# ------------------------------------------------------
# Create a regular square grid in 2 dims.
my_grid = TriangularGrid(31)
print("Working on an equilateral triangular grid with {} nodes.".format(
my_grid.n_points))
# Discretize the GRF on a grid and be done with it.
# From now on we only consider locatoins on the grid.
my_discrete_grf = DiscreteGRF.from_model(myGRF, my_grid)
# ------------------------------------------------------
# Sample and plot
# ------------------------------------------------------
# Sample all components at all locations.
sample = my_discrete_grf.sample()
plot_grid_values(my_grid, sample)
# From now on, we will consider the drawn sample as ground truth.
# ---------------------------------------------------------------
ground_truth = sample
# Save for reproducibility.
np.save("ground_truth.npy", ground_truth.numpy())
# Use it to declare the data feed.
noise_std = torch.tensor([0.1, 0.1])
# Noise distribution
lower_chol = psd_safe_cholesky(torch.diag(noise_std**2))
noise_distr = MultivariateNormal(loc=torch.zeros(n_out), scale_tril=lower_chol)
def data_feed(node_ind):
# Specify mean function
mean = ConstantMean([0.0, 5.0])
# Create the GRF.
myGRF = GRF(mean, covariance)
# Create an equilateral triangular grid in 2 dims.
# Number of respones.
my_grid = TriangularGrid(40)
my_square_grid = SquareGrid(50, 2)
my_discrete_grf = DiscreteGRF.from_model(myGRF, my_grid)
# Sample and plot.
sample = my_discrete_grf.sample()
plot_grid_values(my_grid, sample)
# Sample and plot.
sample = my_discrete_grf.sample()
plot_grid_values(my_grid, sample)
# Sample the continuous version and compare.
sample_cont = myGRF.sample_isotopic(my_grid.points)
plot_grid_values(my_grid, sample_cont)
# 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])
y = torch.tensor(11 * [-6]).float()
# ------------------------------------------------------
# Create a regular square grid in 2 dims.
my_grid = TriangularGrid(31)
print("Working on an equilateral triangular grid with {} nodes.".format(
my_grid.n_points))
# Discretize the GRF on a grid and be done with it.
# From now on we only consider locatoins on the grid.
my_discrete_grf = DiscreteGRF.from_model(myGRF, my_grid)
# ------------------------------------------------------
# Sample and plot
# ------------------------------------------------------
# Sample all components at all locations.
sample = my_discrete_grf.sample()
plot_grid_values(my_grid, sample)
# From now on, we will consider the drawn sample as ground truth.
# ---------------------------------------------------------------
ground_truth = sample
# Use it to declare the data feed.
noise_std = torch.tensor([0.1, 0.1])
# Noise distribution
lower_chol = psd_safe_cholesky(torch.diag(noise_std**2))
noise_distr = MultivariateNormal(loc=torch.zeros(n_out), scale_tril=lower_chol)
def data_feed(node_ind):
noise_realization = noise_distr.sample()
return ground_truth[node_ind] + noise_realization
# Number of respones.
my_grid = TriangularGrid(70)
my_square_grid = SquareGrid(50, 2)
my_discrete_grf = DiscreteGRF.from_model(myGRF, my_grid)
# 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])
y = torch.tensor(11*[-6]).float()
# Since we are working with a discrete GRF, we can only observa data at grid
# nodes. Hence get the ones corresponding to the measured data.
S_y_inds = my_grid.get_closest(S_y)
# Compute the covariance reduction that would result from observing at those
# generalized locations.
cov_reduction = my_discrete_grf.compute_cov_reduction(S_y_inds, L_y,
noise_std=0.05)
# Extract the diagonals.
var_reduction = torch.diagonal(
(torch.diagonal(cov_reduction.isotopic, dim1=0, dim2=1).T),
dim1=1, dim2=2)
plot_grid_values(my_grid, var_reduction,
S_y, L_y, cmap="proba")
# The argument specified the number of cells along 1 dimension, hence total
# size of the grid is roughly the square of this number.
my_grid = TriangularGrid(21)
print("Working on an equilateral triangular grid with {} nodes.".format(
my_grid.n_points))
# Discretize the GRF on a grid and be done with it.
# From now on we only consider locations on the grid.
my_discrete_grf = DiscreteGRF.from_model(myGRF, my_grid)
# ------------------------------------------------------
# Sample and plot
# ------------------------------------------------------
# Sample all components at all locations.
sample = my_discrete_grf.sample()
plot_grid_values(my_grid, sample)
# ------------------------------------------------------
# Observe some data.
# ------------------------------------------------------
# Data observations must be specified by a so-called generalized location.
# A generalized location is a couple of vectors (S, L). The first vector
# specifies WHERE the observations have been made, whereas the second vector
# indicates WHICH component was measured at that location (remember we are
# considering multivariate GRFs).
#
# Example consider S = [[0, 0], [-1, -1]] and L = [0, 8].
# Then, the generalized location (S, L) describes a set of observations that
# consists of one observation of the 0-th component of the field at the points
# (0,0) and one observation of the 8-th component of the field at (-1, -1).
L_y,
y,
noise_std=0.05,
compute_post_cov=True)
mu_cond_sq, K_cond_sq = myGRF.krig_isotopic(my_square_grid.points,
S_y,
L_y,
y,
noise_std=0.05,
compute_post_cov=True)
# Plot.
from meslas.plotting import plot_grid_values, plot_grid_probas
plot_grid_values(my_grid, mu_cond, S_y, L_y)
plot_grid_values(my_square_grid, mu_cond_sq, S_y, L_y)
# Try the variance part.
mu_cond, var_cond = myGRF.krig_isotopic(my_grid.points,
S_y,
L_y,
y,
noise_std=0.05,
compute_post_var=True)
plot_grid_values(my_grid, var_cond, S_y, L_y, cmap="proba")
variance_reduction = myGRF.variance_reduction_isotopic(my_grid.points,
S_y,
L_y,