Sum of Matérn Kernels

Builds Matérn kernel matrices from a list of distances matrices and computes their sum.

Usage

matern_multiple(D_list, length_scales, variances, taus, squared = TRUE)

Arguments

D_list

A list of matrices with pairwise (possibly squared) distances.

length_scales

A vector of length-scale parameters.

variances

A vector of kernel variance parameters.

taus

A vector of smoothness parameters. Values need to be in 0.5, 1.5 and 2.5. If only a single value is provided, it will be used for all components.

squared

If TRUE (default), each distance matrix is assumed to contain squared distances. If FALSE, each distance matrix is assumed to contain raw distances.

Value

A kernel matrix with the same dimensions as the matrices in D_list.

Examples

M1 <- rbind(c(0, 2, 1),
            c(2, 0, 2.5),
            c(1, 2.5, 0))
M2 <- rbind(c(0, 1, 4),
            c(1, 0, 3),
            c(4, 3, 0))
M_list <- list(M1, M2)
matern_multiple(M_list, length_scales = c(1, 2), variances = c(2, 1/2),
  taus = c(0.5, 2.5), squared = FALSE)
#>          [,1]      [,2]      [,3]
#> [1,] 2.500000 1.1500835 1.2823914
#> [2,] 1.150083 2.5000000 0.7145912
#> [3,] 1.282391 0.7145912 2.5000000