Line data Source code
1 : # SPDX-FileCopyrightText: 2025 PairInteraction Developers
2 : # SPDX-License-Identifier: LGPL-3.0-or-later
3 :
4 1 : from __future__ import annotations
5 :
6 1 : import logging
7 1 : from typing import TYPE_CHECKING
8 :
9 1 : import numpy as np
10 1 : import pytest
11 1 : from pairinteraction.perturbative.perturbation_theory import calculate_perturbative_hamiltonian
12 1 : from scipy import sparse
13 :
14 1 : from .utils import no_log_propagation
15 :
16 : if TYPE_CHECKING:
17 : from pairinteraction import SystemPair
18 : from scipy.sparse import csr_matrix
19 :
20 : from .utils import PairinteractionModule
21 :
22 :
23 1 : def _check_sparse_matrices_equal(matrix_a: csr_matrix, matrix_b: csr_matrix) -> bool:
24 : """Check for equality of sparse matrices efficiently.
25 :
26 : This functions compares two sparse matrices in compressed sparse row format on their equality.
27 :
28 : Args:
29 : matrix_a: A sparse matrix in csr format.
30 : matrix_b: A sparse matrix in csr format.
31 :
32 : Returns:
33 : bool: True if matrices are equal, False if not.
34 :
35 : """
36 1 : matrix_a.sort_indices()
37 1 : matrix_b.sort_indices()
38 1 : if not (
39 : matrix_a.format == "csr"
40 : and matrix_b.format == "csr"
41 : and len(matrix_a.indices) == len(matrix_b.indices)
42 : and len(matrix_a.indptr) == len(matrix_b.indptr)
43 : and len(matrix_a.data) == len(matrix_b.data)
44 : ):
45 0 : return False
46 :
47 1 : return bool(
48 : np.all(matrix_a.indices == matrix_b.indices)
49 : and np.all(matrix_a.indptr == matrix_b.indptr)
50 : and np.allclose(matrix_a.data, matrix_b.data, rtol=0, atol=1e-14)
51 : )
52 :
53 :
54 1 : @pytest.fixture
55 1 : def system_pair_sample(pi_module: PairinteractionModule) -> SystemPair:
56 1 : basis = pi_module.BasisAtom(
57 : species="Rb",
58 : n=(59, 63),
59 : l=(0, 1),
60 : m=(-1.5, 1.5),
61 : )
62 1 : system = pi_module.SystemAtom(basis=basis)
63 1 : system.set_diamagnetism_enabled(False)
64 1 : system.set_magnetic_field([0, 0, 1e-3], "gauss")
65 1 : pi_module.diagonalize([system], diagonalizer="eigen")
66 1 : basis_pair = pi_module.BasisPair([system, system], symmetrize=False)
67 1 : system_pair = pi_module.SystemPair(basis_pair)
68 1 : theta = 0
69 1 : r = 12
70 1 : system_pair.set_distance_vector(r * np.array([np.sin(theta), 0, np.cos(theta)]), "micrometer")
71 1 : system_pair.set_interaction_order(3)
72 1 : return system_pair
73 :
74 :
75 1 : def test_perturbative_calculation1(caplog: pytest.LogCaptureFixture) -> None:
76 : """Test of mathematic functionality."""
