#' simulate two point patterns with a shared stochastic structure using a spde model for the laten field
#'
#' @return a list of length two matrices containing the point pattern locations
#'
#'
#'
#' @export
#'
sim.joint <- function(mesh = NULL, field.shared = list(mu = 1, kappa = 1, sigma2 = 1,seed = 1), beta = 1){
mu1 <- field.shared[["mu"]]
k1 <- field.shared[["kappa"]]
s21 <- field.shared[["sigma2"]]
seed1 <- field.shared[["seed"]]
spde <- inla.spde2.matern(mesh = mesh, alpha=2)
proj<-inla.mesh.projector(mesh = mesh)
theta1 <- c(-0.5 * log(4 * pi * s21 * k1^2), log(k1))
Q1 <- inla.spde2.precision(spde, theta1)
## the samples at the mesh nodes
x1 <- mu1 + inla.qsample(Q = Q1, seed = seed1, constr = spde$f$extraconstr)
x2 <- beta*x1 #+ x2
x1 <- rpoispp(as.im(exp(matrix(inla.mesh.project(proj, x1),
length(proj$x),length(proj$y)))/area(ripras(mesh$loc))))
x2 <- rpoispp(as.im(exp(matrix(inla.mesh.project(proj, x2),
length(proj$x),length(proj$y)))/area(ripras(mesh$loc))))
return(list(pp1 = cbind(x1$x,x1$y), pp2 = cbind(x2$x,x2$y)))
}
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