def get_fermion_mass_eigenstates_from_a2(a2, potential, tolerance=1e-6):
"""Extracts spin-1/2 fermion m^2/m0^2 from A2."""
a3 = scalar_sector.get_a3_56x56_from_a2(
a2,
sqrt2=mpmath.sqrt(mpmath.mpf(2)),
einsum=opt_einsum.contract,
conjugate=lambda a: numpy.array([z.conjugate() for z in a.reshape(-1)]
).reshape(a.shape))
na3 = a3.astype(numpy.complex128)
normalized_a3_sq = numpy.einsum('ij,ik->jk', na3, na3.conjugate()) * (
-6 / float(potential)) # Real-Symmetric.
assert numpy.allclose(normalized_a3_sq, normalized_a3_sq.T.conjugate())
eigvals, eigvecs = numpy.linalg.eigh(normalized_a3_sq)
assert numpy.allclose(eigvals, eigvals.real)
assert numpy.allclose(numpy.dot(eigvecs, eigvecs.T.conjugate()),
numpy.eye(56))
aggregated = symmetries.aggregate_eigenvectors(eigvals,
eigvecs,
tolerance=tolerance)
spaces = [numpy.stack(eigvecs, axis=-1) for _, eigvecs in aggregated]
assert all(
numpy.allclose(numpy.eye(space.shape[-1]),
numpy.einsum('ij,ik->jk', space, space.conjugate()))
for space in spaces)
return aggregated
def get_gravitino_mass_eigenstates_from_a1(a1, potential, tolerance=1e-6):
"""Extracts gravitino m^2/m0^2 from A1."""
na1 = a1.astype(numpy.complex128)
normalized_a1_sq = numpy.einsum(
'ij,ik->jk',
na1, na1.conjugate()) * (-6 / float(potential))
assert numpy.allclose(normalized_a1_sq, normalized_a1_sq.T.conjugate())
eigvals, eigvecs = numpy.linalg.eigh(normalized_a1_sq)
assert numpy.allclose(eigvals, eigvals.real)
aggregated = symmetries.aggregate_eigenvectors(eigvals,
eigvecs, tolerance=tolerance)
spaces = [numpy.stack(eigvecs, axis=-1) for _, eigvecs in aggregated]
assert all(numpy.allclose(
numpy.eye(space.shape[-1]),
numpy.einsum('ij,ik->jk', space, space.conjugate())) for space in spaces)
return aggregated
def get_scalar_mass_eigenstates_from_mass_matrix(mass_matrix, tolerance=1e-6):
"""Extracts aggregated scalar masses-squared from the mass matrix."""
eigvals, eigvecs = numpy.linalg.eigh(mass_matrix)
return symmetries.aggregate_eigenvectors(eigvals, eigvecs,
tolerance=tolerance)
