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import numpy as np
from induced_exchange import (
ExchangeBond,
InducedMomentResponse,
MagneticCrystal,
MagneticSite,
SublatticeClassification,
instantaneous_induced_moments,
reciprocal_lattice,
regular_q_mesh,
)
from induced_exchange.downfolding import InducedExchangeDownfolding, inverse_fourier_dressed_jij
from induced_exchange.io_uppasd import load_uppasd
def site(index: int, moment: float, position=(0.0, 0.0, 0.0)) -> MagneticSite:
return MagneticSite(index, index, position, moment, (0.0, 0.0, 1.0))
def crystal(sites, bonds) -> MagneticCrystal:
return MagneticCrystal(np.eye(3), list(sites), list(bonds))
def test_one_robust_one_induced_infers_x_and_evaluates_induced_moment():
model = crystal([site(1, 3.0), site(2, 1.5)], [ExchangeBond(2, 1, (0, 0, 0), 2.0)])
response = InducedMomentResponse(model, [1], [2], mode="j_weighted")
inference = response.infer_x()
assert np.isclose(inference.x[2], 0.5)
assert np.isclose(inference.source_fields[2], 2.0)
# The response API uses dimensionless robust orientation amplitudes and
# returns normalized induced polarization p=m/|m0|.
assert np.allclose(response.response_real_space([4.0]).induced_moments, [4.0])
def test_historical_equal_neighbours_parallel_and_antiparallel_cancel():
model = crystal([site(1, 2.0), site(2, 2.0), site(3, 2.0)], [])
response = InducedMomentResponse(
model,
{"robust": [1, 2]},
{"induced": [3]},
mode="historical",
x={"induced": 1.0},
neighbourhood=[1, 2],
)
assert np.allclose(response.response_real_space([1.0, 1.0]).induced_moments, [2.0])
assert np.allclose(response.response_real_space([1.0, -1.0]).induced_moments, [0.0])
assert response.classification.induced_sublattices == {"induced": (3,)}
def test_unequal_j_weights_are_used_in_reference_inference_and_response():
model = crystal(
[site(1, 1.0), site(2, 1.0), site(3, 3.0)],
[ExchangeBond(3, 1, (0, 0, 0), 2.0), ExchangeBond(3, 2, (0, 0, 0), 1.0)],
)
response = InducedMomentResponse(model, [1, 2], [3])
assert np.isclose(response.infer_x().x[3], 1.0 / 3.0)
assert np.allclose(response.response_real_space([1.0, 2.0]).induced_moments, [4.0 / 3.0])
def test_finite_induced_induced_coupling_matches_direct_matrix_solution():
model = crystal(
[site(1, 1.0), site(2, 0.0), site(3, 0.0)],
[
ExchangeBond(2, 1, (0, 0, 0), 2.0),
ExchangeBond(3, 1, (0, 0, 0), 1.0),
ExchangeBond(2, 3, (0, 0, 0), 0.5),
ExchangeBond(3, 2, (0, 0, 0), 0.25),
],
)
response = InducedMomentResponse(model, [1], [2, 3], x={2: 0.5, 3: 0.25})
expected = np.linalg.solve(
np.eye(2) - np.diag([0.5, 0.25]) @ np.array([[0.0, 0.5], [0.25, 0.0]]),
np.diag([0.5, 0.25]) @ np.array([2.0, 1.0]),
)
result = response.response_real_space([1.0])
assert np.allclose(result.induced_moments, expected)
assert np.all(result.condition_numbers < 10.0)
def test_q_space_solution_matches_real_space_at_gamma_and_exposes_diagnostics():
model = crystal(
[site(1, 1.0), site(2, 1.0), site(3, 1.0)],
[ExchangeBond(3, 1, (0, 0, 0), 2.0), ExchangeBond(3, 2, (0, 0, 0), 1.0)],
)
response = InducedMomentResponse(model, [1, 2], [3], x={3: 0.5})
real = response.response_real_space([2.0, 1.0])
reciprocal = response.response_q([[0.0, 0.0, 0.0]], [[2.0, 1.0]])
assert np.allclose(reciprocal.induced_moments[0], real.induced_moments)
assert np.allclose(reciprocal.m_ind_q_over_m_ind_0[0], [1.0])
assert np.isclose(reciprocal.condition_numbers[0], 1.0)
def test_fractional_q_response_matches_explicitly_converted_cartesian_q():
