## ---- test-mc-beta-std
lapply(
  X = 1,
  FUN = function(i,
                 text,
                 tol) {
    message(text)
    phi <- matrix(
      data = c(
        -0.357, 0.771, -0.450,
        0.0, -0.511, 0.729,
        0, 0, -0.693
      ),
      nrow = 3
    )
    colnames(phi) <- rownames(phi) <- c("x", "m", "y")
    sigma <- matrix(
      data = c(
        0.24455556, 0.02201587, -0.05004762,
        0.02201587, 0.07067800, 0.01539456,
        -0.05004762, 0.01539456, 0.07553061
      ),
      nrow = 3
    )
    vcov_theta <- matrix(
      data = c(
        0.00843, 0.00040, -0.00151, -0.00600, -0.00033,
        0.00110, 0.00324, 0.00020, -0.00061, -0.00115,
        0.00011, 0.00015, 0.00001, -0.00002, -0.00001,
        0.00040, 0.00374, 0.00016, -0.00022, -0.00273,
        -0.00016, 0.00009, 0.00150, 0.00012, -0.00010,
        -0.00026, 0.00002, 0.00012, 0.00004, -0.00001,
        -0.00151, 0.00016, 0.00389, 0.00103, -0.00007,
        -0.00283, -0.00050, 0.00000, 0.00156, 0.00021,
        -0.00005, -0.00031, 0.00001, 0.00007, 0.00006,
        -0.00600, -0.00022, 0.00103, 0.00644, 0.00031,
        -0.00119, -0.00374, -0.00021, 0.00070, 0.00064,
        -0.00015, -0.00005, 0.00000, 0.00003, -0.00001,
        -0.00033, -0.00273, -0.00007, 0.00031, 0.00287,
        0.00013, -0.00014, -0.00170, -0.00012, 0.00006,
        0.00014, -0.00001, -0.00015, 0.00000, 0.00001,
        0.00110, -0.00016, -0.00283, -0.00119, 0.00013,
        0.00297, 0.00063, -0.00004, -0.00177, -0.00013,
        0.00005, 0.00017, -0.00002, -0.00008, 0.00001,
        0.00324, 0.00009, -0.00050, -0.00374, -0.00014,
        0.00063, 0.00495, 0.00024, -0.00093, -0.00020,
        0.00006, -0.00010, 0.00000, -0.00001, 0.00004,
        0.00020, 0.00150, 0.00000, -0.00021, -0.00170,
        -0.00004, 0.00024, 0.00214, 0.00012, -0.00002,
        -0.00004, 0.00000, 0.00006, -0.00005, -0.00001,
        -0.00061, 0.00012, 0.00156, 0.00070, -0.00012,
        -0.00177, -0.00093, 0.00012, 0.00223, 0.00004,
        -0.00002, -0.00003, 0.00001, 0.00003, -0.00013,
        -0.00115, -0.00010, 0.00021, 0.00064, 0.00006,
        -0.00013, -0.00020, -0.00002, 0.00004, 0.00057,
        0.00001, -0.00009, 0.00000, 0.00000, 0.00001,
        0.00011, -0.00026, -0.00005, -0.00015, 0.00014,
        0.00005, 0.00006, -0.00004, -0.00002, 0.00001,
        0.00012, 0.00001, 0.00000, -0.00002, 0.00000,
        0.00015, 0.00002, -0.00031, -0.00005, -0.00001,
        0.00017, -0.00010, 0.00000, -0.00003, -0.00009,
        0.00001, 0.00014, 0.00000, 0.00000, -0.00005,
        0.00001, 0.00012, 0.00001, 0.00000, -0.00015,
        -0.00002, 0.00000, 0.00006, 0.00001, 0.00000,
        0.00000, 0.00000, 0.00010, 0.00001, 0.00000,
        -0.00002, 0.00004, 0.00007, 0.00003, 0.00000,
        -0.00008, -0.00001, -0.00005, 0.00003, 0.00000,
        -0.00002, 0.00000, 0.00001, 0.00005, 0.00001,
        -0.00001, -0.00001, 0.00006, -0.00001, 0.00001,
        0.00001, 0.00004, -0.00001, -0.00013, 0.00001,
        0.00000, -0.00005, 0.00000, 0.00001, 0.00012
      ),
      nrow = 15
    )
    delta_t <- 2
    total <- expm::expm(delta_t * phi)
    total_cov <- ExpCov(
      phi = phi,
      sigma = sigma,
      delta_t = delta_t
    )
    total_std <- matrix(
      data = 0.0,
      nrow = 3,
      ncol = 3
    )
    for (j in 1:3) {
      for (i in 1:3) {
        total_std[i, j] <- (
          sqrt(total_cov[i, i]) * total[i, j]
        ) * (1 / sqrt(total_cov[j, j]))
      }
    }
    answer <- as.vector(
      total_std
    )
    mc <- MCBetaStd(
      phi = phi,
      sigma = sigma,
      vcov_theta = vcov_theta,
      delta_t = delta_t,
      R = 1000,
      seed = 42
    )
    testthat::test_that(
      paste(text, "MCBetaStd"),
      {
        testthat::expect_true(
          all(
            (
              answer - summary(mc)$est
            ) <= tol
          )
        )
      }
    )
    mc <- MCBetaStd(
      phi = phi,
      sigma = sigma,
      vcov_theta = vcov_theta,
      delta_t = 1:5,
      R = 1000,
      seed = NULL,
      test_phi = FALSE
    )
    print(mc)
    summary(mc)
    confint(mc, level = 0.95)
    plot(mc)
    mc <- MCBetaStd(
      phi = phi,
      sigma = sigma,
      vcov_theta = vcov_theta,
      delta_t = 1,
      R = 1000,
      seed = NULL,
      test_phi = FALSE
    )
    print(mc)
    summary(mc)
    confint(mc, level = 0.95)
    testthat::test_that(
      paste(text, "plot error"),
      {
        testthat::expect_error(
          plot(mc)
        )
      }
    )
  },
  text = "test-mc-beta-std",
  tol = 0.01
)