def test_create_basis(V, D, DA, pathname_mesh, sqrt_num_boxes, sensors):
mesh_dictionary, region_dictionary = discretize_fem_mesh(
'square', pathname_mesh, sqrt_num_boxes)
phi = create_basis(V, D)
sigma, set_of_phi, set_of_da = create_sigma(region_dictionary, phi, DA)
# TODO: check why this is sensitive to initial epsilon value
p, ada = opa.optimal_arrangement(sensors, np.asarray(sigma), 100000, 10)
print(p, ada)
return phi, ada, set_of_phi, set_of_da
def adaptation_scheme_replacement(region_dictionary, node_solution, DA, t0,
t_resample, sensors):
node_solution = np.reshape(
node_solution,
(np.shape(node_solution)[0], 1, np.shape(node_solution)[1]))
total_time = np.shape(node_solution)[2]
# Keep start and end times of ada values
ada_vals = {}
# Calculate POD basis for initial set of data for time [0, t0)
truncated_data = node_solution[:, :, 0:t0]
phi = calculate_POD_basis(truncated_data, DA)
sigma, set_of_phi, set_of_da = create_sigma(region_dictionary, phi, DA)
# To start, information from whole field are used
ada_vals[(0, t0 - 1)] = list(set(region_dictionary.values()))
# Estimate optimal placement information from POD basis
p, ada = opa.optimal_arrangement(sensors, np.asarray(sigma), 1000, 10)
sample_start_time = t0
sample_end_time = t0 + t_resample
new_ada = ada
new_data = truncated_data
sigma_data = truncated_data
# TODO: check to make sure all the updated values are being updated correctly
while sample_start_time < total_time:
ada_vals[(sample_start_time,
min(sample_end_time, total_time) - 1)] = new_ada
# Estimate field from sensor arrangement [t0, t1)
# Get field measurements from time t0 to t1, apply estimation technique using selected sensors
print(new_ada)
estimated_vals = np.array([], dtype=np.float64).reshape(
np.shape(node_solution)[0], 0)
for time in range(sample_start_time, min(sample_end_time, total_time)):
y = node_solution[:, :, time] # Get data from original data set
set_of_y = y_set(region_dictionary, new_ada, y)
y_hat = state_estimation_2D(
new_ada, phi, set_of_phi, set_of_da,
set_of_y) # Estimated data -- add noise?
estimated_vals = np.concatenate((estimated_vals, y_hat), axis=1)
# Update POD with information from estimated field
# Add values to ORIGINAL data matrix -- can also add to POD estimated to get "lower order" estimates of field
estimated_vals = estimated_vals[:, np.newaxis, :]
if np.shape(sigma_data)[2] > np.shape(
estimated_vals[:, np.newaxis, :])[2]:
sigma_data = new_data[:, :,
np.shape(estimated_vals[:, np.newaxis, :]
)[2]:np.shape(new_data)[2]]
sigma_data = np.concatenate(
(np.asfarray(sigma_data), np.asfarray(estimated_vals)), axis=2)
else:
sigma_data = estimated_vals
new_data = np.concatenate(
(np.asfarray(new_data), np.asfarray(estimated_vals)), axis=2)
phi = calculate_POD_basis(sigma_data, DA)
new_sigma, set_of_phi, set_of_da = create_sigma(
region_dictionary, phi, DA)
# Calculate new optimal arrangement of sensors
p, new_ada = opa.optimal_arrangement(sensors, np.asarray(new_sigma),
1000, 10)
# Next iteration
sample_start_time = sample_end_time
sample_end_time = sample_start_time + t_resample
return new_data, ada_vals