def test_calculate_gradients_rbf(self):
"""
Test :meth:`bet.sensitivity.gradients.calculate_gradients_rbf`.
"""
self.output_set = sample.sample_set(self.output_dim)
self.cluster_set = grad.sample_l1_ball(self.input_set_centers,
self.num_close, self.rvec)
num_centers = self.input_set_centers.check_num()
self.output_set.set_values(self.cluster_set._values.dot(self.coeffs))
self.cluster_disc = sample.discretization(self.cluster_set,
self.output_set)
self.center_disc = grad.calculate_gradients_rbf(self.cluster_disc,
num_centers)
# Test the method returns the correct size tensor
self.jacobians = self.center_disc._input_sample_set._jacobians
self.assertEqual(self.jacobians.shape, (self.num_centers,
self.output_dim, self.input_dim))
# Test that each vector is normalized or a zero vector
normG = np.linalg.norm(self.jacobians, ord=1, axis=2)
# If its a zero vectors, make it the unit vector in input_dim
self.jacobians[normG==0] = 1.0/self.input_dim
nptest.assert_array_almost_equal(np.linalg.norm(self.jacobians, ord=1,
axis=2), np.ones((self.jacobians.shape[0],
self.jacobians.shape[1])))
def setUp(self):
# Define the parameter space (Lambda)
self.input_dim = 2
self.input_set_rbf = sample.sample_set(self.input_dim)
self.input_set_ffd = sample.sample_set(self.input_dim)
self.input_set_cfd = sample.sample_set(self.input_dim)
self.input_set_centers = sample.sample_set(self.input_dim)
self.output_dim = 2
self.output_set_rbf = sample.sample_set(self.output_dim)
self.output_set_ffd = sample.sample_set(self.output_dim)
self.output_set_cfd = sample.sample_set(self.output_dim)
self.lam_domain = np.zeros((self.input_dim, 2))
self.lam_domain[:, 0] = np.zeros(self.input_dim)
self.lam_domain[:, 1] = np.ones(self.input_dim)
self.input_set_rbf.set_domain(self.lam_domain)
self.input_set_ffd.set_domain(self.lam_domain)
self.input_set_cfd.set_domain(self.lam_domain)
# Choose random centers to cluster points around
self.num_centers = 100
np.random.seed(0)
self.centers = (self.lam_domain[:, 1] - self.lam_domain[:, 0]) * \
np.random.random((self.num_centers, self.input_dim)) + \
self.lam_domain[:, 0]
self.input_set_centers.set_values(self.centers)
self.num_close = self.input_dim + 1
self.rvec = 0.01 * np.ones(self.input_dim)
self.input_set_rbf = grad.sample_l1_ball(self.input_set_centers,
self.num_close, self.rvec)
self.input_set_ffd = grad.pick_ffd_points(self.input_set_centers,
self.rvec)
self.input_set_cfd = grad.pick_cfd_points(self.input_set_centers,
self.rvec)
# Define a vector valued function f : [0,1]x[0,1] -> [x^2, y^2]
def f(x):
f = np.zeros(x.shape)
f[:, 0] = x[:, 0]**2
f[:, 1] = x[:, 1]**2
return f
self.output_set_rbf.set_values(f(self.input_set_rbf.get_values()))
self.output_set_ffd.set_values(f(self.input_set_ffd.get_values()))
self.output_set_cfd.set_values(f(self.input_set_cfd.get_values()))
self.cluster_disc_rbf = sample.discretization(self.input_set_rbf,
self.output_set_rbf)
self.cluster_disc_ffd = sample.discretization(self.input_set_ffd,
self.output_set_ffd)
self.cluster_disc_cfd = sample.discretization(self.input_set_cfd,
self.output_set_cfd)
self.G_exact = np.zeros(
[self.num_centers, self.output_dim, self.input_dim])
self.G_exact[:, 0, 0] = 2 * self.centers[:, 0]
self.G_exact[:, 1, 1] = 2 * self.centers[:, 1]
def setUp(self):
self.input_dim = 2
self.input_set = sample.sample_set(self.input_dim)
self.input_set_centers = sample.sample_set(self.input_dim)
self.output_dim_return = 2
self.num_optsets_return = 5
self.radius = 0.01
np.random.seed(0)
self.num_centers = 10
self.centers = np.random.random((self.num_centers, self.input_dim))
self.input_set_centers.set_values(self.centers)
self.input_set = grad.sample_l1_ball(self.input_set_centers,
self.input_dim + 1, self.radius)
self.output_dim = 28
self.output_set = sample.sample_set(self.output_dim)
coeffs = np.zeros((self.input_dim, 2*self.input_dim))
coeffs = np.append(coeffs, np.random.random((self.input_dim,
self.output_dim - 3 * self.input_dim)), axis=1)
self.coeffs = np.append(coeffs, np.eye(self.input_dim), axis=1)
self.output_set.set_values(self.input_set._values.dot(self.coeffs))
self.my_disc = sample.discretization(self.input_set,
self.output_set)
self.center_disc = grad.calculate_gradients_rbf(\
