## ---- test-total-std
lapply(
  X = 1,
  FUN = function(i,
                 text,
                 tol) {
    message(text)
    answer <- 0.07477656
    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
    )
    delta_t <- 2
    total <- expm::expm(delta_t * phi)
    total_cov <- ExpCov(
      phi = phi,
      sigma = sigma,
      delta_t = delta_t
    )
    ExpMean(
      phi = phi,
      iota = c(0, 0, 0),
      delta_t = delta_t
    )
    ExpMean(
      phi = phi,
      iota = c(.5, .3, .4),
      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]))
      }
    }
    testthat::test_that(
      paste(text, "TotalStd"),
      {
        testthat::expect_true(
          (
            answer - TotalStd(
              phi = phi,
              sigma = sigma,
              delta_t = delta_t
            )$output[3, 1]
          ) <= tol
        )
      }
    )
    testthat::test_that(
      paste(text, "TotalStdVec"),
      {
        testthat::expect_true(
          all(
            (
              as.vector(
                total_std
              ) - as.vector(
                cTMed:::.TotalStdVec(
                  v = c(cTMed:::.Vec(phi), cTMed:::.Vech(sigma)),
                  delta_t = delta_t
                )
              )
            ) <= tol
          )
        )
      }
    )
    testthat::test_that(
      paste(text, "TotalStdDeltaT"),
      {
        testthat::expect_true(
          all(
            (
              as.vector(
                total_std
              ) - as.vector(
                cTMed:::.TotalStdDeltaT(
                  phi = phi,
                  sigma = sigma,
                  delta_t = delta_t
                )
              )[seq_len(3 * 3)]
            ) <= tol
          )
        )
      }
    )
    testthat::test_that(
      paste(text, "MedStd"),
      {
        testthat::expect_true(
          (
            answer - MedStd(
              phi = phi,
              sigma = sigma,
              delta_t = delta_t,
              from = "x",
              to = "y",
              med = "m"
            )$output[, "total"]
          ) <= tol
        )
      }
    )
    med <- MedStd(
      phi = phi,
      sigma = sigma,
      delta_t = 1:5,
      from = "x",
      to = "y",
      med = "m"
    )
    print(med)
    summary(med)
    plot(med)
    plot(med, col = 1:3)
    med <- MedStd(
      phi = phi,
      sigma = sigma,
      delta_t = 1,
      from = "x",
      to = "y",
      med = "m"
    )
    print(med)
    summary(med)
    testthat::test_that(
      paste(text, "plot error"),
      {
        testthat::expect_error(
          plot(med)
        )
      }
    )
    total <- TotalStd(
      phi = phi,
      sigma = sigma,
      delta_t = delta_t
    )
    print(total)
  },
  text = "test-total-std",
  tol = 0.01
)