def compute_vectorfield_pointsvectorcoeff(points, vectors, alpha):
#nb_vectors = vectors.shape[1]
vector_translations = np.dot(np.array(vectors), np.array(alpha))
structured = struct.create_structured(points, vector_translations)
unstructured = gen_unstructured(structured)
return unstructured.copy()
def test_translation_action():
space = odl.uniform_discr(min_pt=[-1],
max_pt=[1],
shape=[128],
dtype='float32',
interp='linear')
points = np.array([[
-0.75,
0.0,
0.2,
0.5,
]])
vectors = np.array([[
0.3,
0.0,
0,
1,
]])
original = struct.create_structured(points, vectors)
translation_action = get_action(space)
translation = np.array([1.0])
expected = translation_action(translation, original)
g = group.Translation(space)
computed = action.apply_element_to_field(g, translation, original)
npt.assert_allclose(computed, expected)
def test_calibration():
space = odl.uniform_discr(min_pt=[-1],
max_pt=[1],
shape=[128],
dtype='float32',
interp='linear')
cell_side = space.cell_sides
#kernel = get_kernel(space)
kernel = get_kernel_gauss(space, 0.2)
def product(f, g):
return struct.scalar_product_structured(f, g, kernel)
#points = space.points()[::2].T
points = np.array([[
-0.75,
0.0,
0.2,
0.5,
]])
vectors = np.array([[
0.3,
0.0,
0,
1,
]])
original = struct.create_structured(points, vectors)
g = group.Translation(space)
translation = np.array([1.0])
translated = action.apply_element_to_field(g, translation, original)
covariance_matrix = struct.make_covariance_matrix(space.points().T, kernel)
noise_l2 = odl.phantom.noise.white_noise(space) * 0.05
decomp = np.linalg.cholesky(covariance_matrix +
1e-5 * np.identity(len(covariance_matrix)))
noise_rkhs = np.dot(decomp, noise_l2)
get_unstructured = struct.get_from_structured_to_unstructured(
space, kernel)
noisy = space.tangent_bundle.element(
get_unstructured(translated) + noise_rkhs)
def act(element, struct):
return action.apply_element_to_field(g, element, struct)
result_calibration = calib.calibrate(original, noisy, g, act, product,
struct.scalar_product_unstructured)
estimated_translated = get_unstructured(act(result_calibration.x,
original))
print('real = {}, computed ={} , log diff = {}'.format(
translation, result_calibration.x,
np.log10(np.abs(translation[0] - result_calibration.x[0]))))
def act(translation, f):
points = struct.get_points(f)
vectors = struct.get_vectors(f)
dim, nb_points = points.shape
points_translated = np.array(
[[points[u][v] + translation[u] for v in range(nb_points)]
for u in range(dim)])
points_translated_projected = proj(points_translated)
return struct.create_structured(points_translated_projected, vectors)
def iterative_scheme(solve_regression, calibration, action, g, kernel,
field_list, sigma0, sigma1, points, nb_iteration):
nb_data = len(field_list)
eval_kernel = struct.make_covariance_matrix(points, kernel)
dim, nb_points = points.shape
def product(vect0, vect1):
return struct.scalar_product_structured(vect0, vect1, kernel)
# initialization with a structured version of first vector field (NOT GOOD)
group_element_init = g.identity
vectors_original = solve_regression(g, [group_element_init],
[field_list[0]], sigma0, sigma1,
points, eval_kernel)
vectors_original_struct = struct.get_structured_vectors_from_concatenated(
vectors_original, nb_points, dim)
original = struct.create_structured(points, vectors_original_struct)
get_unstructured_op = struct.get_from_structured_to_unstructured(
field_list[0].space[0], kernel)
get_unstructured_op(original).show('initialisation')
for k in range(nb_iteration):
velocity_list = calibrate_list(original, field_list, calibration)
group_element_list = [
g.exponential(velocity_list[i]) for i in range(nb_data)
]
vectors_original = solve_regression(g, group_element_list, field_list,
sigma0, sigma1, points,
eval_kernel)
vectors_original_struct = struct.get_structured_vectors_from_concatenated(
vectors_original, nb_points, dim)
original = struct.create_structured(points, vectors_original_struct)
print('iteration {}'.format(k))
get_unstructured_op(original).show('iteration {}'.format(k))
return [original, group_element_list]
vector_syst = np.zeros(dim * nb_points)
basis = np.identity(dim)
