def test_objective_sym_optimum():
sigma = 1.
lmbda = 1.
Z = np.random.randn(100, 2)
L = incomplete_cholesky_gaussian(Z, sigma, eta=0.1)["R"].T
a = develop_gaussian_low_rank.fit_sym(Z, sigma, lmbda, L)
b = develop_gaussian_low_rank.compute_b_sym(Z, L, sigma)
J_opt = develop_gaussian_low_rank.objective_sym(Z, sigma, lmbda, a, L, b)
for _ in range(10):
a_random = np.random.randn(len(Z))
J = develop_gaussian_low_rank.objective_sym(Z, sigma, lmbda, a_random, L)
assert J >= J_opt
def test_objective_sym_optimum():
sigma = 1.
lmbda = 1.
Z = np.random.randn(100, 2)
L = incomplete_cholesky_gaussian(Z, sigma, eta=0.1)["R"].T
a = develop_gaussian_low_rank.fit_sym(Z, sigma, lmbda, L)
b = develop_gaussian_low_rank.compute_b_sym(Z, L, sigma)
J_opt = develop_gaussian_low_rank.objective_sym(Z, sigma, lmbda, a, L, b)
for _ in range(10):
a_random = np.random.randn(len(Z))
J = develop_gaussian_low_rank.objective_sym(Z, sigma, lmbda, a_random,
L)
assert J >= J_opt
def test_objective_sym_matches_full():
sigma = 1.
lmbda = 1.
Z = np.random.randn(100, 2)
K = gaussian_kernel(Z, sigma=sigma)
a_opt = develop_gaussian.fit_sym(Z, sigma, lmbda, K)
J_opt = develop_gaussian.objective_sym(Z, sigma, lmbda, a_opt, K)
L = incomplete_cholesky_gaussian(Z, sigma, eta=0.01)["R"].T
a_opt_chol = develop_gaussian_low_rank.fit_sym(Z, sigma, lmbda, L)
J_opt_chol = develop_gaussian_low_rank.objective_sym(Z, sigma, lmbda, a_opt_chol, L)
assert_almost_equal(J_opt, J_opt_chol, delta=2.)
def test_objective_sym_matches_full():
sigma = 1.
lmbda = 1.
Z = np.random.randn(100, 2)
K = gaussian_kernel(Z, sigma=sigma)
a_opt = develop_gaussian.fit_sym(Z, sigma, lmbda, K)
J_opt = develop_gaussian.objective_sym(Z, sigma, lmbda, a_opt, K)
L = incomplete_cholesky_gaussian(Z, sigma, eta=0.01)["R"].T
a_opt_chol = develop_gaussian_low_rank.fit_sym(Z, sigma, lmbda, L)
J_opt_chol = develop_gaussian_low_rank.objective_sym(
Z, sigma, lmbda, a_opt_chol, L)
assert_almost_equal(J_opt, J_opt_chol, delta=2.)
def test_objective_matches_sym():
sigma = 1.
lmbda = 1.
Z = np.random.randn(100, 2)
kernel = lambda X, Y: gaussian_kernel(X, Y, sigma=sigma)
alpha = np.random.randn(len(Z))
temp = incomplete_cholesky(Z, kernel, eta=0.1)
I, R, nu = (temp["I"], temp["R"], temp["nu"])
R_test = incomplete_cholesky_new_points(Z, Z, kernel, I, R, nu)
b = gaussian_low_rank.compute_b(Z, Z, R.T, R_test.T, sigma)
J_sym = develop_gaussian_low_rank.objective_sym(Z, sigma, lmbda, alpha, R.T, b)
J = gaussian_low_rank.objective(Z, Z, sigma, lmbda, alpha, R.T, R_test.T, b)
assert_close(J, J_sym)
def test_objective_matches_sym():
sigma = 1.
lmbda = 1.
Z = np.random.randn(100, 2)
kernel = lambda X, Y: gaussian_kernel(X, Y, sigma=sigma)
alpha = np.random.randn(len(Z))
temp = incomplete_cholesky(Z, kernel, eta=0.1)
I, R, nu = (temp["I"], temp["R"], temp["nu"])
R_test = incomplete_cholesky_new_points(Z, Z, kernel, I, R, nu)
b = gaussian_low_rank.compute_b(Z, Z, R.T, R_test.T, sigma)
J_sym = develop_gaussian_low_rank.objective_sym(Z, sigma, lmbda, alpha,
R.T, b)
J = gaussian_low_rank.objective(Z, Z, sigma, lmbda, alpha, R.T, R_test.T,
b)
assert_close(J, J_sym)