Line data Source code
1 : # SPDX-FileCopyrightText: 2025 PairInteraction Developers
2 : # SPDX-License-Identifier: LGPL-3.0-or-later
3 :
4 1 : import logging
5 1 : from typing import TYPE_CHECKING
6 :
7 1 : import numpy as np
8 1 : import pairinteraction.real as pi
9 1 : import pytest
10 1 : from pairinteraction import perturbative
11 1 : from pairinteraction.perturbative.perturbation_theory import calculate_perturbative_hamiltonian
12 1 : from scipy import sparse
13 :
14 1 : from .compare_utils import no_log_propagation
15 :
16 : if TYPE_CHECKING:
17 : from scipy.sparse import csr_matrix
18 :
19 :
20 1 : def _check_sparse_matrices_equal(matrix_a: "csr_matrix", matrix_b: "csr_matrix") -> bool:
21 : """Check for equality of sparse matrices efficiently.
22 :
23 : This functions compares two sparse matrices in compressed sparse row format on their equality.
24 :
25 : Args:
26 : matrix_a: A sparse matrix in csr format.
27 : matrix_b: A sparse matrix in csr format.
28 :
29 : Returns:
30 : bool: True if matrices are equal, False if not.
31 :
32 : """
33 1 : matrix_a.sort_indices()
34 1 : matrix_b.sort_indices()
35 1 : if not (
36 : matrix_a.format == "csr"
37 : and matrix_b.format == "csr"
38 : and len(matrix_a.indices) == len(matrix_b.indices)
39 : and len(matrix_a.indptr) == len(matrix_b.indptr)
40 : and len(matrix_a.data) == len(matrix_b.data)
41 : ):
42 0 : return False
43 :
44 1 : return bool(
45 : np.all(matrix_a.indices == matrix_b.indices)
46 : and np.all(matrix_a.indptr == matrix_b.indptr)
47 : and np.allclose(matrix_a.data, matrix_b.data, rtol=0, atol=1e-14)
48 : )
49 :
50 :
51 1 : @pytest.fixture
52 1 : def system_pair_sample() -> pi.SystemPair:
53 1 : basis = pi.BasisAtom(
54 : species="Rb",
55 : n=(59, 63),
56 : l=(0, 1),
57 : m=(-1.5, 1.5),
58 : )
59 1 : system = pi.SystemAtom(basis=basis)
60 1 : system.set_diamagnetism_enabled(False)
61 1 : system.set_magnetic_field([0, 0, 1e-3], "gauss")
62 1 : if not system.is_diagonal:
63 1 : pi.diagonalize([system], diagonalizer="eigen", sort_by_energy=False)
64 1 : basis_pair = pi.BasisPair([system, system])
65 1 : system_pair = pi.SystemPair(basis_pair)
66 1 : theta = 0
67 1 : r = 12
68 1 : system_pair.set_distance_vector(r * np.array([np.sin(theta), 0, np.cos(theta)]), "micrometer")
69 1 : system_pair.set_interaction_order(3)
70 1 : return system_pair
71 :
72 :
73 1 : def test_perturbative_calculation1(caplog: pytest.LogCaptureFixture) -> None:
74 : """Test of mathematic functionality."""
75 1 : hamiltonian = sparse.csr_matrix(
76 : [[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]]
77 : )
78 1 : model_space_indices = [0, 1]
79 :
80 : # Order 0
81 1 : h_eff_dict, eig_perturb = calculate_perturbative_hamiltonian(hamiltonian, model_space_indices, perturbation_order=0)
82 1 : h_eff = sum(h for h in h_eff_dict.values())
83 1 : assert np.any(h_eff == np.array([[0, 0], [0, 1]]))
84 1 : assert _check_sparse_matrices_equal(eig_perturb, sparse.csr_matrix(sparse.eye(2, 5, k=0)))
85 :
86 : # Order 1
87 1 : h_eff_dict, eig_perturb = calculate_perturbative_hamiltonian(hamiltonian, model_space_indices, perturbation_order=1)
