tests/testthat/test.CBrSPDE.R

In rSPDE: Rational Approximations of Fractional Stochastic Partial Differential Equations

context("CBrSPDE.operators")

test_that("Checking covariances of CBrSPDE", {
  set.seed(123)
  nobs <- 100
  s <- seq(from = 0, to = 1, length.out = nobs)
  fem <- rSPDE.fem1d(s)
  sigma <- 1
  d <- 1
  range <- 0.2
  for (nu in c(0.8, 1.7, 2.6)) {
    op2 <- matern.operators(loc_mesh = s, 
    nu = nu, range = range, sigma = sigma,
      d = 1, m = 2,
      parameterization = "matern"
    )
    v <- t(rSPDE.A1d(s, 0.5))
    c.true <- folded.matern.covariance.1d(s, rep(0.5,length(s)), kappa = sqrt(8*nu)/range, nu, sigma)
    Q <- op2$Q
    A <- Diagonal(nobs)
    Abar <- cbind(A, A, A)
    w <- rbind(v, v, v)
    c.approx2 <- (Abar) %*% solve(Q, w)
    res <- sum((c.approx2 - c.true)^2)
    expect_equal(res, 0, tolerance = 1e-4)
  }
})

test_that("Checking loglike of CBrSPDE", {
  set.seed(123)
  nobs <- 100
  s <- seq(from = 0, to = 1, length.out = nobs)
  fem <- rSPDE.fem1d(s)
  range = 0.2
  sigma <- 1
  d <- 1
  for (nu in c(0.8, 1.7, 2.6)) {
    op2 <- matern.operators(loc_mesh = s, nu = nu, range = range, sigma = sigma,
      d = 1, m = 2,
      parameterization = "matern"
    )
    A <- Diagonal(nobs)
    sim_data <- A %*% simulate(op2) + rnorm(dim(A)[1], sd = 0.1)
    loglike2 <- rSPDE.matern.loglike(
      object = op2, Y = sim_data, A = A,
      sigma.e = 0.1, user_nu = nu,
      user_kappa = kappa,
      user_sigma = sigma
    )

    op1 <- matern.operators(
      range = range, sigma = sigma, nu = nu,
      loc_mesh = s, d = 1, type = "operator",
      parameterization = "matern"
    )
    loglike1 <- rSPDE.matern.loglike(op1, sim_data, A, sigma.e = 0.1)

    expect_equal(loglike1, loglike2, tol = 0.3)
  }
})

test_that("Checking Predict of CBrSPDE", {
  set.seed(123)
  nobs <- 100
  s <- seq(from = 0, to = 1, length.out = nobs)
  fem <- rSPDE.fem1d(s)
  range <- 0.2
  sigma <- 1
  d <- 1
  for (nu in c(0.8, 1.7, 2.6)) {
    Aprd <- rSPDE.A1d(s, 0.5)
    op2 <- matern.operators(
      C = fem$C, G = fem$G, nu = nu, range = range, sigma = sigma,
      d = 1, m = 2,
      parameterization = "matern"
    )
    A <- Diagonal(nobs)
    sim_data <- A %*% simulate(op2) + rnorm(dim(A)[1], sd = 0.1)
    predict2 <- predict(
      object = op2, Y = sim_data, A = A, sigma.e = 0.1,
      Aprd = Aprd,
      compute.variances = TRUE
    )

    op1 <- matern.operators(
      range = range, sigma = sigma, nu = nu,
      G = fem$G, C = fem$C, d = 1,
      type = "operator",
      parameterization = "matern"
    )
    predict1 <- predict(
      object = op1, Y = sim_data, A = A, Aprd = Aprd, sigma.e = 0.1,
      compute.variances = TRUE
    )

    expect_equal(as.double(predict1$mean), as.double(predict2$mean), tol = 0.02)
    expect_equal(as.double(predict1$variance),
    as.double(predict2$variance), tol = 0.002)
  }
})

test_that("Checking loglike of CBrSPDE with replicates", {
  set.seed(123)
  nobs <- 100
  s <- seq(from = 0, to = 1, length.out = nobs)
  fem <- rSPDE.fem1d(s)
  range <- 0.2
  sigma <- 1
  d <- 1
  for (nu in c(0.8, 1.7, 2.6)) {
    op2 <- matern.operators(
      loc_mesh = s, nu = nu, range = range, sigma = sigma,
      d = 1, m = 2,
      parameterization = "matern"
    )
    A <- Diagonal(nobs)
    sim_data1 <- A %*% simulate(op2) + rnorm(dim(A)[1], sd = 0.1)
    sim_data2 <- A %*% simulate(op2) + rnorm(dim(A)[1], sd = 0.1)
    sim_data <- cbind(sim_data1, sim_data2)
    loglike2 <- rSPDE.matern.loglike(object = op2,
    Y = sim_data, A = A, sigma.e = 0.1)

    op1 <- matern.operators(
      range = range, sigma = sigma, nu = nu,
      loc_mesh = s, d = 1,
      type = "operator",
      parameterization = "matern"
    )
    loglike1 <- rSPDE.matern.loglike(op1, sim_data, A, sigma.e = 0.1)

    expect_equal(loglike1, loglike2, tol = 0.3)
  }
})