def calculate_error(params, diff, func, grad):
"""Difference between numerical and analytical derivatives, devided by
analytial derivative.
Args:
params(np.array): 1d numpy array of function arguments
diff(np.array): difficulty parameter, controls wiggliness of the function
func(np.array): functions for which derivatives are calculated
grad(np.array): gradients of the functions
Returns:
error(np.array): numpy array of relative errors, calculated for different
methods
"""
method = ["center", "forward", "backward"]
error = {}
for i, m in enumerate(method):
diff_dict = {"diff": diff}
num_der = first_derivative(func,
params,
func_kwargs=diff_dict,
method=m)
analytical_der = grad(params, diff)
error[m] = (num_der - analytical_der) / np.abs(analytical_der).clip(
1e-8, np.inf)
return error
def test_first_derivative_scalar(method):
def f(x):
return x**2
calculated = first_derivative(f, 3.0)
expected = 6.0
aaae(calculated, expected)
def test_first_derivative_jacobian_richardson(
example_function_jacobian_fixtures):
f = example_function_jacobian_fixtures["func"]
fprime = example_function_jacobian_fixtures["func_prime"]
true_grad = fprime(np.ones(3))
numdifftools_grad = Jacobian(f, order=2, n=3, method="central")(np.ones(3))
grad = first_derivative(f, np.ones(3), n_steps=3, method="central")
aaae(numdifftools_grad, grad)
aaae(true_grad, grad)
def test_first_derivative_gradient(binary_choice_inputs, method):
fix = binary_choice_inputs
func = partial(logit_loglike, y=fix["y"], x=fix["x"])
calculated = first_derivative(
func=func,
method=method,
x=fix["params_np"],
n_steps=1,
f0=func(fix["params_np"]),
n_cores=1,
)
expected = logit_loglike_gradient(fix["params_np"], fix["y"], fix["x"])
aaae(calculated, expected, decimal=4)
def test_first_derivative_jacobian(binary_choice_inputs, method):
fix = binary_choice_inputs
func = partial(logit_loglikeobs, y=fix["y"], x=fix["x"])
calculated = first_derivative(
func=func,
method=method,
x=fix["params_np"],
n_steps=1,
base_steps=None,
lower_bounds=np.full(fix["params_np"].shape, -np.inf),
upper_bounds=np.full(fix["params_np"].shape, np.inf),
min_steps=1e-8,
step_ratio=2.0,
f0=func(fix["params_np"]),
n_cores=1,
)
expected = logit_loglikeobs_jacobian(fix["params_np"], fix["y"], fix["x"])
aaae(calculated, expected, decimal=6)
def test_first_derivative_jacobian_works_at_defaults(binary_choice_inputs):
fix = binary_choice_inputs
func = partial(logit_loglikeobs, y=fix["y"], x=fix["x"])
calculated = first_derivative(func=func, x=fix["params_np"])
expected = logit_loglikeobs_jacobian(fix["params_np"], fix["y"], fix["x"])
aaae(calculated, expected, decimal=6)