88 1 : h_eff = sum(h for h in h_eff_dict.values())
89 1 : assert np.any(h_eff == np.array([[0, 1], [1, 1]]))
90 1 : assert _check_sparse_matrices_equal(eig_perturb, sparse.csr_matrix([[1, 0, 0, 0, 0], [0, 1, 0, 0, 0]]))
91 :
92 : # Order 2
93 1 : h_eff_dict, eig_perturb = calculate_perturbative_hamiltonian(hamiltonian, model_space_indices, perturbation_order=2)
94 1 : h_eff = sum(h for h in h_eff_dict.values())
95 1 : a_00 = 0 + 1 * 1 / (0 - 10) + 2 * 2 / (0 - 12)
96 1 : a_01 = 1 + 2 * 3 / (0 - 12)
97 1 : a_10 = 1 + 3 * 2 / (1 - 12)
98 1 : a_11 = 1 + 1 * 1 / (1 - 11) + 3 * 3 / (1 - 12)
99 1 : hamiltonian_new = np.array([[a_00, (a_01 + a_10) / 2], [(a_01 + a_10) / 2, a_11]])
100 1 : assert np.any(h_eff == hamiltonian_new)
101 :
102 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)
103 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)
104 1 : assert _check_sparse_matrices_equal(eig_perturb, sparse.csr_matrix(sparse.vstack([v0, v1])))
105 :
106 : # Order 3
107 1 : with caplog.at_level(logging.ERROR):
108 1 : h_eff_dict, eig_perturb = calculate_perturbative_hamiltonian(
109 : hamiltonian, model_space_indices, perturbation_order=3
110 : )
111 1 : h_eff = sum(h for h in h_eff_dict.values())
112 1 : a_00 -= 2 * 3 * 1 / ((0 - 12) * (1 - 12))
113 1 : a_01 += (
114 : 1 * 1 * 1 / ((1 - 10) * (1 - 11))
115 : + 2 * 1 * 1 / ((1 - 11) * (1 - 12))
116 : - 1 * 1 * 1 / ((0 - 10) * (1 - 10))
117 : - 2 * 2 * 1 / ((1 - 12) * (0 - 12))
118 : )
119 1 : a_10 += (
120 : 1 * 1 * 1 / ((0 - 10) * (0 - 11))
121 : + 2 * 1 * 1 / ((0 - 11) * (0 - 12))
122 : - 1 * 1 * 1 / ((0 - 11) * (1 - 11))
123 : - 3 * 3 * 1 / ((0 - 12) * (1 - 12))
124 : )
125 1 : a_11 += 1 * 1 * 3 / ((1 - 11) * (1 - 12)) + 3 * 1 * 1 / ((1 - 11) * (1 - 12)) - 3 * 2 * 1 / ((1 - 12) * (0 - 12))
126 1 : hamiltonian_new = np.array([[a_00, (a_01 + a_10) / 2], [(a_01 + a_10) / 2, a_11]])
127 1 : assert np.any(h_eff == hamiltonian_new)
128 :
129 1 : v0 = v0 + (
130 : -0.5 * (1 * 1 / (0 - 10) ** 2 + 2 * 2 / (0 - 12) ** 2) * sparse.eye(1, 5, k=0)
131 : + (1 * 1 / ((0 - 10) * (0 - 11)) + 2 * 1 / ((0 - 11) * (0 - 12))) * sparse.eye(1, 5, k=3)
132 : + 1 * 1 / ((0 - 11) * (0 - 1)) * sparse.eye(1, 5, k=3)
133 : + 3 * 1 / ((0 - 1) * (0 - 12)) * sparse.eye(1, 5, k=4)
134 : + 3 * 2 / ((0 - 1) * (0 - 12)) * sparse.eye(1, 5, k=1)
135 : )
136 1 : v1 = v1 + (
137 : -0.5 * (1 * 1 / (1 - 11) ** 2 + 3 * 3 / (1 - 12) ** 2) * sparse.eye(1, 5, k=1)
138 : + 1 * 1 / ((1 - 10) * (1 - 11)) * sparse.eye(1, 5, k=2)
139 : + 1 * 3 / ((1 - 11) * (1 - 12)) * sparse.eye(1, 5, k=3)
140 : + 1 * 1 / ((1 - 11) * (1 - 12)) * sparse.eye(1, 5, k=4)
141 : + 1 * 1 / ((1 - 0) * (1 - 10)) * sparse.eye(1, 5, k=2)
142 : + 2 * 1 / ((1 - 0) * (1 - 12)) * sparse.eye(1, 5, k=4)
143 : + 3 * 2 / ((1 - 0) * (1 - 12)) * sparse.eye(1, 5, k=0)
144 : )
145 1 : assert _check_sparse_matrices_equal(eig_perturb, sparse.csr_matrix(sparse.vstack([v0, v1])))
146 :
147 :
148 1 : def test_c3_with_sample_system(system_pair_sample: pi.SystemPair) -> None:
149 : """Test whether the C3 coefficient with a given system is calculated correctly."""
