def test_rbf_interpolation(self):
"""Test interpolation conditions.
Verify that the RBF interpolates at points.
"""
settings = RbfoptSettings()
for i in range(20):
dim = np.random.randint(1, 20)
num_points = np.random.randint(dim + 1, 50)
node_pos = np.random.uniform(-100, 100, size=(num_points, dim))
node_val = np.random.uniform(0, 100, num_points)
# Possible shapes of the matrix
for rbf_type in self.rbf_types:
settings.rbf = rbf_type
mat = ru.get_rbf_matrix(settings, dim, num_points, node_pos)
rbf_l, rbf_h = ru.get_rbf_coefficients(settings, dim,
num_points, mat,
node_val)
for i in range(num_points):
value = ru.evaluate_rbf(settings, node_pos[i], dim,
num_points, node_pos, rbf_l, rbf_h)
self.assertAlmostEqual(value,
node_val[i],
places=3,
msg='Interpolation failed' +
'with rbf ' + rbf_type)
def test_minimize_rbf_random(self):
"""Check solution of RBF minimization problem on random instances.
This function verifies that the solution of the RBF
minimization problem on small random problems is always no
worse than he best interpolation node.
"""
for i in range(10):
n = np.random.randint(4, 10)
k = np.random.randint(n + 1, n + 10)
var_lower = np.array([-5] * n)
var_upper = np.array([5] * n)
integer_vars = np.sort(np.random.choice(n, np.random.randint(n)))
node_pos = np.random.uniform(-5, 5, size=(k, n))
node_pos[:, integer_vars] = np.around(node_pos[:, integer_vars])
node_val = np.random.uniform(-10, 10, size=k)
best_node_pos = np.argmin(node_val)
for rbf_type in self.rbf_types:
settings = RbfoptSettings(rbf=rbf_type)
A = ru.get_rbf_matrix(settings, n, k, node_pos)
rbf_l, rbf_h = ru.get_rbf_coefficients(settings, n, k, A,
node_val)
sol = aux.minimize_rbf(settings, n, k, var_lower, var_upper,
integer_vars, None, node_pos, rbf_l,
rbf_h, node_pos[best_node_pos])
val = ru.evaluate_rbf(settings, sol, n, k, node_pos, rbf_l,
rbf_h)
self.assertLessEqual(val,
node_val[best_node_pos] + 1.0e-3,
msg='The minimize_rbf solution' +
' is worse than starting point' +
' with rbf ' + rbf_type)
def test_get_rbf_matrix(self):
"""Test basic properties of the RBF matrix (e.g. symmetry, size).
Verify that the RBF matrix is symmetric and it has the correct
size for all types of RBF.
"""
settings = RbfoptSettings()
for i in range(50):
dim = np.random.randint(1, 20)
num_points = np.random.randint(10, 50)
node_pos = np.random.uniform(-100, 100, size=(num_points, dim))
# Possible shapes of the matrix
for rbf_type in self.rbf_types:
settings.rbf = rbf_type
mat = ru.get_rbf_matrix(settings, dim, num_points, node_pos)
self.assertIsInstance(mat, np.ndarray)
self.assertEqual(len(mat.shape), 2)
self.assertAlmostEqual(np.max(mat - mat.transpose()),
0.0,
msg='RBF matrix is not symmetric')
size = num_points
if (ru.get_degree_polynomial(settings) >= 0):
size += 1
if (ru.get_degree_polynomial(settings) > 0):
size += dim**ru.get_degree_polynomial(settings)
self.assertEqual(mat.shape, (size, size))
# Check that exception is raised for unknown RBF types
settings.rbf = 'unknown'
self.assertRaises(ValueError, ru.get_rbf_matrix, settings, dim,
num_points, node_pos)
def test_get_rbf_matrix(self):
"""Test basic properties of the RBF matrix (e.g. symmetry, size).
Verify that the RBF matrix is symmetric and it has the correct
size for all types of RBF.
