# -*- coding: utf-8 -*- """Compute resolution matrix for linear estimators.""" # Authors: olaf.hauk@mrc-cbu.cam.ac.uk # # License: BSD-3-Clause from copy import deepcopy import numpy as np from .. import pick_channels_forward, EvokedArray, SourceEstimate from ..io.constants import FIFF from ..utils import logger, verbose from ..forward.forward import convert_forward_solution from ..minimum_norm import apply_inverse from ..source_estimate import _prepare_label_extraction from ..label import Label @verbose def make_inverse_resolution_matrix(forward, inverse_operator, method='dSPM', lambda2=1. / 9., verbose=None): """Compute resolution matrix for linear inverse operator. Parameters ---------- forward : instance of Forward Forward Operator. inverse_operator : instance of InverseOperator Inverse operator. method : 'MNE' | 'dSPM' | 'sLORETA' Inverse method to use (MNE, dSPM, sLORETA). lambda2 : float The regularisation parameter. %(verbose)s Returns ------- resmat: array, shape (n_orient_inv * n_dipoles, n_orient_fwd * n_dipoles) Resolution matrix (inverse operator times forward operator). The result of applying the inverse operator to the forward operator. If source orientations are not fixed, all source components will be computed (i.e. for n_orient_inv > 1 or n_orient_fwd > 1). The columns of the resolution matrix are the point-spread functions (PSFs) and the rows are the cross-talk functions (CTFs). """ # make sure forward and inverse operator match inv = inverse_operator fwd = _convert_forward_match_inv(forward, inv) # don't include bad channels # only use good channels from inverse operator bads_inv = inv['info']['bads'] # good channels ch_names = [c for c in inv['info']['ch_names'] if (c not in bads_inv)] fwd = pick_channels_forward(fwd, ch_names, ordered=True) # get leadfield matrix from forward solution leadfield = fwd['sol']['data'] invmat = _get_matrix_from_inverse_operator(inv, fwd, method=method, lambda2=lambda2) resmat = invmat.dot(leadfield) logger.info('Dimensions of resolution matrix: %d by %d.' % resmat.shape) return resmat @verbose def _get_psf_ctf(resmat, src, idx, func, mode, n_comp, norm, return_pca_vars, verbose=None): """Get point-spread (PSFs) or cross-talk (CTFs) functions. Parameters ---------- resmat : array, shape (n_dipoles, n_dipoles) Forward Operator. src : Source Space Source space used to compute resolution matrix. %(idx_pctf)s func : str ('psf' | 'ctf') Whether to produce PSFs or CTFs. Defaults to psf. %(mode_pctf)s %(n_comp_pctf_n)s %(norm_pctf)s %(return_pca_vars_pctf)s %(verbose)s Returns ------- %(stcs_pctf)s %(pca_vars_pctf)s """ # check for consistencies in input parameters _check_get_psf_ctf_params(mode, n_comp, return_pca_vars) # backward compatibility if norm is True: norm = 'max' # get relevant vertices in source space verts_all = _vertices_for_get_psf_ctf(idx, src) # vertices used in forward and inverse operator vertno_lh = src[0]['vertno'] vertno_rh = src[1]['vertno'] vertno = [vertno_lh, vertno_rh] # the following will operate on columns of funcs if func == 'ctf': resmat = resmat.T # Functions and variances per label stcs = [] pca_vars = [] for verts in verts_all: # get relevant PSFs or CTFs for specified vertices funcs = resmat[:, verts] # normalise PSFs/CTFs if requested if norm is not None: funcs = _normalise_psf_ctf(funcs, norm) # summarise PSFs/CTFs across vertices if requested pca_var = None # variances computed only if return_pca_vars=True if mode is not None: funcs, pca_var = _summarise_psf_ctf(funcs, mode, n_comp, return_pca_vars) # convert to source estimate stc = SourceEstimate(funcs, vertno, tmin=0., tstep=1.) stcs.append(stc) pca_vars.append(pca_var) # if just one list or label specified, simplify output if len(stcs) == 1: stcs = stc if len(pca_vars) == 1: pca_vars = pca_var if pca_var is not None: return stcs, pca_vars else: return stcs def _check_get_psf_ctf_params(mode, n_comp, return_pca_vars): """Check input parameters of _get_psf_ctf() for consistency.""" if