77 1 : hamiltonian = sparse.csr_matrix(
78 : [[0, 1, 1, 0, 2], [1, 1, 0, 1, 3], [1, 0, 10, 1, 0], [0, 1, 1, 11, 1], [2, 3, 0, 1, 12]]
79 : )
80 1 : model_space_indices = [0, 1]
81 :
82 : # Order 0
83 1 : h_eff_dict, eig_perturb = calculate_perturbative_hamiltonian(hamiltonian, model_space_indices, perturbation_order=0)
84 1 : h_eff = sum(h for h in h_eff_dict.values())
85 1 : assert np.any(h_eff == np.array([[0, 0], [0, 1]]))
86 1 : assert _check_sparse_matrices_equal(eig_perturb, sparse.csr_matrix(sparse.eye(2, 5, k=0)))
87 :
88 : # Order 1
89 1 : h_eff_dict, eig_perturb = calculate_perturbative_hamiltonian(hamiltonian, model_space_indices, perturbation_order=1)
90 1 : h_eff = sum(h for h in h_eff_dict.values())
91 1 : assert np.any(h_eff == np.array([[0, 1], [1, 1]]))
92 1 : assert _check_sparse_matrices_equal(eig_perturb, sparse.csr_matrix([[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]]))
93 :
94 : # Order 2
95 1 : h_eff_dict, eig_perturb = calculate_perturbative_hamiltonian(hamiltonian, model_space_indices, perturbation_order=2)
96 1 : h_eff = sum(h for h in h_eff_dict.values())
97 1 : a_00 = 0 + 1 * 1 / (0 - 10) + 2 * 2 / (0 - 12)
98 1 : a_01 = 1 + 2 * 3 / (0 - 12)
99 1 : a_10 = 1 + 3 * 2 / (1 - 12)
100 1 : a_11 = 1 + 1 * 1 / (1 - 11) + 3 * 3 / (1 - 12)
101 1 : hamiltonian_new = np.array([[a_00, (a_01 + a_10) / 2], [(a_01 + a_10) / 2, a_11]])
102 1 : assert np.any(h_eff == hamiltonian_new)
103 :
104 1 : v0 = sparse.eye(1, 5, k=0) + 1 / (0 - 10) * sparse.eye(1, 5, k=2) + 2 / (0 - 12) * sparse.eye(1, 5, k=4)
105 1 : v1 = sparse.eye(1, 5, k=1) + 1 / (1 - 11) * sparse.eye(1, 5, k=3) + 3 / (1 - 12) * sparse.eye(1, 5, k=4)
106 1 : assert _check_sparse_matrices_equal(eig_perturb, sparse.csr_matrix(sparse.vstack([v0, v1])))
107 :
108 : # Order 3
109 1 : with caplog.at_level(logging.ERROR):
110 1 : h_eff_dict, eig_perturb = calculate_perturbative_hamiltonian(
111 : hamiltonian, model_space_indices, perturbation_order=3
112 : )
113 1 : h_eff = sum(h for h in h_eff_dict.values())
114 1 : a_00 -= 2 * 3 * 1 / ((0 - 12) * (1 - 12))
115 1 : a_01 += (
116 : 1 * 1 * 1 / ((1 - 10) * (1 - 11))
117 : + 2 * 1 * 1 / ((1 - 11) * (1 - 12))
118 : - 1 * 1 * 1 / ((0 - 10) * (1 - 10))
119 : - 2 * 2 * 1 / ((1 - 12) * (0 - 12))
120 : )
121 1 : a_10 += (
122 : 1 * 1 * 1 / ((0 - 10) * (0 - 11))
123 : + 2 * 1 * 1 / ((0 - 11) * (0 - 12))
124 : - 1 * 1 * 1 / ((0 - 11) * (1 - 11))
125 : - 3 * 3 * 1 / ((0 - 12) * (1 - 12))
126 : )
127 1 : a_11 += 1 * 1 * 3 / ((1 - 11) * (1 - 12)) + 3 * 1 * 1 / ((1 - 11) * (1 - 12)) - 3 * 2 * 1 / ((1 - 12) * (0 - 12))
128 1 : hamiltonian_new = np.array([[a_00, (a_01 + a_10) / 2], [(a_01 + a_10) / 2, a_11]])
129 1 : assert np.any(h_eff == hamiltonian_new)
130 :
131 1 : v0 = v0 + (
132 : -0.5 * (1 * 1 / (0 - 10) ** 2 + 2 * 2 / (0 - 12) ** 2) * sparse.eye(1, 5, k=0)
