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.perturbative import _calculate_perturbative_hamiltonian
12 1 : from pairinteraction.units import ureg
13 1 : from scipy import sparse
14 :
15 : if TYPE_CHECKING:
16 : from scipy.sparse import csr_matrix
17 :
18 :
19 : # ---------------------------------------------------------------------------------------
20 : # Helper functions
21 : # ---------------------------------------------------------------------------------------
22 1 : def _check_sparse_matrices_equal(matrix_a: "csr_matrix", matrix_b: "csr_matrix") -> bool:
23 : """Check for equality of sparse matrices efficiently.
24 :
25 : This functions compares two sparse matrices in compressed sparse row format on their equality.
26 :
27 : Args:
28 : matrix_a: A sparse matrix in csr format.
29 : matrix_b: A sparse matrix in csr format.
30 :
31 : Returns:
32 : bool: True if matrices are equal, False if not.
33 :
34 : """
35 1 : matrix_a.sort_indices()
36 1 : matrix_b.sort_indices()
37 1 : if not (
38 : matrix_a.format == "csr"
39 : and matrix_b.format == "csr"
40 : and len(matrix_a.indices) == len(matrix_b.indices)
41 : and len(matrix_a.indptr) == len(matrix_b.indptr)
42 : and len(matrix_a.data) == len(matrix_b.data)
43 : ):
44 0 : return False
45 :
46 1 : return bool(
47 : np.all(matrix_a.indices == matrix_b.indices)
48 : and np.all(matrix_a.indptr == matrix_b.indptr)
49 : and np.allclose(matrix_a.data, matrix_b.data, rtol=0, atol=1e-14)
50 : )
51 :
52 :
53 1 : def _create_system_pair_sample() -> pi.SystemPair:
54 1 : basis = pi.BasisAtom(
55 : species="Rb",
56 : n=(59, 63),
57 : l=(0, 1),
58 : m=(-1.5, 1.5),
59 : )
60 1 : system = pi.SystemAtom(basis=basis)
61 1 : system.set_diamagnetism_enabled(False)
62 1 : system.set_magnetic_field([0, 0, 1e-3], "gauss")
63 1 : if not system.is_diagonal:
64 1 : pi.diagonalize([system], diagonalizer="eigen", sort_by_energy=False)
65 1 : basis_pair = pi.BasisPair([system, system])
66 1 : system_pair = pi.SystemPair(basis_pair)
67 1 : theta = 0
68 1 : r = 12
69 1 : system_pair.set_distance_vector(r * np.array([np.sin(theta), 0, np.cos(theta)]), "micrometer")
70 1 : system_pair.set_interaction_order(3)
71 1 : return system_pair
72 :
73 :
74 : # ---------------------------------------------------------------------------------------
75 : # Tests
76 : # ---------------------------------------------------------------------------------------
77 1 : def test_perturbative_calculation1(caplog: pytest.LogCaptureFixture) -> None:
78 : """Test of mathematic functionality."""
79 1 : hamiltonian = sparse.csr_matrix(
80 : [[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]]
81 : )
82 1 : model_space_indices = [0, 1]
83 :
84 : # Order 0
85 1 : hamiltonian_eff, eig_perturb = _calculate_perturbative_hamiltonian(hamiltonian, model_space_indices, order=0)
86 1 : assert np.any(hamiltonian_eff == np.array([[0, 0], [0, 1]]))
87 1 : assert _check_sparse_matrices_equal(eig_perturb, sparse.csr_matrix(sparse.eye(2, 5, k=0)))
88 :
89 : # Order 1
90 1 : hamiltonian_eff, eig_perturb = _calculate_perturbative_hamiltonian(hamiltonian, model_space_indices, order=1)
