Creates a flexible precision matrix K by allowing linear combinations of base matrices with parameter-dependent coefficients. The model follows the form: K = sum_i f_i(theta) * matrices_i, where f_i depends on the parameter transformation.
generic(
theta_K,
matrices,
h,
trans = NULL,
mesh = NULL,
zero_trace = FALSE,
model = "generic",
param_name = NULL,
param_trans = NULL,
...
)The parameter vector (in real scale). If missing, initialized as double(0)
A list of matrices to be combined with parameter-dependent coefficients
The integration weights vector
Transformation for each parameter. Must be a list where each element is a character vector defining transformations for each matrix. For example, `trans=list(kappa=c("exp2", "identity", "null"))` means parameter 'kappa' affects matrix 1 with exp2 transformation, matrix 2 with identity, and doesn't affect matrix 3. Available transformations: "identity", "exp", "exp2", "exp4", "sqrt", "square", "log", "tanh"
The mesh object
Whether the trace of K should be zero
The model type name
Additional arguments (ignored)
This function can be used to represent various models like AR1, Matern, and RW1 in a unified framework.
The `generic` function provides a flexible way to construct precision matrices by combining existing matrices with transformed parameters. Here's how it works:
1. Each parameter in `theta_K` can affect one or more matrices in the `matrices` list 2. The `trans` list defines how each parameter transforms before multiplying each matrix 3. For each matrix, the coefficients from all parameters are multiplied together 4. The final K is the sum of all transformed matrices
Common use cases:
- **AR1 model**: K = rho * C + G (where rho is between -1 and 1) - **Matern (alpha=2)**: K = kappa^2 * C + G (where kappa > 0) - **Matern (alpha=4)**: K = kappa^4 * C + 2*kappa^2 * G + G * Cinv * G
if (FALSE) { # \dontrun{
# AR1 model with rho = 0.5
ar1_obj <- ar1(1:10, rho = 0.5)
g <- name2fun("tanh", inv = TRUE)
generic_ar1 <- generic(
theta_K = c(rho = g(0.5)), # Transform from real scale
trans = list(rho = c("tanh", "null")), # Apply tanh to first matrix
matrices = list(ar1_obj$C, ar1_obj$G),
h = ar1_obj$h
)
# Matern model with kappa = 2
mesh <- fmesher::fm_mesh_1d(seq(0, 1, length.out = 10))
matern_obj <- matern(mesh)
log_kappa <- log(2)
generic_matern <- generic(
theta_K = c(kappa = log_kappa),
trans = list(kappa = c("exp2", "null")), # exp(2*kappa) for C, nothing for G
matrices = list(matern_obj$C, matern_obj$G),
h = matern_obj$h
)
# Matern model with alpha = 4 and kappa = 2
mesh <- fmesher::fm_mesh_2d(cbind(x = runif(20), y = runif(20)))
matern_obj <- matern(mesh, alpha = 4)
C <- matern_obj$C
G <- matern_obj$G
Cinv <- C; diag(Cinv) <- 1 / Matrix::diag(C)
generic_matern4 <- generic(
theta_K = c(kappa = log(2)),
trans = list(kappa = c("exp4", "exp2", "null")),
matrices = list(C, 2*G, G %*% Cinv %*% G),
h = matern_obj$h
)
} # }