data("Russett")
blocks <- list(
  agriculture = Russett[, seq(3)],
  industry = Russett[, 4:5],
  politic = Russett[, 6:11]
)

bias <- FALSE
sqrt_N <- sqrt(NROW(blocks[[1]]) + bias - 1)

blocks3 <- lapply(blocks, scale)
blocks3 <- lapply(blocks3, function(x) {
  return(x / sqrt(ncol(x)))
})
blocks2 <- scaling(blocks, scale = TRUE, scale_block = TRUE, bias = bias)
test_that("scaling_default_1", {
  expect_true(sum(abs(blocks3[[2]] - blocks2[[2]])) < 1e-14)
})

test_that("scale_block = 'inertia' leads to unit Frobenius norm", {
  b <- scaling(blocks, scale = TRUE, scale_block = TRUE, bias = bias)
  for (j in seq_along(b)) {
    expect_equal(norm(b[[j]] / sqrt_N, type = "F"), 1, tolerance = 1e-14)
  }
  b <- scaling(blocks, scale = FALSE, scale_block = TRUE, bias = bias)
  for (j in seq_along(b)) {
    expect_equal(norm(b[[j]] / sqrt_N, type = "F"), 1, tolerance = 1e-14)
  }
})

test_that("scale_block = 'lambda1' leads to top eigenvalue of covariance
          matrix being equal to one", {
  b <- scaling(blocks, scale = TRUE, scale_block = "lambda1", bias = bias)
  for (j in seq_along(b)) {
    expect_equal(eigen(crossprod(b[[j]] / sqrt_N))$values[1],
      1,
      tolerance = 1e-14
    )
  }
  b <- scaling(blocks, scale = FALSE, scale_block = "lambda1", bias = bias)
  for (j in seq_along(b)) {
    expect_equal(eigen(crossprod(b[[j]] / sqrt_N))$values[1],
      1,
      tolerance = 1e-14
    )
  }
})

test_that("another value of scale_block does not lead to further scaling", {
  b <- scaling(blocks, scale = TRUE, scale_block = "none", bias = bias)
  b_ref <- lapply(blocks, scale)
  for (j in seq_along(b)) {
    expect_true(sum(abs(b[[j]] - b_ref[[j]])) < 1e-14)
  }
  b <- scaling(blocks, scale = FALSE, scale_block = "none", bias = bias)
  b_ref <- lapply(blocks, scale, center = TRUE, scale = FALSE)
  for (j in seq_along(b)) {
    expect_true(sum(abs(b[[j]] - b_ref[[j]])) < 1e-14)
  }
})