def test_homoscedastic_doptimality_criterion(self):
poly_degree = 3
num_design_pts = 11
design_samples = np.linspace(-1, 1, num_design_pts)
noise_multiplier = None
design_factors = univariate_monomial_basis_matrix(
poly_degree, design_samples)
homog_outer_prods = compute_homoscedastic_outer_products(
design_factors)
doptimality_criterion_wrapper = partial(doptimality_criterion,
homog_outer_prods,
design_factors)
diffs = check_derivative(doptimality_criterion_wrapper, num_design_pts)
#print (diffs)
assert diffs.min() < 5e-5, diffs
mu = np.random.uniform(0, 1, (num_design_pts))
mu /= mu.sum()
M1 = homog_outer_prods.dot(mu)
print(np.linalg.det(M1),
doptimality_criterion_wrapper(mu, return_grad=False))
assert np.allclose(
np.log(np.linalg.det(np.linalg.inv(M1))),
doptimality_criterion_wrapper(mu, return_grad=False))
jac = lambda x: doptimality_criterion(homog_outer_prods,
design_factors, x)[1]
hess_matvec = lambda x, p: doptimality_criterion(
homog_outer_prods, design_factors, x, return_hessian=True)[2].dot(p
)
pya.check_hessian(jac, hess_matvec, mu[:, np.newaxis])
def test_rosenbrock_function_gradient_and_hessian_prod(self):
benchmark = setup_benchmark("rosenbrock", nvars=2)
init_guess = benchmark.variable.get_statistics('mean')+\
benchmark.variable.get_statistics('std')
errors = pya.check_gradients(benchmark.fun,
benchmark.jac,
init_guess,
disp=False)
assert errors.min() < 1e-5
errors = pya.check_hessian(benchmark.jac,
benchmark.hessp,
init_guess,
disp=False)
assert errors.min() < 1e-5
def test_ishigami_function_gradient_and_hessian(self):
benchmark = setup_benchmark("ishigami", a=7, b=0.1)
init_guess = benchmark.variable.get_statistics('mean')+\
benchmark.variable.get_statistics('std')
errors = pya.check_gradients(benchmark.fun,
benchmark.jac,
init_guess,
disp=False)
assert errors.min() < 2e-7
hess_matvec = lambda x, v: np.dot(benchmark.hess(x), v)
errors = pya.check_hessian(benchmark.jac,
hess_matvec,
init_guess,
disp=False)
assert errors.min() < 2e-7
