def test_eigenvectors(self):
evec = self.tica_obj.eigenvectors
_, evec_ref = eig_corr(self.cov_ref, self.cov_tau_ref, sign_maxelement=True)
assert (np.all(evec.shape == (2, 2)))
np.testing.assert_allclose(evec, evec_ref)
evec_nr = self.tica_obj_nr.eigenvectors
_, evec_ref = eig_corr(self.cov_ref_nr, self.cov_tau_ref_nr, sign_maxelement=True)
assert (np.all(evec_nr.shape == (2, 2)))
np.testing.assert_allclose(evec_ref, evec_nr)
def test_eigenvalues(self):
eval = self.tica_obj.eigenvalues
eval_ref, _ = eig_corr(self.cov_ref, self.cov_tau_ref)
assert len(eval) == 2
assert np.max(np.abs(eval) < 1)
np.testing.assert_allclose(eval_ref, eval)
eval_nr = self.tica_obj_nr.eigenvalues
eval_ref, _ = eig_corr(self.cov_ref_nr, self.cov_tau_ref_nr)
assert len(eval_nr) == 2
assert np.max(np.abs(eval_nr) < 1)
np.testing.assert_allclose(eval_ref, eval_nr)
def _diagonalize(self):
# diagonalize with low rank approximation
self._logger.debug("diagonalize Cov and Cov_tau.")
eigenvalues, eigenvectors = eig_corr(self._covar.cov,
self._covar.cov_tau,
self.epsilon,
sign_maxelement=True)
if self.kinetic_map and self.commute_map:
raise ValueError(
'Trying to use both kinetic_map and commute_map. Use either or.'
)
if self.kinetic_map: # scale by eigenvalues
eigenvectors *= eigenvalues[None, :]
if self.commute_map: # scale by (regularized) timescales
timescales = 1 - self.lag / np.log(np.abs(eigenvalues))
# dampen timescales smaller than the lag time, as in section 2.5 of ref. [5]
regularized_timescales = 0.5 * timescales * np.maximum(
np.tanh(np.pi * ((timescales - self.lag) / self.lag) + 1), 0)
eigenvectors *= np.sqrt(regularized_timescales / 2)
self._logger.debug("finished diagonalisation.")
# compute cumulative variance
cumvar = np.cumsum(np.abs(eigenvalues)**2)
cumvar /= cumvar[-1]
self._model.update_model_params(cumvar=cumvar,
eigenvalues=eigenvalues,
eigenvectors=eigenvectors)
self._estimated = True
def _diagonalize(self):
# diagonalize with low rank approximation
self.logger.debug("Diagonalize Cov and Cov_tau.")
Wktau = self._model.cov_tau[self._model.column_indices, :]
try:
eigenvalues, eigenvectors = eig_corr(self._oasis.Wk, Wktau, self.epsilon, sign_maxelement=True)
except ZeroRankError:
raise ZeroRankError('All input features are constant in all time steps. '
'No dimension would be left after dimension reduction.')
self.logger.debug("Finished diagonalization.")
# compute cumulative variance
cumvar = np.cumsum(np.abs(eigenvalues) ** 2)
cumvar /= cumvar[-1]
self._model.update_model_params(cumvar=cumvar,
eigenvalues=eigenvalues,
eigenvectors=eigenvectors)
self._estimated = True