from meslas.sampling import GRF # Dimension of the response. n_out = 2 # Spatial Covariance. matern_cov = Matern32(lmbda=0.1, sigma=1.0) # Cross covariance. cross_cov = UniformMixing(gamma0=0.9, sigmas=[np.sqrt(0.25), np.sqrt(0.6)]) covariance = FactorCovariance(matern_cov, cross_cov, n_out=n_out) # Specify mean function mean = ConstantMean([1.0, 0]) # Create the GRF. myGRF = GRF(mean, covariance) # Create a regular square grid in 2 dims. # Number of repsones. dim = 2 my_grid = Grid(100, dim) # Sample all components at all locations. sample = myGRF.sample_grid(my_grid) # Plot. from meslas.plotting import plot_2d_slice plot_2d_slice(sample)
# Create a regular square grid in 2 dims.
# Number of respones.
dim = 2
my_grid = Grid(100, dim)
# Observe some data.
S_y = torch.tensor([[0.2, 0.1], [0.2, 0.2], [0.2, 0.3], [0.2, 0.4], [0.2, 0.5],
[0.2, 0.6], [0.2, 0.7], [0.2, 0.8], [0.2, 0.9], [0.2, 1.0],
[0.6, 0.5]])
L_y = torch.tensor([0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0]).long()
y = torch.tensor(11 * [-6])
mu_cond_grid, mu_cond_list, mu_cond_iso, K_cond_list, K_cond_iso = myGRF.krig_grid(
my_grid, S_y, L_y, y, noise_std=0.05, compute_post_cov=True)
# Compute coverage function on grid.
# Plot.
from meslas.plotting import plot_2d_slice, plot_krig_slice
plot_krig_slice(mu_cond_grid, S_y, L_y)
"""
K_cond_diag = torch.diagonal(K_cond_iso, dim1=0, dim2=1).T
lower = torch.tensor([-1.0, -1.0]).double()
coverage = coverage_fct_fixed_location(mu_cond_iso, K_cond_diag, lower, upper=None)
plot_2d_slice(coverage.reshape(my_grid.shape), title="Excursion Probability",
cmin=0, cmax=1.0)
"""
mu_cond_grid, mu_cond_list, mu_cond_iso, K_cond_list, K_cond_iso = myGRF.krig_grid(
my_grid, S_y, L_y, y, noise_std=0.05, compute_post_cov=True)
# Plot.
from meslas.plotting import plot_2d_slice, plot_krig_slice
plot_krig_slice(mu_cond_grid, S_y, L_y)
# Sample from the posterior.
from torch.distributions.multivariate_normal import MultivariateNormal
distr = MultivariateNormal(loc=mu_cond_list, covariance_matrix=K_cond_list)
sample = distr.sample()
# Reshape to a regular grid.
grid_sample = my_grid.isotopic_vector_to_grid(sample, n_out)
plot_krig_slice(grid_sample, S_y, L_y)
# Now compute and plot coverage function.
# Need only cross-covariances at fixed locations.
K_cond_diag = torch.diagonal(K_cond_iso, dim1=0, dim2=1).T
lower = torch.tensor([-1.0, -1.0]).double()
coverage = coverage_fct_fixed_location(mu_cond_iso,
K_cond_diag,
lower,
upper=None)
plot_2d_slice(coverage.reshape(my_grid.shape),
title="Excursion Probability",
cmin=0,
cmax=1.0)