91 1 : assert np.any(hamiltonian_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 : hamiltonian_eff, eig_perturb = _calculate_perturbative_hamiltonian(hamiltonian, model_space_indices, order=2)
96 1 : a_00 = 0 + 1 * 1 / (0 - 10) + 2 * 2 / (0 - 12)
97 1 : a_01 = 1 + 2 * 3 / (0 - 12)
98 1 : a_10 = 1 + 3 * 2 / (1 - 12)
99 1 : a_11 = 1 + 1 * 1 / (1 - 11) + 3 * 3 / (1 - 12)
100 1 : hamiltonian_new = np.array([[a_00, (a_01 + a_10) / 2], [(a_01 + a_10) / 2, a_11]])
101 1 : assert np.any(hamiltonian_eff == hamiltonian_new)
102 :
103 1 : v0 = (
104 : sparse.eye(1, 5, k=0, format="csr")
105 : + 1 / (0 - 10) * sparse.eye(1, 5, k=2, format="csr")
106 : + 2 / (0 - 12) * sparse.eye(1, 5, k=4, format="csr")
107 : )
108 1 : v1 = (
109 : sparse.eye(1, 5, k=1, format="csr")
110 : + 1 / (1 - 11) * sparse.eye(1, 5, k=3, format="csr")
111 : + 3 / (1 - 12) * sparse.eye(1, 5, k=4, format="csr")
112 : )
113 1 : assert _check_sparse_matrices_equal(eig_perturb, sparse.csr_matrix(sparse.vstack([v0, v1])))
114 :
115 : # Order 3
116 1 : with caplog.at_level(logging.ERROR):
117 1 : hamiltonian_eff, eig_perturb = _calculate_perturbative_hamiltonian(hamiltonian, model_space_indices, order=3)
118 1 : a_00 -= 2 * 3 * 1 / ((0 - 12) * (1 - 12))
119 1 : a_01 += (
120 : 1 * 1 * 1 / ((1 - 10) * (1 - 11))
121 : + 2 * 1 * 1 / ((1 - 11) * (1 - 12))
122 : - 1 * 1 * 1 / ((0 - 10) * (1 - 10))
123 : - 2 * 2 * 1 / ((1 - 12) * (0 - 12))
124 : )
125 1 : a_10 += (
126 : 1 * 1 * 1 / ((0 - 10) * (0 - 11))
127 : + 2 * 1 * 1 / ((0 - 11) * (0 - 12))
128 : - 1 * 1 * 1 / ((0 - 11) * (1 - 11))
129 : - 3 * 3 * 1 / ((0 - 12) * (1 - 12))
130 : )
131 1 : a_11 += 1 * 1 * 3 / ((1 - 11) * (1 - 12)) + 3 * 1 * 1 / ((1 - 11) * (1 - 12)) - 3 * 2 * 1 / ((1 - 12) * (0 - 12))
132 1 : hamiltonian_new = np.array([[a_00, (a_01 + a_10) / 2], [(a_01 + a_10) / 2, a_11]])
133 1 : assert np.any(hamiltonian_eff == hamiltonian_new)
134 :
135 1 : v0 += (
136 : -0.5 * (1 * 1 / (0 - 10) ** 2 + 2 * 2 / (0 - 12) ** 2) * sparse.eye(1, 5, k=0, format="csr")
137 : + (1 * 1 / ((0 - 10) * (0 - 11)) + 2 * 1 / ((0 - 11) * (0 - 12))) * sparse.eye(1, 5, k=3, format="csr")
138 : + 1 * 1 / ((0 - 11) * (0 - 1)) * sparse.eye(1, 5, k=3, format="csr")
139 : + 3 * 1 / ((0 - 1) * (0 - 12)) * sparse.eye(1, 5, k=4, format="csr")
140 : + 3 * 2 / ((0 - 1) * (0 - 12)) * sparse.eye(1, 5, k=1, format="csr")
141 : )
142 1 : v1 += (
143 : -0.5 * (1 * 1 / (1 - 11) ** 2 + 3 * 3 / (1 - 12) ** 2) * sparse.eye(1, 5, k=1, format="csr")
144 : + 1 * 1 / ((1 - 10) * (1 - 11)) * sparse.eye(1, 5, k=2, format="csr")
145 : + 1 * 3 / ((1 - 11) * (1 - 12)) * sparse.eye(1, 5, k=3, format="csr")
146 : + 1 * 1 / ((1 - 11) * (1 - 12)) * sparse.eye(1, 5, k=4, format="csr")
147 : + 1 * 1 / ((1 - 0) * (1 - 10)) * sparse.eye(1, 5, k=2, format="csr")
148 : + 2 * 1 / ((1 - 0) * (1 - 12)) * sparse.eye(1, 5, k=4, format="csr")
149 : + 3 * 2 / ((1 - 0) * (1 - 12)) * sparse.eye(1, 5, k=0, format="csr")
150 : )
151 1 : assert _check_sparse_matrices_equal(eig_perturb, sparse.csr_matrix(sparse.vstack([v0, v1])))
152 :
153 :
154 1 : def test_c3_with_system() -> None:
155 : """Test whether the C3 coefficient with a given system is calculated correctly."""