self.my_disc, self.num_centers)
self.input_set_centers = self.center_disc.get_input_sample_set()
self.inner_prod_tol = 0.9
self.measskew_tol = np.inf
def setUp(self):
self.Lambda_dim = 2
self.num_qois_return = 2
self.num_optsets_return = 5
self.radius = 0.01
np.random.seed(0)
self.num_centers = 10
self.centers = np.random.random((self.num_centers, self.Lambda_dim))
self.samples = grad.sample_l1_ball(self.centers, self.Lambda_dim + 1,
self.radius)
self.num_qois = 28
coeffs = np.zeros((self.Lambda_dim, 2 * self.Lambda_dim))
coeffs = np.append(coeffs,
np.random.random(
(self.Lambda_dim,
self.num_qois - 3 * self.Lambda_dim)),
axis=1)
self.coeffs = np.append(coeffs, np.eye(self.Lambda_dim), axis=1)
self.data = self.samples.dot(self.coeffs)
self.G = grad.calculate_gradients_rbf(self.samples, self.data,
self.centers)
self.inner_prod_tol = 0.9
self.cond_tol = np.inf
def setUp(self):
# Define the parameter space (Lambda)
self.input_dim = 2
self.input_set_rbf = sample.sample_set(self.input_dim)
self.input_set_ffd = sample.sample_set(self.input_dim)
self.input_set_cfd = sample.sample_set(self.input_dim)
self.input_set_centers = sample.sample_set(self.input_dim)
self.output_dim = 2
self.output_set_rbf = sample.sample_set(self.output_dim)
self.output_set_ffd = sample.sample_set(self.output_dim)
self.output_set_cfd = sample.sample_set(self.output_dim)
self.lam_domain = np.zeros((self.input_dim, 2))
self.lam_domain[:, 0] = np.zeros(self.input_dim)
self.lam_domain[:, 1] = np.ones(self.input_dim)
self.input_set_rbf.set_domain(self.lam_domain)
self.input_set_ffd.set_domain(self.lam_domain)
self.input_set_cfd.set_domain(self.lam_domain)
# Choose random centers to cluster points around
self.num_centers = 100
np.random.seed(0)
self.centers = (self.lam_domain[:, 1] - self.lam_domain[:, 0]) * \
np.random.random((self.num_centers, self.input_dim)) + \
self.lam_domain[:, 0]
self.input_set_centers.set_values(self.centers)
self.num_close = self.input_dim + 1
self.rvec = 0.01 * np.ones(self.input_dim)
self.input_set_rbf = grad.sample_l1_ball(self.input_set_centers,
self.num_close, self.rvec)
self.input_set_ffd = grad.pick_ffd_points(self.input_set_centers,
self.rvec)
self.input_set_cfd = grad.pick_cfd_points(self.input_set_centers,
self.rvec)
# Define a vector valued function f : [0,1]x[0,1] -> [x^2, y^2]
def f(x):
f = np.zeros(x.shape)
f[:, 0] = x[:, 0]**2
f[:, 1] = x[:, 1]**2
return f
self.output_set_rbf.set_values(f(self.input_set_rbf.get_values()))
self.output_set_ffd.set_values(f(self.input_set_ffd.get_values()))
self.output_set_cfd.set_values(f(self.input_set_cfd.get_values()))
self.cluster_disc_rbf = sample.discretization(
self.input_set_rbf, self.output_set_rbf)
self.cluster_disc_ffd = sample.discretization(
self.input_set_ffd, self.output_set_ffd)
self.cluster_disc_cfd = sample.discretization(
self.input_set_cfd, self.output_set_cfd)
self.G_exact = np.zeros([self.num_centers, self.output_dim,
self.input_dim])
self.G_exact[:, 0, 0] = 2 * self.centers[:, 0]
self.G_exact[:, 1, 1] = 2 * self.centers[:, 1]
def setUp(self):
self.input_dim = 2
self.input_set = sample.sample_set(self.input_dim)
self.input_set_centers = sample.sample_set(self.input_dim)
self.output_dim_return = 2
self.num_optsets_return = 5
self.radius = 0.01
np.random.seed(0)
self.num_centers = 10
self.centers = np.random.random((self.num_centers, self.input_dim))
self.input_set_centers.set_values(self.centers)
self.input_set = grad.sample_l1_ball(self.input_set_centers,
self.input_dim + 1, self.radius)
self.output_dim = 28
self.output_set = sample.sample_set(self.output_dim)
coeffs = np.zeros((self.input_dim, 2 * self.input_dim))
coeffs = np.append(coeffs,
np.random.random(
(self.input_dim,
self.output_dim - 3 * self.input_dim)),
axis=1)
self.coeffs = np.append(coeffs, np.eye(self.input_dim), axis=1)
self.output_set.set_values(self.input_set._values.dot(self.coeffs))
self.my_disc = sample.discretization(self.input_set, self.output_set)
self.center_disc = grad.calculate_gradients_rbf(\
self.my_disc, self.num_centers)
self.input_set_centers = self.center_disc.get_input_sample_set()
self.inner_prod_tol = 0.9
self.measskew_tol = np.inf
def test_sample_l1_ball(self):
"""
Test :meth:`bet.sensitivity.gradients.sample_l1_ball`.