133 : + (1 * 1 / ((0 - 10) * (0 - 11)) + 2 * 1 / ((0 - 11) * (0 - 12))) * sparse.eye(1, 5, k=3)
134 : + 1 * 1 / ((0 - 11) * (0 - 1)) * sparse.eye(1, 5, k=3)
135 : + 3 * 1 / ((0 - 1) * (0 - 12)) * sparse.eye(1, 5, k=4)
136 : + 3 * 2 / ((0 - 1) * (0 - 12)) * sparse.eye(1, 5, k=1)
137 : )
138 1 : v1 = v1 + (
139 : -0.5 * (1 * 1 / (1 - 11) ** 2 + 3 * 3 / (1 - 12) ** 2) * sparse.eye(1, 5, k=1)
140 : + 1 * 1 / ((1 - 10) * (1 - 11)) * sparse.eye(1, 5, k=2)
141 : + 1 * 3 / ((1 - 11) * (1 - 12)) * sparse.eye(1, 5, k=3)
142 : + 1 * 1 / ((1 - 11) * (1 - 12)) * sparse.eye(1, 5, k=4)
143 : + 1 * 1 / ((1 - 0) * (1 - 10)) * sparse.eye(1, 5, k=2)
144 : + 2 * 1 / ((1 - 0) * (1 - 12)) * sparse.eye(1, 5, k=4)
145 : + 3 * 2 / ((1 - 0) * (1 - 12)) * sparse.eye(1, 5, k=0)
146 : )
147 1 : assert _check_sparse_matrices_equal(eig_perturb, sparse.csr_matrix(sparse.vstack([v0, v1])))
148 :
149 :
150 1 : def test_c3_with_sample_system(pi_module: PairinteractionModule, system_pair_sample: SystemPair) -> None:
151 : """Test whether the C3 coefficient with a given system is calculated correctly."""
152 1 : ket1 = pi_module.KetAtom("Rb", n=61, l=0, j=0.5, m=0.5)
153 1 : ket2 = pi_module.KetAtom("Rb", n=61, l=1, j=1.5, m=0.5)
154 1 : c3_obj = pi_module.C3(ket1, ket2)
155 1 : c3_obj._distance_vector = None # avoid warning due when setting system pair
156 1 : c3_obj.system_pair = system_pair_sample
157 :
158 1 : c3 = c3_obj.get(unit="planck_constant * gigahertz * micrometer^3")
159 1 : assert np.isclose(-0.5 * c3, 3.1515)
160 :
161 :
162 1 : def test_c3(pi_module: PairinteractionModule) -> None:
163 : """Test whether the C3 coefficient with automatically constructed system is calculated correctly."""
164 1 : ket1 = pi_module.KetAtom("Rb", n=61, l=0, j=0.5, m=0.5)
165 1 : ket2 = pi_module.KetAtom("Rb", n=61, l=1, j=1.5, m=0.5)
166 1 : c3_obj = pi_module.C3(ket1, ket2)
167 :
168 1 : c3_obj.set_electric_field([0, 0, 0], "volt/cm")
169 1 : c3_obj.set_magnetic_field([0, 0, 10], "gauss")
170 :
171 1 : c3 = c3_obj.get(unit="planck_constant * gigahertz * micrometer^3")
172 1 : assert np.isclose(-0.5 * c3, 3.2188)
173 :
174 :
175 1 : def test_c6_with_sample_system(pi_module: PairinteractionModule, system_pair_sample: SystemPair) -> None:
176 : """Test whether the C6 coefficient with a given system is calculated correctly."""
177 1 : ket = pi_module.KetAtom(species="Rb", n=61, l=0, j=0.5, m=0.5)
178 1 : c6_obj = pi_module.C6(ket, ket)
179 1 : c6_obj._distance_vector = None # avoid warning due when setting system pair
180 1 : c6_obj.system_pair = system_pair_sample
181 :
182 1 : c6 = c6_obj.get(unit="planck_constant * gigahertz * micrometer^6")
183 1 : assert np.isclose(c6, -167.880)
184 :
185 :
186 1 : def test_c6(pi_module: PairinteractionModule) -> None:
187 : """Test whether the C6 coefficient with automatically constructed system is calculated correctly."""