156 1 : system_pair = _create_system_pair_sample()
157 :
158 1 : ket_tuple_list = [
159 : (pi.KetAtom("Rb", n=61, l=0, j=0.5, m=0.5), pi.KetAtom("Rb", n=61, l=1, j=1.5, m=0.5)),
160 : (pi.KetAtom("Rb", n=61, l=1, j=1.5, m=0.5), pi.KetAtom("Rb", n=61, l=0, j=0.5, m=0.5)),
161 : ]
162 1 : c3 = perturbative.get_c3_from_system(
163 : system_pair=system_pair, ket_tuple_list=ket_tuple_list, unit="planck_constant * gigahertz * micrometer^3"
164 : )
165 1 : assert np.isclose(-0.5 * c3, 3.1515)
166 :
167 :
168 1 : def test_c3_create_system() -> None:
169 : """Test whether the C3 coefficient with automatically constructed system is calculated correctly."""
170 1 : ket_tuple_list = [
171 : (pi.KetAtom("Rb", n=61, l=0, j=0.5, m=0.5), pi.KetAtom("Rb", n=61, l=1, j=1.5, m=0.5)),
172 : (pi.KetAtom("Rb", n=61, l=1, j=1.5, m=0.5), pi.KetAtom("Rb", n=61, l=0, j=0.5, m=0.5)),
173 : ]
174 1 : magnetic_field = ureg.Quantity([0, 0, 10], "gauss")
175 1 : electric_field = ureg.Quantity([0, 0, 0], "volt/cm")
176 1 : distance_vector = ureg.Quantity([0, 0, 500], "micrometer")
177 :
178 1 : system = perturbative.create_system_for_perturbative(
179 : ket_tuple_list, electric_field, magnetic_field, distance_vector
180 : )
181 :
182 1 : c3 = perturbative.get_c3_from_system(
183 : system_pair=system, ket_tuple_list=ket_tuple_list, unit="planck_constant * gigahertz * micrometer^3"
184 : )
185 1 : assert np.isclose(-0.5 * c3, 3.2188)
186 :
187 :
188 1 : def test_c6_with_system() -> None:
189 : """Test whether the C6 coefficient with a given system is calculated correctly."""
190 1 : system_pair = _create_system_pair_sample()
191 1 : ket_atom = pi.KetAtom(species="Rb", n=61, l=0, j=0.5, m=0.5)
192 1 : c6 = perturbative.get_c6_from_system(
193 : ket_tuple=(ket_atom, ket_atom), system_pair=system_pair, unit="planck_constant * gigahertz * micrometer^6"
194 : )
195 1 : assert np.isclose(c6, 167.92)
196 :
197 :
198 1 : def test_c6_create_system() -> None:
199 : """Test whether the C6 coefficient with automatically constructed system is calculated correctly."""
200 1 : magnetic_field = ureg.Quantity([0, 0, 10], "gauss")
201 1 : electric_field = ureg.Quantity([0, 0, 0], "volt/cm")
202 1 : distance_vector = ureg.Quantity([0, 0, 500], "micrometer")
203 1 : ket_atom = pi.KetAtom(species="Rb", n=61, l=0, j=0.5, m=0.5)
204 :
205 1 : system = perturbative.create_system_for_perturbative(
206 : [(ket_atom, ket_atom)], electric_field, magnetic_field, distance_vector
207 : )
208 :
209 1 : c6 = perturbative.get_c6_from_system(
210 : ket_tuple=(ket_atom, ket_atom), system_pair=system, unit="planck_constant * gigahertz * micrometer^6"
211 : )
212 1 : assert np.isclose(c6, 169.189)
213 :
214 :
215 1 : def test_resonance_detection(caplog: pytest.LogCaptureFixture) -> None:
216 : """Test whether resonance is correctly detected."""
217 1 : system_pair = _create_system_pair_sample()
218 1 : ket_tuple_list = [
219 : (pi.KetAtom(species="Rb", n=61, l=0, j=0.5, m=0.5), pi.KetAtom(species="Rb", n=61, l=1, j=0.5, m=0.5))
220 : ]
221 1 : with (
222 : pytest.raises(ValueError, match="Perturbative Calculation not possible due to resonances."),
223 : caplog.at_level(logging.CRITICAL),
224 : ):
225 1 : perturbative.get_effective_hamiltonian_from_system(
226 : ket_tuple_list=ket_tuple_list, system_pair=system_pair, order=2, required_overlap=0.8
227 : )
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