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156 lines
5.6 KiB
Python
156 lines
5.6 KiB
Python
import pytest
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import numpy as np
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from numpy.random import seed
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from numpy.testing import assert_allclose
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from scipy.linalg.lapack import _compute_lwork
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from scipy.stats import ortho_group, unitary_group
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from scipy.linalg import cossin, get_lapack_funcs
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REAL_DTYPES = (np.float32, np.float64)
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COMPLEX_DTYPES = (np.complex64, np.complex128)
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DTYPES = REAL_DTYPES + COMPLEX_DTYPES
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@pytest.mark.parametrize('dtype_', DTYPES)
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@pytest.mark.parametrize('m, p, q',
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[
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(2, 1, 1),
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(3, 2, 1),
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(3, 1, 2),
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(4, 2, 2),
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(4, 1, 2),
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(40, 12, 20),
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(40, 30, 1),
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(40, 1, 30),
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(100, 50, 1),
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(100, 50, 50),
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])
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@pytest.mark.parametrize('swap_sign', [True, False])
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def test_cossin(dtype_, m, p, q, swap_sign):
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seed(1234)
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if dtype_ in COMPLEX_DTYPES:
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x = np.array(unitary_group.rvs(m), dtype=dtype_)
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else:
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x = np.array(ortho_group.rvs(m), dtype=dtype_)
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u, cs, vh = cossin(x, p, q,
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swap_sign=swap_sign)
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assert_allclose(x, u @ cs @ vh, rtol=0., atol=m*1e3*np.finfo(dtype_).eps)
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assert u.dtype == dtype_
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# Test for float32 or float 64
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assert cs.dtype == np.real(u).dtype
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assert vh.dtype == dtype_
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u, cs, vh = cossin([x[:p, :q], x[:p, q:], x[p:, :q], x[p:, q:]],
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swap_sign=swap_sign)
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assert_allclose(x, u @ cs @ vh, rtol=0., atol=m*1e3*np.finfo(dtype_).eps)
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assert u.dtype == dtype_
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assert cs.dtype == np.real(u).dtype
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assert vh.dtype == dtype_
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_, cs2, vh2 = cossin(x, p, q,
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compute_u=False,
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swap_sign=swap_sign)
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assert_allclose(cs, cs2, rtol=0., atol=10*np.finfo(dtype_).eps)
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assert_allclose(vh, vh2, rtol=0., atol=10*np.finfo(dtype_).eps)
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u2, cs2, _ = cossin(x, p, q,
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compute_vh=False,
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swap_sign=swap_sign)
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assert_allclose(u, u2, rtol=0., atol=10*np.finfo(dtype_).eps)
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assert_allclose(cs, cs2, rtol=0., atol=10*np.finfo(dtype_).eps)
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_, cs2, _ = cossin(x, p, q,
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compute_u=False,
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compute_vh=False,
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swap_sign=swap_sign)
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assert_allclose(cs, cs2, rtol=0., atol=10*np.finfo(dtype_).eps)
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def test_cossin_mixed_types():
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seed(1234)
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x = np.array(ortho_group.rvs(4), dtype=np.float64)
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u, cs, vh = cossin([x[:2, :2],
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np.array(x[:2, 2:], dtype=np.complex128),
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x[2:, :2],
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x[2:, 2:]])
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assert u.dtype == np.complex128
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assert cs.dtype == np.float64
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assert vh.dtype == np.complex128
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assert_allclose(x, u @ cs @ vh, rtol=0.,
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atol=1e4 * np.finfo(np.complex128).eps)
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def test_cossin_error_incorrect_subblocks():
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with pytest.raises(ValueError, match="be due to missing p, q arguments."):
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cossin(([1, 2], [3, 4, 5], [6, 7], [8, 9, 10]))
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def test_cossin_error_empty_subblocks():
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with pytest.raises(ValueError, match="x11.*empty"):
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cossin(([], [], [], []))
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with pytest.raises(ValueError, match="x12.*empty"):
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cossin(([1, 2], [], [6, 7], [8, 9, 10]))
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with pytest.raises(ValueError, match="x21.*empty"):
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cossin(([1, 2], [3, 4, 5], [], [8, 9, 10]))
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with pytest.raises(ValueError, match="x22.*empty"):
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cossin(([1, 2], [3, 4, 5], [2], []))
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def test_cossin_error_missing_partitioning():
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with pytest.raises(ValueError, match=".*exactly four arrays.* got 2"):
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cossin(unitary_group.rvs(2))
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with pytest.raises(ValueError, match=".*might be due to missing p, q"):
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cossin(unitary_group.rvs(4))
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def test_cossin_error_non_iterable():
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with pytest.raises(ValueError, match="containing the subblocks of X"):
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cossin(12j)
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def test_cossin_error_non_square():
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with pytest.raises(ValueError, match="only supports square"):
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cossin(np.array([[1, 2]]), 1, 1)
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def test_cossin_error_partitioning():
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x = np.array(ortho_group.rvs(4), dtype=np.float64)
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with pytest.raises(ValueError, match="invalid p=0.*0<p<4.*"):
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cossin(x, 0, 1)
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with pytest.raises(ValueError, match="invalid p=4.*0<p<4.*"):
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cossin(x, 4, 1)
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with pytest.raises(ValueError, match="invalid q=-2.*0<q<4.*"):
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cossin(x, 1, -2)
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with pytest.raises(ValueError, match="invalid q=5.*0<q<4.*"):
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cossin(x, 1, 5)
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@pytest.mark.parametrize("dtype_", DTYPES)
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def test_cossin_separate(dtype_):
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seed(1234)
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m, p, q = 250, 80, 170
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pfx = 'or' if dtype_ in REAL_DTYPES else 'un'
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X = ortho_group.rvs(m) if pfx == 'or' else unitary_group.rvs(m)
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X = np.array(X, dtype=dtype_)
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drv, dlw = get_lapack_funcs((pfx + 'csd', pfx + 'csd_lwork'),[X])
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lwval = _compute_lwork(dlw, m, p, q)
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lwvals = {'lwork': lwval} if pfx == 'or' else dict(zip(['lwork',
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'lrwork'],
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lwval))
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*_, theta, u1, u2, v1t, v2t, _ = \
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drv(X[:p, :q], X[:p, q:], X[p:, :q], X[p:, q:], **lwvals)
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(u1_2, u2_2), theta2, (v1t_2, v2t_2) = cossin(X, p, q, separate=True)
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assert_allclose(u1_2, u1, rtol=0., atol=10*np.finfo(dtype_).eps)
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assert_allclose(u2_2, u2, rtol=0., atol=10*np.finfo(dtype_).eps)
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assert_allclose(v1t_2, v1t, rtol=0., atol=10*np.finfo(dtype_).eps)
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assert_allclose(v2t_2, v2t, rtol=0., atol=10*np.finfo(dtype_).eps)
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assert_allclose(theta2, theta, rtol=0., atol=10*np.finfo(dtype_).eps)
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