"""
settings = RbfoptSettings()
for i in range(50):
dim = np.random.randint(1, 20)
num_points = np.random.randint(10, 50)
node_pos = np.random.uniform(-100, 100, size=(num_points,dim))
# Possible shapes of the matrix
for rbf_type in self.rbf_types:
settings.rbf = rbf_type
mat = ru.get_rbf_matrix(settings, dim, num_points, node_pos)
self.assertIsInstance(mat, np.matrix)
self.assertAlmostEqual(np.max(mat - mat.transpose()), 0.0,
msg='RBF matrix is not symmetric')
size = num_points
if (ru.get_degree_polynomial(settings) >= 0):
size += 1
if (ru.get_degree_polynomial(settings) > 0):
size += dim ** ru.get_degree_polynomial(settings)
self.assertEqual(mat.shape, (size, size))
# Check that exception is raised for unknown RBF types
settings.rbf = 'unknown'
self.assertRaises(ValueError, ru.get_rbf_matrix, settings,
dim, num_points, node_pos)
def evaluateRBF(input):
#Single input for parallel processing
points, model = input
# Write error message
if len(points) == 0:
sys.stdout.write("No points to evaluate!\n")
sys.stdout.flush()
# Number of nodes at current iterbfopt_algtion
k = len(model.node_pos)
# Compute indices of fast node evaluations (sparse format)
fast_node_index = (np.nonzero(model.node_is_fast)[0]
if model.two_phase_optimization else np.array([]))
# Rescale nodes if necessary
tfv = rbfopt_utils.transform_function_values(model.l_settings,
np.array(model.node_val),
model.fmin, model.fmax,
fast_node_index)
(scaled_node_val, scaled_fmin, scaled_fmax, node_err_bounds,
rescale_function) = tfv
# Compute the matrices necessary for the algorithm
Amat = rbfopt_utils.get_rbf_matrix(model.l_settings, model.n, k,
np.array(model.node_pos))
# Get coefficients for the exact RBF
rc = rbfopt_utils.get_rbf_coefficients(model.l_settings, model.n, k, Amat,
scaled_node_val)
if (fast_node_index):
# RBF with some fast function evaluations
rc = aux.get_noisy_rbf_coefficients(model.l_settings, model.n, k,
Amat[:k, :k], Amat[:k, k:],
scaled_node_val, fast_node_index,
node_err_bounds, rc[0], rc[1])
(rbf_l, rbf_h) = rc
# Evaluate RBF
if len(points) <= 1:
values = []
for point in points:
values.append(
rbfopt_util.evaluate_rbf(model.l_settings, point, model.n, k,
np.array(model.node_pos), rbf_l,
rbf_h))
return values
else:
return rbfopt_utils.bulk_evaluate_rbf(model.l_settings,
np.array(points), model.n, k,
np.array(model.node_pos), rbf_l,
rbf_h)
def test_get_model_quality_estimate(self):
"""Test the get_model_quality_estimate function.
"""
for rbf in [
'cubic', 'thin_plate_spline', 'multiquadric', 'linear',
'gaussian'
]:
settings = RbfoptSettings(rbf=rbf)
error = ru.get_model_quality_estimate(settings, self.n, self.k,
self.node_pos, self.node_val,
self.k)
# Create a copy of the interpolation nodes and values
sorted_idx = self.node_val.argsort()
sorted_node_val = self.node_val[sorted_idx]
# Initialize the arrays used for the cross-validation
cv_node_pos = self.node_pos[sorted_idx[1:]]
cv_node_val = self.node_val[sorted_idx[1:]]
# The node that was left out
rm_node_pos = self.node_pos[sorted_idx[0]]
rm_node_val = self.node_val[sorted_idx[0]]
# Estimate of the model error
loo_error = 0.0
for i in range(self.k):
# Compute the RBF interpolant with one node left out
Amat = ru.get_rbf_matrix(settings, self.n, self.k - 1,
cv_node_pos)
rbf_l, rbf_h = ru.get_rbf_coefficients(settings, self.n,
self.k - 1, Amat,
cv_node_val)
# Compute value of the interpolant at the removed node
predicted_val = ru.evaluate_rbf(settings, rm_node_pos, self.n,
self.k - 1, cv_node_pos, rbf_l,
rbf_h)
# Update leave-one-out error
loc = np.searchsorted(sorted_node_val, predicted_val)
loo_error += abs(loc - i)
# Update the node left out
if (i < self.k - 1):
tmp = cv_node_pos[i].copy()
cv_node_pos[i] = rm_node_pos
rm_node_pos = tmp
cv_node_val[i], rm_node_val = rm_node_val, cv_node_val[i]
self.assertAlmostEqual(loo_error,
error,
msg='Model selection procedure ' +
'miscomputed the error')
def test_rbf_interpolation_cat(self):
"""Test interpolation conditions with categorical variables.