"""
self.samples = grad.sample_l1_ball(self.centers, self.num_close,
self.rvec)
# Test that the samples are within max(rvec) of center (l1 dist)
self.repeat = np.repeat(self.centers, self.num_close, axis=0)
nptest.assert_array_less(np.linalg.norm(self.samples[self.num_centers:]\
- self.repeat, 1, axis=1), np.max(self.rvec))
# Test the method returns the correct dimensions
self.assertEqual(self.samples.shape, ((self.num_close+1) * \
self.num_centers, self.Lambda_dim))
def test_sample_l1_ball(self):
"""
Test :meth:`bet.sensitivity.gradients.sample_l1_ball`.
"""
self.samples = grad.sample_l1_ball(self.centers, self.num_close,
self.rvec)
# Test that the samples are within max(rvec) of center (l1 dist)
self.repeat = np.repeat(self.centers, self.num_close, axis=0)
nptest.assert_array_less(np.linalg.norm(self.samples[self.num_centers:]\
- self.repeat, 1, axis=1), np.max(self.rvec))
# Test the method returns the correct dimensions
self.assertEqual(self.samples.shape, ((self.num_close+1) * \
self.num_centers, self.Lambda_dim))
def setUp(self):
self.Lambda_dim = 4
self.num_qois_return = 4
self.num_optsets_return = 5
self.radius = 0.01
np.random.seed(0)
self.num_centers = 10
self.centers = np.random.random((self.num_centers, self.Lambda_dim))
self.samples = grad.sample_l1_ball(self.centers, self.Lambda_dim + 1, self.radius)
self.num_qois = 20
coeffs = np.random.random((self.Lambda_dim, self.num_qois - self.Lambda_dim))
self.coeffs = np.append(coeffs, np.eye(self.Lambda_dim), axis=1)
self.data = self.samples.dot(self.coeffs)
self.G = grad.calculate_gradients_rbf(self.samples, self.data, self.centers)
def test_calculate_gradients_rbf(self):
"""
Test :meth:`bet.sensitivity.gradients.calculate_gradients_rbf`.
"""
self.samples = grad.sample_l1_ball(self.centers, self.num_close,
self.rvec)
self.data = self.samples.dot(self.coeffs)
self.G = grad.calculate_gradients_rbf(self.samples, self.data,
self.centers)
# Test the method returns the correct size tensor
self.assertEqual(self.G.shape, (self.num_centers, self.num_qois,
self.Lambda_dim))
# Test that each vector is normalized or a zero vector
normG = np.linalg.norm(self.G, axis=2)
# If its a zero vectors, make it the unit vector in Lambda_dim
self.G[normG==0] = 1.0/np.sqrt(self.Lambda_dim)
nptest.assert_array_almost_equal(np.linalg.norm(self.G, axis=2),
np.ones((self.G.shape[0], self.G.shape[1])))
def test_calculate_gradients_rbf(self):
"""
Test :meth:`bet.sensitivity.gradients.calculate_gradients_rbf`.
