# Dimension of the response.
n_out = 2
# Spatial Covariance.
matern_cov = Matern32(lmbda=0.1, sigma=1.0)
# Cross covariance.
cross_cov = UniformMixing(gamma0=0.0, sigmas=[np.sqrt(1.0), np.sqrt(1.5)])
covariance = FactorCovariance(matern_cov, cross_cov, n_out=n_out)
# Specify mean function
mean = ConstantMean([0.0, 0.0])
# Create the GRF.
myGRF = GRF(mean, covariance)
# 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)
matern_cov = Matern32(lmbda=0.5, sigma=1.0)
# Cross covariance.
cross_cov = UniformMixing(gamma0=0.2, sigmas=[2.25, 2.25])
covariance = FactorCovariance(spatial_cov=matern_cov,
cross_cov=cross_cov,
n_out=n_out)
# Specify mean function, here it is a linear trend that decreases with the
# horizontal coordinate.
beta0s = np.array([5.8, 24.0])
beta1s = np.array([[0, -4.0], [0, -3.8]])
mean = LinearMean(beta0s, beta1s)
# Create the GRF.
myGRF = GRF(mean, covariance)
# ------------------------------------------------------
# DISCRETIZE EVERYTHING
# ------------------------------------------------------
# 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
# Dimension of the response. n_out = 2 # Spatial Covariance. matern_cov = Matern32(lmbda=0.1, sigma=1.0) # Cross covariance. cross_cov = UniformMixing(gamma0=0.4, sigmas=[np.sqrt(1.0), np.sqrt(5.5)]) covariance = FactorCovariance(matern_cov, cross_cov, n_out=n_out) # 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)
# Spatial Covariance.
matern_cov = Matern32(lmbda=0.1, sigma=1.0)
# Cross covariance.
cross_cov = UniformMixing(
gamma0=0.0,
sigmas=[np.sqrt(0.25),
np.sqrt(0.3),
np.sqrt(0.4),
np.sqrt(0.5)])
covariance = FactorCovariance(matern_cov, cross_cov, n_out=n_out)
# Specify mean function
mean = ConstantMean([1.0, -2.0, 4.0, 33.0])
# Create the GRF.
myGRF = GRF(mean, covariance)
# Array of locations.
S1 = torch.Tensor([[0, 0], [0, 1], [0, 2], [3, 0]]).float()
S2 = torch.Tensor([[0, 0], [3, 0], [5, 4]]).float()
# Corresponding response indices.
L1 = torch.Tensor([0, 0, 0, 1]).long()
L2 = torch.Tensor([0, 3, 0]).long()
# Test the sampling.
print(myGRF.sample(S1, L1))
# Dimension of the response.
n_out = 2
# Spatial Covariance.
matern_cov = Matern32(lmbda=0.1, sigma=1.0)
# Cross covariance.
cross_cov = UniformMixing(gamma0=0.0, sigmas=[np.sqrt(1.0), np.sqrt(1.5)])
covariance = FactorCovariance(matern_cov, cross_cov, n_out=n_out)
# Specify mean function
mean = ConstantMean([0.0, 0.0])
# Create the GRF.
myGRF = GRF(mean, covariance)
# Create an equilateral triangular grid in 2 dims.
# Number of respones.
my_grid = TriangularGrid(40)
print(my_grid.n_points)
# 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()
# Predict at some points.
S2 = torch.Tensor([[0.2, 0.1], [0, 0], [3, 0], [5, 4]]).float()
# Dimension of the response.
n_out = 2
# Spatial Covariance.
matern_cov = Matern32(lmbda=0.1, sigma=1.0)
# Cross covariance.
cross_cov = UniformMixing(gamma0=0.0, sigmas=[np.sqrt(1.0), np.sqrt(1.5)])
covariance = FactorCovariance(matern_cov, cross_cov, n_out=n_out)
# Specify mean function
mean = ConstantMean([0.0, 0.0])
# 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)
print(my_grid.n_points)
# 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()
mu_cond, K_cond = myGRF.krig_isotopic(my_grid.points,