def test_scipy(method: str, method_options: Options, compute_jacobian: bool, use_weights: bool) -> None:
"""Test that the solution to the example fixed point problem from scipy.optimize.fixed_point is reasonably close to
the exact solution. Also verify that the configuration can be formatted.
"""
def contraction(x: Array) -> ContractionResults:
"""Evaluate the contraction."""
c1 = np.array([10, 12])
c2 = np.array([3, 5])
x0, x = x, np.sqrt(c1 / (x + c2))
weights = np.ones_like(x) if use_weights else None
jacobian = -0.5 * np.eye(2) * x / (x0 + c2) if compute_jacobian else None
return x, weights, jacobian
# simple methods do not accept an analytic Jacobian
if compute_jacobian and method not in {'hybr', 'lm'}:
return pytest.skip("This method does not accept an analytic Jacobian.")
# initialize the configuration and test that it can be formatted
iteration = Iteration(method, method_options, compute_jacobian)
assert str(iteration)
# define the exact solution
exact_values = np.array([1.4920333, 1.37228132])
# test that the solution is reasonably close (use the exact values if the iteration routine will just return them)
start_values = exact_values if method == 'return' else np.ones_like(exact_values)
computed_values, stats = iteration._iterate(start_values, contraction)
assert stats.converged
np.testing.assert_allclose(exact_values, computed_values, rtol=0, atol=1e-5)
def test_scipy(method: Union[str, Callable], method_options: Options, tol: float) -> None:
"""Test that the solution to the example fixed point problem from scipy.optimize.fixed_point is reasonably close to
the exact solution. Also verify that the configuration can be formatted.
"""
# test that the configuration can be formatted
if method != 'return':
method_options = method_options.copy()
method_options['tol'] = tol
iteration = Iteration(method, method_options)
assert str(iteration)
# test that the solution is reasonably close (use the exact values if the iteration routine will just return them)
contraction = lambda x: np.sqrt(np.array([10, 12]) / (x + np.array([3, 5])))
exact_values = np.array([1.4920333, 1.37228132])
start_values = exact_values if method == 'return' else np.ones_like(exact_values)
computed_values = iteration._iterate(start_values, contraction)[0]
np.testing.assert_allclose(exact_values, computed_values, rtol=0, atol=10 * tol)