188 1 : ket = pi_module.KetAtom(species="Rb", n=61, l=0, j=0.5, m=0.5)
189 1 : c6_obj = pi_module.C6(ket, ket)
190 :
191 1 : c6_obj.set_electric_field([0, 0, 0], "volt/cm")
192 1 : c6_obj.set_magnetic_field([0, 0, 10], "gauss")
193 :
194 1 : c6 = c6_obj.get(unit="planck_constant * gigahertz * micrometer^6")
195 1 : assert np.isclose(c6, -169.135)
196 :
197 :
198 1 : def test_symmetrized_basis_pair_is_rejected(pi_module: PairinteractionModule) -> None:
199 : """Test that a symmetrized basis pair cannot be used for the effective Hamiltonian."""
200 1 : ket1 = pi_module.KetAtom("Rb", n=61, l=0, j=0.5, m=0.5)
201 1 : ket2 = pi_module.KetAtom("Rb", n=61, l=1, j=1.5, m=0.5)
202 1 : system = pi_module.SystemAtom(pi_module.BasisAtom("Rb", n=(60, 62), l=(0, 1)))
203 1 : pi_module.diagonalize([system], diagonalizer="eigen")
204 1 : basis_pair = pi_module.BasisPair.from_kets(
205 : [(ket1, ket2)], system_atoms=(system, system), delta_energy=3, delta_energy_unit="GHz", symmetrize=True
206 : )
207 :
208 1 : eff_system = pi_module.EffectiveSystemPair([(ket1, ket2), (ket2, ket1)])
209 1 : with pytest.raises(ValueError, match="must not be symmetrized"):
210 1 : eff_system.basis_pair = basis_pair
211 1 : with pytest.raises(ValueError, match="must not be symmetrized"):
212 1 : eff_system.system_pair = pi_module.SystemPair(basis_pair)
213 :
214 :
215 1 : def test_exact_resonance_detection(
216 : pi_module: PairinteractionModule, system_pair_sample: SystemPair, capsys: pytest.CaptureFixture[str]
217 : ) -> None:
218 : """Test whether resonance with infinite admixture is correctly detected."""
219 1 : ket1 = pi_module.KetAtom("Rb", n=61, l=0, j=0.5, m=0.5)
220 1 : ket2 = pi_module.KetAtom("Rb", n=61, l=1, j=1.5, m=0.5)
221 1 : eff_system = pi_module.EffectiveSystemPair([(ket1, ket2)])
222 1 : eff_system.system_pair = system_pair_sample
223 :
224 : # workaround to test for errors, without showing them in the std output
225 1 : with no_log_propagation("pairinteraction"), np.errstate(invalid="ignore"):
226 1 : eff_system.get_effective_hamiltonian()
227 1 : captured = capsys.readouterr()
228 1 : assert "gets a large dressing (inf overlap)" in captured.err
229 1 : assert "|Rb:61,P_3/2,1/2; Rb:61,S_1/2,1/2⟩" in captured.err
230 :
231 :
232 1 : def test_near_resonance_detection(pi_module: PairinteractionModule, capsys: pytest.CaptureFixture[str]) -> None:
233 : """Test whether a near resonance is correctly detected."""
234 1 : ket1 = pi_module.KetAtom("Rb", n=60, l=0, j=0.5, m=0.5)
235 1 : ket2 = pi_module.KetAtom("Rb", n=61, l=0, j=0.5, m=0.5)
236 1 : eff_system = pi_module.EffectiveSystemPair([(ket1, ket2), (ket2, ket1)])
237 1 : eff_system.set_magnetic_field([0, 0, 245], "gauss")
238 1 : eff_system.set_distance(10, 35.1, "micrometer")
239 :
240 : # workaround to test for errors, without showing them in the std output
241 1 : with no_log_propagation("pairinteraction"):
242 1 : eff_system.create_basis_pair(number_of_kets=100)
243 1 : eff_system.get_effective_hamiltonian()
244 1 : eff_system.check_for_resonances(0.01)
245 1 : captured = capsys.readouterr()
246 1 : assert "The most perturbing states are" in captured.err
247 1 : assert "Rb:60,P_3/2,1/2; Rb:60,P_3/2,3/2" in captured.err
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