test_that("canonical correlations invariant to permutation", {

  set.seed(1)

  n <- 10
  T_len <- 6

  X <- list(
    lapply(seq_len(n), function(i) matrix(rnorm(T_len * 3), T_len, 3)),
    lapply(seq_len(n), function(i) matrix(rnorm(T_len * 2), T_len, 2))
  )

  fit1 <- mcca_fit(method = "kernel", X = X, ncomp = 2)

  perm <- sample(seq_len(n))

  X_perm <- lapply(X, function(block) block[perm])

  fit2 <- mcca_fit(method = "kernel", X = X_perm, ncomp = 2)

  expect_equal(fit1$values, fit2$values, tolerance = 1e-6)

})