def test_takagi_factorization_real_neg_imag_neg(rank, dtype):
a = get_random_complex_symmetric_matrices(10, rank, dtype)
a = sm.to_complex(a.real * -1, a.imag * -1)
eigenvalues, s = sm.takagi_eig(a)
assert_sds_equals_a(s, eigenvalues, a)
def test_takagi_factorization_eigval_equals_eig(rank, dtype):
a = get_random_complex_symmetric_matrices(10, rank, dtype)
eig, s = sm.takagi_eig(a)
eigvals = sm.takagi_eigvals(a)
assert_sds_equals_a(s, eigvals, a)
np.testing.assert_allclose(eig, eigvals, atol=1e-5, rtol=1e-5)
def test_takagi_factorization_imag_identity(rank, dtype):
a = sm.identity_like(get_random_complex_symmetric_matrices(
10, rank, dtype))
a = sm.to_complex(a.imag, a.real)
eigenvalues, s = sm.takagi_eig(a)
assert_sds_equals_a(s, eigenvalues, a)
def test_takagi_factorization_idem_takagi_fact():
real_a = torch.Tensor([[[0.222662581850819, 0.98644223215106],
[0.98644223215106, 0.27907583542894]]])
imag_a = torch.Tensor([[[0.204990135642257, 1.28603437847092],
[1.28603437847092, 1.18098457998164]]])
a = sm.to_complex(real_a, imag_a)
eigenvalues, s = sm.takagi_eig(a)
assert_sds_equals_a(s, eigenvalues, a)
def test_takagi_factorization_real_identity(rank, dtype):
a = sm.identity_like(get_random_complex_symmetric_matrices(
10, rank, dtype))
eigenvalues, s = sm.takagi_eig(a)
assert_sds_equals_a(s, eigenvalues, a)
np.testing.assert_allclose(a, s, atol=1e-5, rtol=1e-5)
np.testing.assert_allclose(torch.ones_like(eigenvalues),
eigenvalues,
atol=1e-5,
rtol=1e-5)
def test_takagi_factorization_real_diagonal(rank, dtype):
real_a = torch.diag_embed(torch.rand((10, rank), dtype=dtype).real * 10)
a = torch.complex(real_a, torch.zeros_like(real_a))
eigenvalues, s = sm.takagi_eig(a)
assert_sds_equals_a(s, eigenvalues, a)
# real part of eigenvectors is made of vectors with one 1 and all zeros
real_part = torch.sum(torch.abs(s.real), dim=-1)
np.testing.assert_allclose(torch.ones_like(real_part),
real_part,
atol=1e-5,
rtol=1e-5)
# imaginary part of eigenvectors is all zeros
np.testing.assert_allclose(torch.zeros(1),
torch.sum(s.imag),
atol=1e-5,
rtol=1e-5)
def test_takagi_factorization_large_values(rank, dtype):
a = get_random_complex_symmetric_matrices(10, rank, dtype) * 10
eigenvalues, s = sm.takagi_eig(a)
assert_sds_equals_a(s, eigenvalues, a)
