def test_svd_flip(shape, chunks):
# Verify that sign-corrected SVD results can still
# be used to reconstruct inputs
x = da.random.random(size=shape, chunks=chunks)
u, s, v = da.linalg.svd(x)
# Validate w/ dask inputs
uf, vf = svd_flip(u, v)
np.testing.assert_almost_equal(np.asarray(np.dot(uf * s, vf)), x, decimal=9)
# Validate w/ numpy inputs
uc, vc = svd_flip(*da.compute(u, v))
np.testing.assert_almost_equal(np.asarray(np.dot(uc * s, vc)), x, decimal=9)
def test_svd_supported_array_shapes(chunks, shape):
# Test the following cases for tall-skinny, short-fat and square arrays:
# - no chunking
# - chunking that contradicts shape (e.g. a 10x100 array with 9x100 chunks)
# - chunking that aligns with shape (e.g. a 10x100 array with 10x9 chunks)
x = np.random.random(shape)
dx = da.from_array(x, chunks=chunks)
du, ds, dv = da.linalg.svd(dx)
du, dv = da.compute(du, dv)
nu, ns, nv = np.linalg.svd(x, full_matrices=False)
# Correct signs before comparison
du, dv = svd_flip(du, dv)
nu, nv = svd_flip(nu, nv)
assert_eq(du, nu)
assert_eq(ds, ns)
assert_eq(dv, nv)
def test_svd_flip_correction(shape, chunks, dtype):
# Verify that sign-corrected SVD results can still
# be used to reconstruct inputs
x = da.random.random(size=shape, chunks=chunks).astype(dtype)
u, s, v = da.linalg.svd(x)
# Choose precision in evaluation based on float precision
decimal = 9 if np.dtype(dtype).itemsize > 4 else 6
# Validate w/ dask inputs
uf, vf = svd_flip(u, v)
assert uf.dtype == u.dtype
assert vf.dtype == v.dtype
np.testing.assert_almost_equal(np.asarray(np.dot(uf * s, vf)), x, decimal=decimal)
# Validate w/ numpy inputs
uc, vc = svd_flip(*da.compute(u, v))
assert uc.dtype == u.dtype
assert vc.dtype == v.dtype
np.testing.assert_almost_equal(np.asarray(np.dot(uc * s, vc)), x, decimal=decimal)
def test_svd_flip_sign(dtype, u_based):
if sys.platform == "win32" and dtype in ["f16", "c32"]:
pytest.skip("128-bit floats not supported on windows")
x = np.array(
[[1, -1, 1, -1], [1, -1, 1, -1], [-1, 1, 1, -1], [-1, 1, 1, -1]],
dtype=dtype)
u, v = svd_flip(x, x.T, u_based_decision=u_based)
assert u.dtype == x.dtype
assert v.dtype == x.dtype
# Verify that all singular vectors have same
# sign except for the last one (i.e. last column)
y = x.copy()
y[:, -1] *= y.dtype.type(-1)
assert_eq(u, y)
assert_eq(v, y.T)
def test_svd_flip_sign(dtype, u_based):
try:
x = np.array(
[[1, -1, 1, -1], [1, -1, 1, -1], [-1, 1, 1, -1], [-1, 1, 1, -1]],
dtype=dtype,
)
except TypeError:
pytest.skip("128-bit floats not supported by NumPy")
u, v = svd_flip(x, x.T, u_based_decision=u_based)
assert u.dtype == x.dtype
assert v.dtype == x.dtype
# Verify that all singular vectors have same
# sign except for the last one (i.e. last column)
y = x.copy()
y[:, -1] *= y.dtype.type(-1)
assert_eq(u, y)
assert_eq(v, y.T)
