scalar or vector beamformer?
    is_free_ori = is_free_ori if pick_ori in [None, 'vector'] else False
    is_ssp = bool(info['projs'])

    filters = Beamformer(
        kind='LCMV', weights=W, data_cov=data_cov, noise_cov=noise_cov,
        whitener=whitener, weight_norm=weight_norm, pick_ori=pick_ori,
        ch_names=ch_names, proj=proj, is_ssp=is_ssp, vertices=vertno,
        is_free_ori=is_free_ori, n_sources=forward['nsource'],
        src_type=src_type, source_nn=forward['source_nn'].copy(),
        subject=subject_from, rank=rank_int, max_power_ori=max_power_ori,
        inversion=inversion)

    return filters


def _apply_lcmv(data, filters, info, tmin):
    """Apply LCMV spatial filter to data for source reconstruction."""
    if isinstance(data, np.ndarray) and data.ndim == 2:
        data = [data]
        return_single = True
    else:
        return_single = False

    W = filters['weights']

    for i, M in enumerate(data):
        if len(M) != len(filters['ch_names']):
            raise ValueError('data and picks must have the same length')

        if not return_single:
            logger.info("Processing epoch : %d" % (i + 1))

        M = _proj_whiten_data(M, info['projs'], filters)

        # project to source space using beamformer weights
        vector = False
        if filters['is_free_ori']:
            sol = np.dot(W, M)
            if filters['pick_ori'] == 'vector':
                vector = True
            else:
                logger.info('combining the current components...')
                sol = combine_xyz(sol)
        else:
            # Linear inverse: do computation here or delayed
            if (M.shape[0] < W.shape[0] and
                    filters['pick_ori'] != 'max-power'):
                sol = (W, M)
            else:
                sol = np.dot(W, M)

        tstep = 1.0 / info['sfreq']

        # compatibility with 0.16, add src_type as None if not present:
        filters, warn_text = _check_src_type(filters)

        yield _make_stc(sol, vertices=filters['vertices'], tmin=tmin,
                        tstep=tstep, subject=filters['subject'],
                        vector=vector, source_nn=filters['source_nn'],
                        src_type=filters['src_type'], warn_text=warn_text)

    logger.info('[done]')


@verbose
def apply_lcmv(evoked, filters, *, verbose=None):
    """Apply Linearly Constrained Minimum Variance (LCMV) beamformer weights.

    Apply Linearly Constrained Minimum Variance (LCMV) beamformer weights
    on evoked data.

    Parameters
    ----------
    evoked : Evoked
        Evoked data to invert.
    filters : instance of Beamformer
        LCMV spatial filter (beamformer weights).
        Filter weights returned from :func:`make_lcmv`.
    %(verbose)s

    Returns
    -------
    stc : SourceEstimate | VolSourceEstimate | VectorSourceEstimate
        Source time courses.

    See Also
    --------
    make_lcmv, apply_lcmv_raw, apply_lcmv_epochs, apply_lcmv_cov

    Notes
    -----
    .. versionadded:: 0.18
    """
    _check_reference(evoked)

    info = evoked.info
    data = evoked.data
    tmin = evoked.times[0]

    sel = _check_channels_spatial_filter(evoked.ch_names, filters)
    data = data[sel]

    stc = _apply_lcmv(data=data, filters=filters, info=info,
                      tmin=tmin)

    return next(stc)


@verbose
def apply_lcmv_epochs(epochs, filters, *, return_generator=False,
                      verbose=None):
    """Apply Linearly Constrained Minimum Variance (LCMV) beamformer weights.

    Apply Linearly Constrained Minimum Variance (LCMV) beamformer weights
    on single trial data.

    Parameters
    ----------
    epochs : Epochs
        Single trial epochs.
    filters : instance of Beamformer
        LCMV spatial filter (beamformer weights)
        Filter weights returned from :func:`make_lcmv`.
    return_generator : bool
         Return a generator object instead of a list. This allows iterating
         over the stcs without having to keep them all in memory.
    %(verbose)s

    Returns
    -------
    stc: list | generator of (SourceEstimate | VolSourceEstimate)
        The source estimates for all epochs.

    See Also
    --------
    make_lcmv, apply_lcmv_raw, apply_lcmv, apply_lcmv_cov
    """
    _check_reference(epochs)

    info = epochs.info
    tmin = epochs.times[0]

    sel = _check_channels_spatial_filter(epochs.ch_names, filters)
    data = epochs.get_data()[:, sel, :]
    stcs = _apply_lcmv(data=data, filters=filters, info=info,
                       tmin=tmin)

    if not return_generator:
        stcs = [s for s in stcs]

    return stcs


@verbose
def apply_lcmv_raw(raw, filters, start=None, stop=None, *, verbose=None):
    """Apply Linearly Constrained Minimum Variance (LCMV) beamformer weights.

    Apply Linearly Constrained Minimum Variance (LCMV) beamformer weights
    on raw data.

    Parameters
    ----------
    raw : mne.io.Raw
        Raw data to invert.
    filters : instance of Beamformer
        LCMV spatial filter (beamformer weights).
        Filter weights returned from :func:`make_lcmv`.
    start : int
        Index of first time sample (index not time is seconds).
    stop : int
        Index of first time sample not to include (index not time is seconds).
    %(verbose)s

    Returns
    -------
    stc : SourceEstimate | VolSourceEstimate
        Source time courses.

    See Also
    --------
    make_lcmv, apply_lcmv_epochs, apply_lcmv, apply_lcmv_cov
    """
    _check_reference(raw)

    info = raw.info

    sel = _check_channels_spatial_filter(raw.ch_names, filters)
    data, times = raw[sel, start:stop]
    tmin = times[0]

    stc = _apply_lcmv(data=data, filters=filters, info=info, tmin=tmin)

    return next(stc)


@verbose
def apply_lcmv_cov(data_cov, filters, verbose=None):
    """Apply Linearly Constrained  Minimum Variance (LCMV) beamformer weights.

    Apply Linearly Constrained Minimum Variance (LCMV) beamformer weights
    to a data covariance matrix to estimate source power.

    Parameters
    ----------
    data_cov : instance of Covariance
        Data covariance matrix.
    filters : instance of Beamformer
        LCMV spatial filter (beamformer weights).
        Filter weights returned from :func:`make_lcmv`.
    %(verbose)s

    Returns
    -------
    stc : SourceEstimate | VolSourceEstimate
        Source power.

    See Also
    --------
    make_lcmv, apply_lcmv, apply_lcmv_epochs, apply_lcmv_raw
    """
    sel = _check_channels_spatial_filter(data_cov.ch_names, filters)
    sel_names = [data_cov.ch_names[ii] for ii in sel]
    data_cov = pick_channels_cov(data_cov, sel_names)

    n_orient = filters['weights'].shape[0] // filters['n_sources']
    # Need to project and whiten along both dimensions
    data = _proj_whiten_data(data_cov['data'].T, data_cov['projs'], filters)
    data = _proj_whiten_data(data.T, data_cov['projs'], filters)
    del data_cov
    source_power = _compute_power(data, filters['weights'], n_orient)

    # compatibility with 0.16, add src_type as None if not present:
    filters, warn_text = _check_src_type(filters)

    return _make_stc(source_power, vertices=filters['vertices'],
                     src_type=filters['src_type'], tmin=0., tstep=1.,
                     subject=filters['subject'],
                     source_nn=filters['source_nn'], warn_text=warn_text)