150 1 : ket1 = pi.KetAtom("Rb", n=61, l=0, j=0.5, m=0.5)
151 1 : ket2 = pi.KetAtom("Rb", n=61, l=1, j=1.5, m=0.5)
152 1 : c3_obj = perturbative.C3(ket1, ket2)
153 1 : c3_obj._distance_vector = None # avoid warning due when setting system pair
154 1 : c3_obj.system_pair = system_pair_sample
155 :
156 1 : c3 = c3_obj.get(unit="planck_constant * gigahertz * micrometer^3")
157 1 : assert np.isclose(-0.5 * c3, 3.1515)
158 :
159 :
160 1 : def test_c3() -> None:
161 : """Test whether the C3 coefficient with automatically constructed system is calculated correctly."""
162 1 : ket1 = pi.KetAtom("Rb", n=61, l=0, j=0.5, m=0.5)
163 1 : ket2 = pi.KetAtom("Rb", n=61, l=1, j=1.5, m=0.5)
164 1 : c3_obj = perturbative.C3(ket1, ket2)
165 :
166 1 : c3_obj.set_electric_field([0, 0, 0], "volt/cm")
167 1 : c3_obj.set_magnetic_field([0, 0, 10], "gauss")
168 :
169 1 : c3 = c3_obj.get(unit="planck_constant * gigahertz * micrometer^3")
170 1 : assert np.isclose(-0.5 * c3, 3.2188)
171 :
172 :
173 1 : def test_c6_with_sample_system(system_pair_sample: pi.SystemPair) -> None:
174 : """Test whether the C6 coefficient with a given system is calculated correctly."""
175 1 : ket = pi.KetAtom(species="Rb", n=61, l=0, j=0.5, m=0.5)
176 1 : c6_obj = perturbative.C6(ket, ket)
177 1 : c6_obj._distance_vector = None # avoid warning due when setting system pair
178 1 : c6_obj.system_pair = system_pair_sample
179 :
180 1 : c6 = c6_obj.get(unit="planck_constant * gigahertz * micrometer^6")
181 1 : assert np.isclose(c6, 167.880)
182 :
183 :
184 1 : def test_c6() -> None:
185 : """Test whether the C6 coefficient with automatically constructed system is calculated correctly."""
186 1 : ket = pi.KetAtom(species="Rb", n=61, l=0, j=0.5, m=0.5)
187 1 : c6_obj = perturbative.C6(ket, ket)
188 :
189 1 : c6_obj.set_electric_field([0, 0, 0], "volt/cm")
190 1 : c6_obj.set_magnetic_field([0, 0, 10], "gauss")
191 :
192 1 : c6 = c6_obj.get(unit="planck_constant * gigahertz * micrometer^6")
193 1 : assert np.isclose(c6, 169.149)
194 :
195 :
196 1 : def test_exact_resonance_detection(system_pair_sample: pi.SystemPair, capsys: pytest.CaptureFixture[str]) -> None:
197 : """Test whether resonance with infinite admixture is correctly detected."""
198 1 : ket1 = pi.KetAtom("Rb", n=61, l=0, j=0.5, m=0.5)
199 1 : ket2 = pi.KetAtom("Rb", n=61, l=1, j=1.5, m=0.5)
200 1 : eff_system = perturbative.EffectiveSystemPair([(ket1, ket2)])
201 1 : eff_system.system_pair = system_pair_sample
202 :
203 : # workaround to test for errors, without showing them in the std output
204 1 : with no_log_propagation("pairinteraction"):
205 1 : eff_system.get_effective_hamiltonian()
206 1 : captured = capsys.readouterr()
207 1 : assert "Detected 'inf' entries" in captured.err
208 1 : assert "|~Rb:61,P_3/2,1/2; Rb:61,S_1/2,1/2⟩ has infinite admixture" in captured.err
209 :
210 :
211 1 : def test_near_resonance_detection(capsys: pytest.CaptureFixture[str]) -> None:
212 : """Test whether a near resonance is correctly detected."""
213 1 : ket1 = pi.KetAtom("Rb", n=60, l=0, j=0.5, m=0.5)
214 1 : ket2 = pi.KetAtom("Rb", n=61, l=0, j=0.5, m=0.5)
215 1 : eff_system = perturbative.EffectiveSystemPair([(ket1, ket2), (ket2, ket1)])
216 1 : eff_system.set_magnetic_field([0, 0, 245], "gauss")
217 1 : eff_system.set_minimum_number_of_ket_pairs(100)
218 1 : eff_system.set_distance(10, 35.1, "micrometer")
219 1 : eff_system.get_effective_hamiltonian()
220 :
221 : # workaround to test for errors, without showing them in the std output
222 1 : with no_log_propagation("pairinteraction"):
223 1 : eff_system.check_for_resonances(0.99)
224 1 : captured = capsys.readouterr()
225 1 : assert "The most perturbing states are" in captured.err
226 1 : assert "Rb:60,P_3/2,1/2; Rb:60,P_3/2,3/2" in captured.err
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