Verify that the RBF interpolates at points.
"""
settings = RbfoptSettings()
for i in range(20):
dim = np.random.randint(5, 15)
cat_dim = 8
# We need enough points to ensure the system is not singular
num_points = np.random.randint(2 * (dim + cat_dim), 60)
node_pos = np.hstack((np.random.uniform(-100,
100,
size=(num_points, dim)),
np.zeros(shape=(num_points, cat_dim))))
# Pick random categorical values
for j in range(num_points):
node_pos[j, dim + np.random.choice(4)] = 1
node_pos[j, dim + 4 + np.random.choice(4)] = 1
categorical_info = (np.array([0, 1]),
np.array([j + 2 for j in range(dim)]),
[(0, 0, np.array([dim + j for j in range(4)])),
(1, 0,
np.array([dim + 4 + j for j in range(4)]))])
node_val = np.random.uniform(0, 100, num_points)
# Possible shapes of the matrix
for rbf_type in self.rbf_types:
settings.rbf = rbf_type
mat = ru.get_rbf_matrix(settings, dim + cat_dim, num_points,
node_pos)
rbf_l, rbf_h = ru.get_rbf_coefficients(settings, dim + cat_dim,
num_points, mat,
node_val,
categorical_info)
for i in range(num_points):
value = ru.evaluate_rbf(settings, node_pos[i],
dim + cat_dim, num_points,
node_pos, rbf_l, rbf_h)
self.assertAlmostEqual(value,
node_val[i],
places=4,
msg='Interpolation failed ' +
'with rbf ' + rbf_type)
def test_get_model_quality_estimate(self):
"""Test the get_model_quality_estimate function.
"""
for rbf in ['cubic', 'thin_plate_spline', 'multiquadric',
'linear', 'gaussian']:
settings = RbfoptSettings(rbf=rbf)
error = ru.get_model_quality_estimate(
settings, self.n, self.k, self.node_pos,
self.node_val, self.k)
# Create a copy of the interpolation nodes and values
sorted_idx = self.node_val.argsort()
sorted_node_val = self.node_val[sorted_idx]
# Initialize the arrays used for the cross-validation
cv_node_pos = self.node_pos[sorted_idx[1:]]
cv_node_val = self.node_val[sorted_idx[1:]]
# The node that was left out
rm_node_pos = self.node_pos[sorted_idx[0]]
rm_node_val = self.node_val[sorted_idx[0]]
# Estimate of the model error
loo_error = 0.0
for i in range(self.k):
# Compute the RBF interpolant with one node left out
Amat = ru.get_rbf_matrix(settings, self.n, self.k-1,
cv_node_pos)
rbf_l, rbf_h = ru.get_rbf_coefficients(
settings, self.n, self.k-1, Amat, cv_node_val)
# Compute value of the interpolant at the removed node
predicted_val = ru.evaluate_rbf(settings, rm_node_pos,
self.n, self.k-1,
cv_node_pos, rbf_l, rbf_h)
# Update leave-one-out error
loc = np.searchsorted(sorted_node_val, predicted_val)
loo_error += abs(loc - i)
# Update the node left out
if (i < self.k - 1):
tmp = cv_node_pos[i].copy()
cv_node_pos[i] = rm_node_pos
rm_node_pos = tmp
cv_node_val[i], rm_node_val = rm_node_val, cv_node_val[i]
self.assertAlmostEqual(loo_error, error,
msg='Model selection procedure ' +
'miscomputed the error')
def test_rbf_interpolation(self):
"""Test interpolation conditions.
Verify that the RBF interpolates at points.
"""
settings = RbfoptSettings()
for i in range(20):
dim = np.random.randint(1, 20)
num_points = np.random.randint(10, 50)
node_pos = np.random.uniform(-100, 100, size=(num_points,dim))
node_val = np.random.uniform(0, 100, num_points)
# Possible shapes of the matrix
for rbf_type in self.rbf_types:
settings.rbf = rbf_type
mat = ru.get_rbf_matrix(settings, dim, num_points, node_pos)
rbf_l, rbf_h = ru.get_rbf_coefficients(
settings, dim, num_points, mat, node_val)
for i in range(num_points):
value = ru.evaluate_rbf(settings, node_pos[i], dim,
num_points, node_pos, rbf_l, rbf_h)
self.assertAlmostEqual(value, node_val[i], places=4,
msg='Interpolation failed' +
'with rbf ' + rbf_type)