test_that("Pseudo-log is invertible", {
  trans <- transform_pseudo_log()
  expect_equal(
    trans$inverse(trans$transform(-10:10)),
    -10:10
  )
})

test_that("Modulus is invertible for negative and positive numbers", {
  trans <- transform_modulus(p = .1)
  expect_equal(trans$inv(trans$trans(-10:10)), -10:10)
  trans <- transform_modulus(p = -2)
  expect_equal(trans$inv(trans$trans(-10:10)), -10:10)
  trans <- transform_modulus(p = 1)
  expect_equal(trans$inv(trans$trans(-10:10)), -10:10)
})

test_that("Boxcox gives error for negative values", {
  trans <- transform_boxcox(p = .1)
  expect_error(trans$trans(-10:10))
  trans <- transform_boxcox(p = -2)
  expect_error(trans$trans(-10:10))
})

test_that("Boxcox can handle NA values", {
  trans <- transform_boxcox(p = 0)
  expect_equal(trans$trans(c(1, NA_real_)), c(0, NA_real_))
})

test_that("Boxcox is invertible", {
  trans <- transform_boxcox(p = .1)
  expect_equal(trans$inv(trans$trans(0:10)), 0:10)
  trans <- transform_boxcox(p = -2)
  expect_equal(trans$inv(trans$trans(0:10)), 0:10)
  trans <- transform_boxcox(p = 1)
  expect_equal(trans$inv(trans$trans(0:10)), 0:10)
})

test_that("Yeo-Johnson is invertible", {
  x <- c(-12345, 12345, -0.12345, 0.12345, -10:10)

  trans <- transform_yj(p = -1.5)
  expect_equal(trans$inverse(trans$transform(x)), x)

  trans <- transform_yj(p = 0)
  expect_equal(trans$inverse(trans$transform(x)), x)

  trans <- transform_yj(p = 0.7)
  expect_equal(trans$inverse(trans$transform(x)), x)

  trans <- transform_yj(p = 1.5)
  expect_equal(trans$inverse(trans$transform(x)), x)

  trans <- transform_yj(p = 2)
  expect_equal(trans$inverse(trans$transform(x)), x)
})

test_that("Yeo-Johnson is identity function for p = 1", {
  x <- c(-12345, 12345, -0.12345, 0.12345, -10:10)
  trans <- transform_yj(p = 1)
  expect_equal(trans$transform(x), x)
})

test_that("Yeo-Johnson transforms NAs to NAs without error", {
  x <- c(1, 2, NA, 4)
  trans <- transform_yj(p = 1)
  expect_equal(trans$transform(x), x)
})

test_that("Yeo-Johnson transform works", {
  # example data adpated from recipes package
  # https://github.com/tidymodels/recipes/blob/master/tests/testthat/test_YeoJohnson.R
  n <- 20
  set.seed(1)
  x <- data.frame(
    x1 = exp(rnorm(n, mean = .1)),
    x2 = 1 / rnorm(n),
    x3 = rexp(n)
  )

  lambdas <- c(
    x1 = -0.2727204451,
    x2 =  1.139292543,
    x3 = -1.012702061
  )

  expected_data <- data.frame(
    x1 = c(
      0.435993557749438, 0.754696454247318, 0.371327932207827,
      1.46113017436327, 0.82204097731098, 0.375761562702297, 0.89751975937422,
      1.02175936118846, 0.940739811377902, 0.54984302797741, 1.41856737837093,
      0.850587387615876, 0.437701618670981, 0.112174615510591, 1.21942112715274,
      0.654589551748501, 0.666780580127795, 1.12625135443351, 1.0636850911955,
      0.949680956411546
    ),
    x2 = c(
      1.15307873387121, 1.36532999080347,
      17.4648439780388, -0.487746797875704, 1.74452440065935, -13.3640721541574,
      -5.35805967319061, -0.653901985285932, -1.90735599477338, 2.65253432454371,
      0.76771137336975, -7.79484535687973, 2.87484976680907, -13.8738947581599,
      -0.696856395842167, -2.17745353101028, -2.28384276604207, -12.7261652971783,
      0.95585544349634, 1.40099012093008
    ),
    x3 = c(
      0.49061104973894, 0.49670370366879, 0.338742419511653,
      0.663722100577351, 0.296260662322359, 0.681346128666408,
      0.757581280603711, 0.357148961119583, 0.371872889850153,
      0.49239057672598, 0.173259524331095, 0.235933290139909, 0.52297977893566,
      0.434927187456966, 0.0822501770191215, 0.523479652016858,
      0.197977570919824, 0.608108816144845, 0.821913792446345,
      0.300608495427594
    )
  )