for k0 in range(nb_points):
for l0 in range(dim):
vector_syst[dim * k0 + l0] += np.dot(eval_field.T[k0], basis[:,
l0])
eval_kernel = struct.make_covariance_matrix(points, kernel)
matrix_syst = np.kron(eval_kernel, basis)
alpha_concatenated = np.linalg.solve(matrix_syst, vector_syst)
alpha = struct.get_structured_vectors_from_concatenated(
alpha_concatenated, nb_points, dim)
structured = struct.create_structured(points, alpha)
structured_list.append(structured.copy())
unstructured_list.append(get_unstructured_op(structured).copy())
#
#%% See projection
#plt.plot(points[0] , points[1], 'xb')
for i in range(nbdata):
space.tangent_bundle.element([
vector_fields_list[i][:, :, u] for u in range(2)
])[0].show('truth' + str(i), clim=[-5, 5])
plt.plot(param.T[i][0::2], param.T[i][1::2], 'xb')
unstructured_list[i][0].show('projected' + str(i), clim=[-5, 5])
plt.plot(param.T[i][0::2], param.T[i][1::2], 'xb')
# kern_discr = kern_app_point(mg)
#
# unstructured += space.tangent_bundle.element([kern_discr * vect for vect in vectors[:, k]]).copy()
#
# return unstructured
get_unstructured_op_generate = struct.get_from_structured_to_unstructured(
space, kernel_generate)
#%% define data
dim = 1
nb_pt_generate = 3
points_truth = np.random.uniform(low=-1.0, high=1.0, size=nb_pt_generate)
vectors_truth = np.random.uniform(low=-1.0, high=1.0, size=nb_pt_generate)
original = struct.create_structured(points_truth, vectors_truth)
original_unstructured = get_unstructured_op_generate(original)
data_list = []
nb_data = 10
translation_list = np.random.uniform(low=-1.0, high=1.0, size=nb_data)
covariance_matrix = struct.make_covariance_matrix(space.points().T,
kernel_generate)
noise_l2 = odl.phantom.noise.white_noise(odl.ProductSpace(space,
nb_data)) * 0.1
decomp = np.linalg.cholesky(covariance_matrix +
1e-4 * np.identity(len(covariance_matrix)))
noise_rkhs = [np.dot(decomp, noise_l2[i]) for i in range(nb_data)]
pts_space = space.points().T
#data_list=[]
#for i in range(nb_data):
# pts_displaced = g.apply(np.array([-translation_list[i]]), pts_space)
def mult_scalar_structured_np(scal, structured):
points = structured[0:dim]
vectors = structured[dim:2 * dim]
vectors_mult = scal * vectors
return struct.create_structured(points, vectors_mult)
#%%% Visualize results
def kernel_np(x, y):
#si = tf.shape(x)[0]
return np.exp(-sum([(x[i] - y[i])**2 for i in range(dim)]) / (sigma**2))
get_unstructured_op = struct.get_from_structured_to_unstructured(
space, kernel_np)
structured_computed = []
unstructured_computed = []
fac = []
for i in range(nbdatamax):
structured_temp = struct.create_structured(points_list[i],
np.dot(vectors_list[i], alpha))
prod = struct.scalar_product_structured(structured_temp,
structured_list[i], kernel_np)
squared_norm = struct.scalar_product_structured(structured_temp,
structured_temp, kernel_np)
fac.append(prod / squared_norm)
structured_computed.append(structured_temp.copy())
unstructured_computed.append(get_unstructured_op(structured_temp).copy())
#
for i in range(nbdatamax):
get_unstructured_op(structured_list[i]).show(
'unstructured data {}'.format(i))
(fac[i] * unstructured_computed[i]).show(
'unstructured computed {}'.format(i))
#
dx = round((xmax - xmin) / (fac * sigma_kernel))
ymin = -3.0
ymax = 3.0
dy = round((ymax - ymin) / (fac * sigma_kernel))
points_list_gen = []
for i in range(dx + 1):
for j in range(dy + 1):
points_list_gen.append([
xmin + fac * sigma_kernel * i * 1.0,
ymin + fac * sigma_kernel * j * 1.0
])
points_list_gen = np.array(points_list_gen)
nb_pts_gen = len(points_list_gen)
vectors_truth = np.random.uniform(low=-1.0, high=1.0, size=[2, nb_pts_gen])
original = struct.create_structured(points_list_gen.T, vectors_truth)
original_unstructured = get_unstructured_op(original)
data_list = []
nb_data = 10
translation_list = np.random.uniform(low=-1.0, high=1.0, size=[2, nb_data])
scaling_list = np.abs(np.random.normal(1, 1, nb_data)) #1. + np.zeros(nb_data)
theta_list = np.random.uniform(low=-np.pi, high=np.pi, size=nb_data)
param_transfor_list = np.array([
g.exponential(
np.array([
scaling_list[i], theta_list[i], translation_list[0, i],
translation_list[1, i]
])) for i in range(nb_data)
])