diff --git a/meegkit/utils/covariances.py b/meegkit/utils/covariances.py index 36b107f..bed601a 100644 --- a/meegkit/utils/covariances.py +++ b/meegkit/utils/covariances.py @@ -503,5 +503,15 @@ def ehess(X, U): problem = Problem(manifold=manifold, cost=cost, euclidean_gradient=egrad, euclidean_hessian=ehess) Xsol = solver.run(problem, initial_point=U0) - - return S0, Xsol.point + X = Xsol.point + + # The Grassmann manifold only fixes the *subspace* spanned by X, so X carries + # an arbitrary internal rotation. Diagonalise the k×k projected matrix to + # obtain proper Ritz pairs: after rotation, X.T @ L @ X is diagonal and each + # column of X is a genuine approximate eigenvector of L. + T = X.T @ L @ X + T = (T + T.T) / 2 # symmetrise against numerical noise + S, R = linalg.eigh(T) + X = X @ R + + return np.real(S), np.real(X) diff --git a/tests/test_cov.py b/tests/test_cov.py index ff24e49..f33fa87 100644 --- a/tests/test_cov.py +++ b/tests/test_cov.py @@ -1,4 +1,5 @@ import numpy as np +import pytest from numpy.testing import assert_almost_equal from meegkit.utils import convmtx, tscov, tsxcov @@ -88,6 +89,32 @@ def test_convmtx(): ]) ) + +def test_nonlinear_eigenspace_consistent_eigpairs(): + """Each returned eigenvalue must match the Rayleigh quotient of its column.""" + pytest.importorskip("pymanopt") + from meegkit.utils.covariances import nonlinear_eigenspace + + A = rng.standard_normal((6, 6)) + L = A.T @ A + np.eye(6) * 1e-6 + + S, X = nonlinear_eigenspace(L, 6) + # X.T @ L @ X 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