model = crystal(
[site(1, 1.0), site(2, 1.0)],
[
ExchangeBond(2, 1, (1.0, 0.0, 0.0), 2.0),
ExchangeBond(2, 1, (-1.0, 0.0, 0.0), 2.0),
ExchangeBond(1, 2, (1.0, 0.0, 0.0), 2.0),
ExchangeBond(1, 2, (-1.0, 0.0, 0.0), 2.0),
],
)
response = InducedMomentResponse(model, [1], [2], x=0.25)
q_fractional = np.asarray([[0.25, 0.0, 0.0], [0.125, 0.25, 0.0]])
q_cartesian = reciprocal_lattice(model.cell).fractional_to_cartesian(q_fractional)
fractional = response.response_q(q_fractional, [[1.0], [0.5]], coordinates="fractional")
cartesian = response.response_q(q_cartesian, [[1.0], [0.5]], coordinates="cartesian")
assert np.allclose(fractional.q_cartesian, q_cartesian)
assert np.allclose(fractional.induced_moments, cartesian.induced_moments)
assert np.allclose(fractional.source_fields, cartesian.source_fields)
def test_pair_complete_j_weighted_downfolding_has_adjoint_cross_blocks_and_hermitian_dressing():
model = crystal(
[site(1, 2.0), site(2, 0.8)],
[
ExchangeBond(1, 1, (1.0, 0.0, 0.0), 8.0),
ExchangeBond(1, 1, (-1.0, 0.0, 0.0), 8.0),
ExchangeBond(2, 2, (1.0, 0.0, 0.0), 0.8),
ExchangeBond(2, 2, (-1.0, 0.0, 0.0), 0.8),
ExchangeBond(2, 1, (0.5, 0.0, 0.0), 1.2),
ExchangeBond(2, 1, (-0.5, 0.0, 0.0), 1.2),
ExchangeBond(1, 2, (0.5, 0.0, 0.0), 1.2),
ExchangeBond(1, 2, (-0.5, 0.0, 0.0), 1.2),
],
)
q = [[0.25, 0.0, 0.0]]
result = InducedExchangeDownfolding(
InducedMomentResponse(model, [1], [2], mode="j_weighted", x=0.5)
).evaluate(q)
assert np.allclose(result.k_rm, np.swapaxes(result.k_mr.conj(), 1, 2))
assert result.dressed_hermiticity.is_hermitian
assert not any("K_Mm differs" in warning for warning in result.warnings)
def test_induced_toy_nonzero_q_has_no_false_block_adjoint_warning():
loaded = load_uppasd("examples/induced_toy/inpsd.dat", energy_unit="meV")
response = InducedMomentResponse(loaded.model, [1], [2], mode="j_weighted", x=0.5)
result = InducedExchangeDownfolding(response).evaluate([[0.25, 0.0, 0.0]])
assert result.kernel_hermiticity.is_hermitian
assert result.dressed_hermiticity.is_hermitian
assert not any("K_Mm differs from K_mM" in warning for warning in result.warnings)
def test_convenience_wrapper_is_algebraic_and_does_not_propagate():
model = crystal([site(1, 1.0), site(2, 2.0)], [ExchangeBond(2, 1, (0, 0, 0), 3.0)])
values = instantaneous_induced_moments(model, [2.0], [1], [2], x={2: 0.5})
assert np.allclose(values, [3.0])
def test_classification_is_explicit_and_never_based_on_moment_size():
classification = SublatticeClassification.from_inputs({"Fe": [1]}, {"Pt": [2]})
assert classification.robust_sites == (1,)
assert classification.induced_sites == (2,)
def test_near_singular_induced_response_is_flagged_without_regularization():
model = crystal(
[site(1, 1.0), site(2, 1.0)],
[ExchangeBond(2, 1, (0, 0, 0), 1.0), ExchangeBond(2, 2, (0, 0, 0), 2.0)],
)
response = InducedMomentResponse(model, [1], [2], x={2: 0.5})
result = response.response_real_space([1.0])
assert result.singular[0]
assert any("not regularized" in warning for warning in result.warnings)
assert np.isnan(result.induced_moments).all()
def test_variational_one_induced_site_matches_analytic_dressed_exchange_and_energy():
model = crystal(
[site(1, 1.0), site(2, 1.0)],
[
ExchangeBond(1, 1, (0, 0, 0), 1.5),
ExchangeBond(2, 1, (0, 0, 0), 2.0),
ExchangeBond(1, 2, (0, 0, 0), 2.0),
],
)
response = InducedMomentResponse(model, [1], [2], x={2: 0.5})
downfolding = InducedExchangeDownfolding(response)
result = downfolding.evaluate([[0.0, 0.0, 0.0]])
