test_that("Lambda_linear_form works", {
  expect_no_error(L_t <- Lambda_linear_form(t = 1:10, alpha = 0, beta = 0, t0 = 1))
  expect_identical(L_t, rep(0, 10))

  expect_no_error(L_t <- Lambda_linear_form(t = 1:10, alpha = 1, beta = 0, t0 = 1))
  expect_identical(L_t, as.double(0:9))

  expect_no_error(L_t <- Lambda_linear_form(t = 1:10, alpha = 1, beta = 1, t0 = 1))
  expect_identical(L_t, 0:9 + (1:10)^2 / 2 - 1 / 2)
})


test_that("Lambda_inv_linear_form works", {
  L_t <- Lambda_linear_form(t = 1:10, alpha = 0, beta = 1, t0 = 1)
  expect_identical(
    as.double(1:10),
    Lambda_inv_linear_form(z = L_t, alpha = 0, beta = 1, t0 = 1)
  )

  L_t <- Lambda_linear_form(t = 1:10, alpha = 1, beta = 0, t0 = 1)
  expect_identical(
    as.double(1:10),
    Lambda_inv_linear_form(z = L_t, alpha = 1, beta = 0, t0 = 1)
  )

  L_t <- Lambda_linear_form(t = 1:10, alpha = 1, beta = 1, t0 = 1)
  expect_identical(
    as.double(1:10),
    Lambda_inv_linear_form(z = L_t, alpha = 1, beta = 1, t0 = 1)
  )

  expect_error(
    Lambda_inv_linear_form(z = rep(0, 10), alpha = 0, beta = 0, t0 = 1)
  )
})


test_that("get_step_majorizer() works", {
  expect_no_error(l1 <- get_step_majorizer(
    fun = abs,
    breaks = -10:10, is_monotone = FALSE, K = 1
  ))
  l1_fun <- stats::approxfun(y = l1, x = -10:9, method = "constant", rule = 2)
  x <- seq(-10, 10, length.out = 1000)
  expect_true(sum(l1_fun(x) < abs(x)) == 0)
})