"""
self.samples = grad.sample_l1_ball(self.centers, self.num_close,
self.rvec)
self.data = self.samples.dot(self.coeffs)
self.G = grad.calculate_gradients_rbf(self.samples, self.data,
self.centers)
# Test the method returns the correct size tensor
self.assertEqual(self.G.shape,
(self.num_centers, self.num_qois, self.Lambda_dim))
# Test that each vector is normalized or a zero vector
normG = np.linalg.norm(self.G, ord=1, axis=2)
# If its a zero vectors, make it the unit vector in Lambda_dim
self.G[normG == 0] = 1.0 / self.Lambda_dim
nptest.assert_array_almost_equal(
np.linalg.norm(self.G, ord=1, axis=2),
np.ones((self.G.shape[0], self.G.shape[1])))
def setUp(self):
self.Lambda_dim = 2
self.num_qois_return = 2
self.num_optsets_return = 5
self.radius = 0.01
np.random.seed(0)
self.num_centers = 10
self.centers = np.random.random((self.num_centers, self.Lambda_dim))
self.samples = grad.sample_l1_ball(self.centers,
self.Lambda_dim + 1, self.radius)
self.num_qois = 28
coeffs = np.zeros((self.Lambda_dim, 2*self.Lambda_dim))
coeffs = np.append(coeffs, np.random.random((self.Lambda_dim,
self.num_qois - 3 * self.Lambda_dim)), axis=1)
self.coeffs = np.append(coeffs, np.eye(self.Lambda_dim), axis=1)
self.data = self.samples.dot(self.coeffs)
self.G = grad.calculate_gradients_rbf(self.samples, self.data,
self.centers)
self.inner_prod_tol = 0.9
self.cond_tol = sys.float_info[0]
def setUp(self):
# Define the parameter space (Lambda)
self.Lambda_dim = 2
self.num_qois = 2
self.lam_domain = np.zeros((self.Lambda_dim, 2))
self.lam_domain[:, 0] = np.zeros(self.Lambda_dim)
self.lam_domain[:, 1] = np.ones(self.Lambda_dim)
# Choose random centers to cluster points around
self.num_centers = 100
np.random.seed(0)
self.centers = (self.lam_domain[:,1] - self.lam_domain[:,0]) * \
np.random.random((self.num_centers,self.Lambda_dim)) + \
self.lam_domain[:,0]
self.num_close = self.Lambda_dim + 1
self.rvec = 0.01 * np.ones(self.Lambda_dim)
self.samples_rbf = grad.sample_l1_ball(self.centers, self.num_close,
self.rvec)
self.samples_ffd = grad.pick_ffd_points(self.centers, self.rvec)
self.samples_cfd = grad.pick_cfd_points(self.centers, self.rvec)
# Define a vector valued function f : [0,1]x[0,1] -> [x^2, y^2]
def f(x):
f = np.zeros(x.shape)
f[:, 0] = x[:, 0]**2
f[:, 1] = x[:, 1]**2
return f
self.data_nonlin_rbf = f(self.samples_rbf)
self.data_nonlin_ffd = f(self.samples_ffd)
self.data_nonlin_cfd = f(self.samples_cfd)
self.G_exact = np.zeros(
[self.num_centers, self.num_qois, self.Lambda_dim])
self.G_exact[:, 0, 0] = 2 * self.centers[:, 0]
self.G_exact[:, 1, 1] = 2 * self.centers[:, 1]
def setUp(self):
# Define the parameter space (Lambda)
self.Lambda_dim = 2
self.num_qois = 2
self.lam_domain = np.zeros((self.Lambda_dim, 2))
self.lam_domain[:,0] = np.zeros(self.Lambda_dim)
self.lam_domain[:,1] = np.ones(self.Lambda_dim)
# Choose random centers to cluster points around
self.num_centers = 100
np.random.seed(0)
self.centers = (self.lam_domain[:,1] - self.lam_domain[:,0]) * \
np.random.random((self.num_centers,self.Lambda_dim)) + \
self.lam_domain[:,0]
self.num_close = self.Lambda_dim + 1
self.rvec = 0.01 * np.ones(self.Lambda_dim)
self.samples_rbf = grad.sample_l1_ball(self.centers, self.num_close,
self.rvec)
self.samples_ffd = grad.pick_ffd_points(self.centers, self.rvec)
self.samples_cfd = grad.pick_cfd_points(self.centers, self.rvec)
# Define a vector valued function f : [0,1]x[0,1] -> [x^2, y^2]
def f(x):
f = np.zeros(x.shape)
f[:, 0] = x[:, 0]**2
f[:, 1] = x[:, 1]**2
return f
self.data_nonlin_rbf = f(self.samples_rbf)
self.data_nonlin_ffd = f(self.samples_ffd)
self.data_nonlin_cfd = f(self.samples_cfd)
self.G_exact = np.zeros([self.num_centers, self.num_qois,
self.Lambda_dim])
self.G_exact[:, 0, 0] = 2 * self.centers[:, 0]
self.G_exact[:, 1, 1] = 2 * self.centers[:, 1]