# J_eff = J_MM + K_Mm X K_mM = 1.5 + 2 * 0.5 * 2.
assert np.allclose(result.raw_robust[0], [[1.5]])
assert np.allclose(result.delta_induced[0], [[2.0]])
assert np.allclose(result.dressed[0], [[3.5]])
check = downfolding.energy_equivalence(result, [1.7])
assert check.equivalent
assert np.allclose(check.stationary_induced, [[[1.7]]])
def test_downfolding_includes_induced_induced_propagation():
model = crystal(
[site(1, 1.0), site(2, 1.0), site(3, 1.0)],
[
ExchangeBond(2, 1, (0, 0, 0), 2.0),
ExchangeBond(1, 2, (0, 0, 0), 2.0),
ExchangeBond(3, 1, (0, 0, 0), 1.0),
ExchangeBond(1, 3, (0, 0, 0), 1.0),
ExchangeBond(2, 3, (0, 0, 0), 0.5),
ExchangeBond(3, 2, (0, 0, 0), 0.5),
],
)
response = InducedMomentResponse(model, [1], [2, 3], x={2: 0.5, 3: 0.25})
result = InducedExchangeDownfolding(response).evaluate([[0.0, 0.0, 0.0]])
expected_operator = np.linalg.solve(
np.eye(2) - np.diag([0.5, 0.25]) @ np.array([[0.0, 0.5], [0.5, 0.0]]),
np.diag([0.5, 0.25]),
)
expected_delta = np.array([[2.0, 1.0]]) @ expected_operator @ np.array([[2.0], [1.0]])
assert np.allclose(result.response_operator[0], expected_operator)
assert np.allclose(result.delta_induced[0], expected_delta)
def test_downfolding_marks_singular_induced_block_without_regularization():
model = crystal(
[site(1, 1.0), site(2, 1.0)],
[
ExchangeBond(2, 2, (0, 0, 0), 2.0),
ExchangeBond(2, 1, (0, 0, 0), 1.0),
ExchangeBond(1, 2, (0, 0, 0), 1.0),
],
)
result = InducedExchangeDownfolding(
InducedMomentResponse(model, [1], [2], x=0.5)
).evaluate([[0.0, 0.0, 0.0]])
assert result.singular[0]
assert np.isnan(result.dressed[0]).all()
assert any("not regularized" in warning for warning in result.warnings)
def test_downfolding_has_no_dressing_without_induced_sites_or_when_x_is_zero():
model = crystal(
[site(1, 1.0), site(2, 1.0)],
[ExchangeBond(1, 1, (0, 0, 0), 2.0), ExchangeBond(2, 1, (0, 0, 0), 4.0)],
)
no_induced = InducedExchangeDownfolding(
InducedMomentResponse(model, [1], [], x=0.0)
).evaluate([[0.0, 0.0, 0.0]])
zero_x = InducedExchangeDownfolding(
InducedMomentResponse(model, [1], [2], x=0.0)
).evaluate([[0.0, 0.0, 0.0]])
assert np.allclose(no_induced.dressed, no_induced.raw_robust)
assert np.allclose(zero_x.dressed, zero_x.raw_robust)
assert np.allclose(zero_x.delta_induced, 0.0)
def test_ordering_diagnostic_and_inverse_transform_are_explicit_about_sampling():
model = crystal(
[site(1, 1.0), site(2, 1.0)],
[
ExchangeBond(1, 1, (1, 0, 0), 1.0),
ExchangeBond(1, 1, (-1, 0, 0), 1.0),
ExchangeBond(2, 1, (0, 0, 0), 1.0),
ExchangeBond(1, 2, (0, 0, 0), 1.0),
],
)
response = InducedMomentResponse(model, [1], [2], x=0.0)
downfolding = InducedExchangeDownfolding(response)
result = downfolding.evaluate([[0.0, 0.0, 0.0], [0.5, 0.0, 0.0]])
comparison = downfolding.ordering_comparison(result)
assert comparison.changed is False
assert comparison.diagnostic.startswith("No —")
real_space = inverse_fourier_dressed_jij(result, displacements=[[1.0, 0.0, 0.0]])
assert real_space.values.shape == (1, 1, 1)
assert real_space.raw_values is not None
assert real_space.delta_values is not None
assert real_space.shell_diagnostics[0]["dressed_max_abs"] == 2.0
assert any("finite-q reconstructions" in warning for warning in real_space.warnings)
def test_inverse_default_support_is_robust_block_and_flags_small_mesh_aliasing():
model = crystal(
[site(1, 1.0), site(2, 1.0, position=(0.5, 0.0, 0.0))],
[
ExchangeBond(1, 1, (2, 0, 0), 0.1),
ExchangeBond(1, 1, (-2, 0, 0), 0.1),
ExchangeBond(1, 2, (0.5, 0, 0), 3.0),
ExchangeBond(2, 1, (0.5, 0, 0), 3.0),
],
)
response = InducedMomentResponse(model, [1], [2], x=0.0)
result = InducedExchangeDownfolding(response).evaluate(
regular_q_mesh(model, (4, 4, 4), coordinates="fractional"),
coordinates="fractional",
)
assert set(result.source_displacements) == {(2.0, 0.0, 0.0), (-2.0, 0.0, 0.0)}
real_space = inverse_fourier_dressed_jij(result)
assert any("q mesh is too small" in warning for warning in real_space.warnings)
assert not any(np.allclose(displacement, (0.5, 0.0, 0.0)) for displacement in real_space.displacements)
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