mode in [None, 'sum', 'mean'] and n_comp > 1: msg = 'n_comp must be 1 for mode=%s.' % mode raise ValueError(msg) if mode != 'pca' and return_pca_vars: msg = 'SVD variances can only be returned if mode=''pca''.' raise ValueError(msg) def _vertices_for_get_psf_ctf(idx, src): """Get vertices in source space for PSFs/CTFs in _get_psf_ctf().""" # idx must be list # if label(s) specified get the indices, otherwise just carry on if type(idx[0]) is Label: # specify without source time courses, gets indices per label verts_labs, _ = _prepare_label_extraction( stc=None, labels=idx, src=src, mode='mean', allow_empty=False, use_sparse=False) # verts_labs can be list of lists # concatenate indices per label across hemispheres # one list item per label verts = [] for v in verts_labs: # if two hemispheres present if type(v) is list: # indices for both hemispheres in one list this_verts = np.concatenate((v[0], v[1])) else: this_verts = np.array(v) verts.append(this_verts) # check if list of list or just list else: if type(idx[0]) is list: # if list of list of integers verts = idx else: # if list of integers verts = [idx] return verts def _normalise_psf_ctf(funcs, norm): """Normalise PSFs/CTFs in _get_psf_ctf().""" # normalise PSFs/CTFs if specified if norm == 'max': maxval = max(-funcs.min(), funcs.max()) funcs = funcs / maxval elif norm == 'norm': # normalise to maximum norm across columns norms = np.linalg.norm(funcs, axis=0) funcs = funcs / norms.max() return funcs def _summarise_psf_ctf(funcs, mode, n_comp, return_pca_vars): """Summarise PSFs/CTFs across vertices.""" from scipy import linalg s_var = None # only computed for return_pca_vars=True if mode == 'maxval': # pick PSF/CTF with maximum absolute value absvals = np.maximum(-np.min(funcs, axis=0), np.max(funcs, axis=0)) if n_comp > 1: # only keep requested number of sorted PSFs/CTFs sortidx = np.argsort(absvals) maxidx = sortidx[-n_comp:] else: # faster if only one required maxidx = absvals.argmax() funcs = funcs[:, maxidx] elif mode == 'maxnorm': # pick PSF/CTF with maximum norm norms = np.linalg.norm(funcs, axis=0) if n_comp > 1: # only keep requested number of sorted PSFs/CTFs sortidx = np.argsort(norms) maxidx = sortidx[-n_comp:] else: # faster if only one required maxidx = norms.argmax() funcs = funcs[:, maxidx] elif mode == 'sum': # sum across PSFs/CTFs funcs = np.sum(funcs, axis=1) elif mode == 'mean': # mean of PSFs/CTFs funcs = np.mean(funcs, axis=1) elif mode == 'pca': # SVD across PSFs/CTFs # compute SVD of PSFs/CTFs across vertices u, s, _ = linalg.svd(funcs, full_matrices=False) funcs = u[:, :n_comp] # if explained variances for SVD components requested if return_pca_vars: # explained variance of individual SVD components s2 = s * s s_var = 100 * s2[:n_comp] / s2.sum() return funcs, s_var @verbose def get_point_spread(resmat, src, idx, mode=None, n_comp=1, norm=False, return_pca_vars=False, verbose=None): """Get point-spread (PSFs) functions for vertices. Parameters ---------- resmat : array, shape (n_dipoles, n_dipoles) Forward Operator. src : instance of SourceSpaces Source space used to compute resolution matrix. %(idx_pctf)s %(mode_pctf)s %(n_comp_pctf_n)s %(norm_pctf)s %(return_pca_vars_pctf)s %(verbose)s Returns ------- %(stcs_pctf)s %(pca_vars_pctf)s """ return _get_psf_ctf(resmat, src, idx, func='psf', mode=mode, n_comp=n_comp, norm=norm, return_pca_vars=return_pca_vars) @verbose def get_cross_talk(resmat, src, idx, mode=None, n_comp=1, norm=False, return_pca_vars=False, verbose=None): """Get cross-talk (CTFs) function for vertices. Parameters ---------- resmat : array, shape (n_dipoles, n_dipoles) Forward Operator. src : instance of SourceSpaces Source space used to compute resolution matrix. %(idx_pctf)s %(mode_pctf)s %(n_comp_pctf_n)s %(norm_pctf)s %(return_pca_vars_pctf)s %(verbose)s Returns ------- %(stcs_pctf)s %(pca_vars_pctf)s """ return _get_psf_ctf(resmat, src, idx, func='ctf', mode=mode, n_comp=n_comp, norm=norm, return_pca_vars=return_pca_vars) def _convert_forward_match_inv(fwd, inv): """Ensure forward and inverse operators match. Inverse operator and forward operator must have same surface orientations, but can have different source orientation constraints. """ # did inverse operator use fixed orientation? is_fixed_inv = _check_fixed_ori(inv) # did forward operator use fixed orientation? is_fixed_fwd = _check_fixed_ori(fwd) # if inv or fwd fixed: do nothing # if inv loose: surf_ori must be True # if inv free: surf_ori must be False if not is_fixed_inv and not is_fixed_fwd: is_loose_inv = not (inv['orient_prior']['data'] == 1.).all() if is_loose_inv: if not fwd['surf_ori']: fwd = convert_forward_solution(fwd, surf_ori=True) elif fwd['surf_ori']: # free orientation, change fwd fwd = convert_forward_solution(fwd, surf_ori=False) return fwd def _prepare_info(inverse_operator): """Get a usable dict.""" # in order to convert sub-leadfield matrix to evoked data type (pretending # it's an epoch, see in loop below), uses 'info' from inverse solution # because this has all the correct projector information info = deepcopy(inverse_operator['info']) with info._unlock(): info['sfreq'] = 1000. # necessary info['projs'] = inverse_operator['projs'] return info def _get_matrix_from_inverse_operator(inverse_operator, forward, method='dSPM', lambda2=1. / 9.): """Get inverse matrix from an inverse operator. Currently works only for fixed/loose orientation constraints For loose orientation constraint, the CTFs are computed for the normal component (pick_ori='normal'). Parameters ---------- inverse_operator : instance of InverseOperator The inverse operator. forward : instance of Forward The forward operator. method : 'MNE' | 'dSPM' | 'sLORETA' Inverse methods (for apply_inverse). lambda2 : float The regularization parameter (for apply_inverse). Returns ------- invmat : array, shape (n_dipoles, n_channels) Inverse matrix associated with inverse operator and specified parameters. """ # make sure forward and inverse operators match with respect to # surface orientation _convert_forward_match_inv(forward, inverse_operator) info_inv = _prepare_info(inverse_operator) # only use channels that are good for inverse operator and forward sol ch_names_inv = info_inv['ch_names'] n_chs_inv = len(ch_names_inv) bads_inv = inverse_operator['info']['bads'] # indices of bad channels ch_idx_bads = [ch_names_inv.index(ch) for ch in bads_inv] # create identity matrix as input for inverse operator # set elements to zero for non-selected channels id_mat = np.eye(n_chs_inv) # convert identity matrix to evoked data type (pretending it's an epoch) ev_id = EvokedArray(id_mat, info=info_inv, tmin=0.) # apply inverse operator to identity matrix in order to get inverse matrix # free orientation constraint not possible because apply_inverse would # combine components # check if inverse operator uses fixed source orientations is_fixed_inv = _check_fixed_ori(inverse_operator) # choose pick_ori according to inverse operator if is_fixed_inv: pick_ori = None else: pick_ori = 'vector' # columns for bad channels will be zero invmat_op = apply_inverse(ev_id, inverse_operator, lambda2=lambda2, method=method, pick_ori=pick_ori) # turn source estimate into numpy array invmat = invmat_op.data # remove columns for bad channels # take into account it may be 3D array invmat = np.delete(invmat, ch_idx_bads, axis=invmat.ndim - 1) # if 3D array, i.e. multiple values per location (fixed and loose), # reshape into 2D array if invmat.ndim == 3: v0o1 = invmat[0, 1].copy() v3o2 = invmat[3, 2].copy() shape = invmat.shape invmat = invmat.reshape(shape[0] * shape[1], shape[2]) # make sure that reshaping worked assert np.array_equal(v0o1, invmat[1]) assert np.array_equal(v3o2, invmat[11]) logger.info("Dimension of Inverse Matrix: %s" % str(invmat.shape)) return invmat def _check_fixed_ori(inst): """Check if inverse or forward was computed for fixed orientations.""" is_fixed = inst['source_ori'] != FIFF.FIFFV_MNE_FREE_ORI return is_fixed