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resolution_matrix.py
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resolution_matrix.py
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# -*- 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 mne.minimum_norm.inverse import InverseOperator
from .. import pick_channels_forward, EvokedArray
from ..io.constants import FIFF
from ..utils import logger, verbose, _validate_type
from ..forward.forward import convert_forward_solution, Forward
from ..minimum_norm import apply_inverse
from ..source_estimate import (_prepare_label_extraction, _make_stc,
_get_src_type)
from ..source_space import SourceSpaces, _get_vertno
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, vector=False, verbose=None):
"""Get point-spread (PSFs) or cross-talk (CTFs) functions."""
# 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
src_orig = src
_validate_type(src_orig, (InverseOperator, Forward, SourceSpaces), 'src')
if not isinstance(src, SourceSpaces):
src = src['src']
verts_all = _vertices_for_get_psf_ctf(idx, src)
vertno = _get_vertno(src)
n_verts = sum(len(v) for v in vertno)
src_type = _get_src_type(src, vertno)
subject = src._subject
if vector and src_type == 'surface':
_validate_type(src_orig, (Forward, InverseOperator), 'src',
extra='when creating a vector surface source estimate')
nn = src_orig['source_nn']
else:
nn = np.repeat(np.eye(3, 3)[np.newaxis], n_verts, 0)
n_r, n_c = resmat.shape
if (((n_verts != n_r) and (n_r / 3 != n_verts))
or ((n_verts != n_c) and (n_c / 3 != n_verts))):
msg = ('Number of vertices (%d) and corresponding dimension of'
'resolution matrix (%d, %d) do not match' %
(n_verts, n_r, n_c))
raise ValueError(msg)
# the following will operate on columns of funcs
if func == 'ctf':
resmat = resmat.T
n_r, n_c = n_c, n_r
# Functions and variances per label
stcs = []
pca_vars = []
# if 3 orientations per vertex, redefine indices to columns of resolution
# matrix
if n_verts != n_c:
# change indices to three indices per vertex
for [i, verts] in enumerate(verts_all):
verts_vec = np.empty(3 * len(verts), dtype=int)
for [j, v] in enumerate(verts):
verts_vec[3 * j: 3 * j + 3] = \
3 * verts[j] + np.array([0, 1, 2])
verts_all[i] = verts_vec # use these as indices
for verts in verts_all:
# get relevant PSFs or CTFs for specified vertices
if type(verts) is int:
verts = [verts] # to keep array dimensions
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, nn)
if not vector: # if one value per vertex requested
if n_verts != n_r: # if 3 orientations per vertex, combine
funcs_int = np.empty([int(n_r / 3), funcs.shape[1]])
for i in np.arange(0, n_verts):
funcs_vert = funcs[3 * i:3 * i + 3, :]
funcs_int[i, :] = np.sqrt((funcs_vert ** 2).sum(axis=0))
funcs = funcs_int
stc = _make_stc(
funcs, vertno, src_type, tmin=0., tstep=1., subject=subject,
vector=vector, source_nn=nn)
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 isinstance(idx[0], 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, nn):
"""Summarise PSFs/CTFs across vertices."""
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, keepdims=True)
elif mode == 'mean': # mean of PSFs/CTFs
funcs = np.mean(funcs, axis=1, keepdims=True)
elif mode == 'pca': # SVD across PSFs/CTFs
# compute SVD of PSFs/CTFs across vertices
u, s, _ = np.linalg.svd(funcs, full_matrices=False, compute_uv=True)
if n_comp > 1:
funcs = u[:, :n_comp]
else:
funcs = u[:, 0, np.newaxis]
# 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, vector=False, verbose=None):
"""Get point-spread (PSFs) functions for vertices.
Parameters
----------
resmat : array, shape (n_dipoles, n_dipoles)
Forward Operator.
src : instance of SourceSpaces | instance of InverseOperator | instance of Forward
Source space used to compute resolution matrix.
Must be an InverseOperator if ``vector=True`` and a surface
source space is used.
%(idx_pctf)s
%(mode_pctf)s
%(n_comp_pctf_n)s
%(norm_pctf)s
%(return_pca_vars_pctf)s
%(vector_pctf)s
%(verbose)s
Returns
-------
%(stcs_pctf)s
%(pca_vars_pctf)s
""" # noqa: E501
return _get_psf_ctf(resmat, src, idx, func='psf', mode=mode, n_comp=n_comp,
norm=norm, return_pca_vars=return_pca_vars,
vector=vector)
@verbose
def get_cross_talk(resmat, src, idx, mode=None, *, n_comp=1, norm=False,
return_pca_vars=False, vector=False, verbose=None):
"""Get cross-talk (CTFs) function for vertices.
Parameters
----------
resmat : array, shape (n_dipoles, n_dipoles)
Forward Operator.
src : instance of SourceSpaces | instance of InverseOperator | instance of Forward
Source space used to compute resolution matrix.
Must be an InverseOperator if ``vector=True`` and a surface
source space is used.
%(idx_pctf)s
%(mode_pctf)s
%(n_comp_pctf_n)s
%(norm_pctf)s
%(return_pca_vars_pctf)s
%(vector_pctf)s
%(verbose)s
Returns
-------
%(stcs_pctf)s
%(pca_vars_pctf)s
""" # noqa: E501
return _get_psf_ctf(resmat, src, idx, func='ctf', mode=mode, n_comp=n_comp,
norm=norm, return_pca_vars=return_pca_vars,
vector=vector)
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.
"""
_validate_type(fwd, Forward, 'fwd')
_validate_type(inv, InverseOperator, 'inverse_operator')
# 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:
inv_surf_ori = inv._is_surf_ori
if inv_surf_ori != fwd['surf_ori']:
fwd = convert_forward_solution(
fwd, surf_ori=inv_surf_ori, force_fixed=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']
info['custom_ref_applied'] = False
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