Streaming Polyphase Factor Decomposition / SKAT

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1 import unittest
2 import numpy as np
3 
4 from residual_completion import residual_rank_bounds, complete_residual_range, stream_complete_residual_range
5 
6 
7 class ResidualCompletionTests(unittest.TestCase):
8     def test_completed_core_matches_full_spectrum(self):
9         rng = np.random.default_rng(31)
10         A = rng.normal(size=(18, 14))
11         U = rng.normal(size=(18, 9))
12         c = complete_residual_range(A, U)
13         sv_true = np.linalg.svd(A, compute_uv=False)
14         self.assertLess(
15             np.linalg.norm(c.completed_singular_values - sv_true) / np.linalg.norm(sv_true),
16             1e-12,
17         )
18 
19     def test_rank_bounds_are_valid(self):
20         rng = np.random.default_rng(32)
21         A = rng.normal(size=(20, 15))
22         U = rng.normal(size=(20, 12))
23         Q, _ = np.linalg.qr(U, mode='reduced')
24         F = A - Q @ (Q.T @ A)
25         rank = np.linalg.matrix_rank(F, tol=1e-10)
26         b = residual_rank_bounds(A, U)
27         self.assertLessEqual(b.integer_lower_bound, rank)
28         self.assertGreaterEqual(b.orthogonal_complement_upper_bound, rank)
29 
30     def test_streamed_completion_matches_full_spectrum(self):
31         rng = np.random.default_rng(33)
32         A = rng.normal(size=(21, 17))
33         U = rng.normal(size=(21, 11))
34         truth = np.linalg.svd(A, compute_uv=False)
35         for bs in (1, 3, 7, 20):
36             c = stream_complete_residual_range(A, U, block_size=bs)
37             rel = np.linalg.norm(c.completed_singular_values-truth)/np.linalg.norm(truth)
38             self.assertLess(rel, 1e-11)
39 
40 
41 if __name__ == '__main__':
42     unittest.main(verbosity=2)

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