spacetime.operators {rSPDE} | R Documentation |
Space-time random fields
Description
spacetime.operators
is used for computing a FEM approximation of a Gaussian
random field defined as a solution to the SPDE
d u + \gamma(\kappa^2 + \kappa^{d/2}\rho \cdot\nabla - \Delta)^\alpha u = \sigma dW_C.
where C is a Whittle-Matern covariance operator with smoothness parameter
\beta
and range parameter \kappa
Usage
spacetime.operators(
mesh_space = NULL,
mesh_time = NULL,
space_loc = NULL,
time_loc = NULL,
graph = NULL,
kappa = NULL,
sigma = NULL,
gamma = NULL,
rho = NULL,
alpha = NULL,
beta = NULL,
graph_dirichlet = TRUE,
bounded_rho = TRUE
)
Arguments
mesh_space |
Spatial mesh for FEM approximation |
mesh_time |
Temporal mesh for FEM approximation |
space_loc |
Locations of mesh nodes for spatial mesh for 1d models. |
time_loc |
Locations of temporal mesh nodes. |
graph |
An optional |
kappa |
Positive spatial range parameter |
sigma |
Positive variance parameter |
gamma |
Temporal range parameter. |
rho |
Drift parameter. Real number on metric graphs and one-dimensional spatial domains, a vector with two number on 2d domains. |
alpha |
Integer smoothness parameter alpha. |
beta |
Integer smoothness parameter beta. |
graph_dirichlet |
For models on metric graphs, use Dirichlet vertex conditions at vertices of degree 1?
When |
bounded_rho |
Logical. Specifies whether |
Value
An object of type spacetimeobj.
Examples
s <- seq(from = 0, to = 20, length.out = 101)
t <- seq(from = 0, to = 20, length.out = 31)
op_cov <- spacetime.operators(space_loc = s, time_loc = t,
kappa = 5, sigma = 10, alpha = 1,
beta = 2, rho = 1, gamma = 0.05)
Q <- op_cov$Q
v <- rep(0,dim(Q)[1])
v[1565] <- 1
Sigma <- solve(Q,v)
image(matrix(Sigma, nrow=length(s), ncol = length(t)))