def test_richardson_solve_precision(self):
"""Check that precision is maintained even across many orders of magnitude."""
matrix = (jnp.eye(50) -
jnp.diag(jnp.full([49], 0.1), -1)).astype("float32")
b = jnp.array([1.] + [0.] * 49, dtype="float32")
x_est = linear_solvers.richardson_solve(lambda x: matrix @ x,
b,
iterations=50)
x_expected = jnp.power(10., -jnp.arange(50)).astype("float32")
# Both the closed-form and estimated values should round off to zero at the
# same time; the only limit should be the resolution of float32 and not
# any inaccuracies during the solve.
np.testing.assert_allclose(x_est, x_expected, atol=0, rtol=1e-5)
def structured_iter_solve(m1, m2, m3, b1, b2):
return linear_solvers.richardson_solve(functools.partial(
structured_matvec, m1, m2, m3), (b1, b2),
iterations=200)
def iter_solve(matrix, b):
return linear_solvers.richardson_solve(lambda x: matrix @ x,
b,
iterations=100)