def test_cholesky():
rng = np.random.RandomState(4829)
m, n = 100, 100
A = rng.normal(size=(m, n))
b = rng.normal(size=(m, ))
x0, _, _, _ = np.linalg.lstsq(A, b)
x1, _ = _cholesky(A, b, 0, transpose=False)
x2, _ = _cholesky(A, b, 0, transpose=True)
assert np.allclose(x0, x1)
assert np.allclose(x0, x2)
def test_conjgrad():
rng = np.random.RandomState(4829)
A, b = get_system(1000, 100, 2, rng=rng)
sigma = 0.1 * A.max()
x0, _ = _cholesky(A, b, sigma)
x1, _ = _conjgrad(A, b, sigma, tol=1e-3)
x2, _ = _block_conjgrad(A, b, sigma, tol=1e-3)
assert np.allclose(x0, x1, atol=1e-6, rtol=1e-3)
assert np.allclose(x0, x2, atol=1e-6, rtol=1e-3)
def test_scipy_solvers():
rng = np.random.RandomState(4829)
A, b = get_system(1000, 100, 2, rng=rng)
sigma = 0.1 * A.max()
x0, _ = _cholesky(A, b, sigma)
x1, _ = _conjgrad_scipy(A, b, sigma)
x2, _ = _lsmr_scipy(A, b, sigma)
assert np.allclose(x0, x1, atol=1e-5, rtol=1e-3)
assert np.allclose(x0, x2, atol=1e-5, rtol=1e-3)
def test_conjgrad():
rng = np.random.RandomState(4829)
m, n = 100, 100
d = 1
A = rng.normal(size=(m, n))
b = rng.normal(size=(m, d))
sigma = 1
x0 = _cholesky(A, b, sigma)
x1, i = _conjgrad(A, b, sigma, tol=1e-3)
# assert np.allclose(x0, x1, atol=1e-3, rtol=1e-5)
assert np.allclose(x0, x1, atol=1e-5, rtol=1e-3)