  expect_equal(transform_yj(lambdas[1])$transform(x[[1]]), expected_data[[1]])
  expect_equal(transform_yj(lambdas[2])$transform(x[[2]]), expected_data[[2]])
  expect_equal(transform_yj(lambdas[3])$transform(x[[3]]), expected_data[[3]])
})

test_that("probability transforms have domain (0,1)", {
  expect_equal(transform_logit()$domain, c(0, 1))
  expect_equal(transform_probit()$domain, c(0, 1))
})

# Derivatives -------------------------------------------------------------

test_that("transform_asn derivatives work", {
  trans <- transform_asn()
  expect_equal(trans$d_transform(c(0, 0.5, 1)), c(Inf, 2, Inf))
  expect_equal(trans$d_inverse(c(0, pi/2, pi)), c(0, 0.5, 0))
  x <- seq(0.1, 0.9, length.out = 10)
  expect_equal(trans$d_transform(x), 1 / trans$d_inverse(trans$transform(x)))
  expect_equal(trans$d_inverse(x), 1 / trans$d_transform(trans$inverse(x)))
})

test_that("transform_atanh derivatives work", {
  trans <- transform_atanh()
  expect_equal(trans$d_transform(c(-1, 0, 1)), c(Inf, 1, Inf))
  expect_equal(trans$d_inverse(c(-log(2), 0, log(2))), c(0.64, 1, 0.64))
  x <- seq(-0.9, 0.9, length.out = 10)
  expect_equal(trans$d_transform(x), 1 / trans$d_inverse(trans$transform(x)))
  expect_equal(trans$d_inverse(x), 1 / trans$d_transform(trans$inverse(x)))
})

test_that("transform_asinh derivatives work", {
  trans <- transform_asinh()
  expect_equal(trans$d_transform(c(-1, 0, 1)), c(sqrt(2) / 2, 1, sqrt(2) / 2))
  expect_equal(trans$d_inverse(c(-log(2), 0, log(2))), c(1.25, 1, 1.25))
  x <- seq(-0.9, 0.9, length.out = 10)
  expect_equal(trans$d_transform(x), 1 / trans$d_inverse(trans$transform(x)))
  expect_equal(trans$d_inverse(x), 1 / trans$d_transform(trans$inverse(x)))
})

test_that("transform_boxcox derivatives work", {
  trans <- transform_boxcox(p = 0, offset = 1)
  expect_equal(trans$d_transform(c(0, 1, 2)), c(1, 1/2, 1/3))
  expect_equal(trans$d_inverse(c(0, 1, 2)), exp(c(0, 1, 2)))
  x <- 0:10
  expect_equal(trans$d_transform(x), 1 / trans$d_inverse(trans$transform(x)))
  expect_equal(trans$d_inverse(x), 1 / trans$d_transform(trans$inverse(x)))

  trans <- transform_boxcox(p = 2, offset = 2)
  expect_equal(trans$d_transform(c(0, 1, 2)), c(2, 3, 4))
  expect_equal(trans$d_inverse(c(0, 0.5, 4)), c(1, sqrt(2) / 2, 1/3))
  expect_equal(trans$d_transform(x), 1 / trans$d_inverse(trans$transform(x)))
  expect_equal(trans$d_inverse(x), 1 / trans$d_transform(trans$inverse(x)))
})

test_that("transform_modulus derivatives work", {
  trans <- transform_modulus(p = 0, offset = 1)
  expect_equal(trans$d_transform(c(-2, -1, 1, 2)), c(1/3, 1/2, 1/2, 1/3))
  expect_equal(trans$d_inverse(c(-2, -1, 1, 2)), exp(c(2, 1, 1, 2)))
  x <- c(-10:-2, 2:10)
  expect_equal(trans$d_transform(x), 1 / trans$d_inverse(trans$transform(x)))
  expect_equal(trans$d_inverse(x), 1 / trans$d_transform(trans$inverse(x)))

  trans <- transform_modulus(p = 2, offset = 2)
  expect_equal(trans$d_transform(c(-2, -1, 1, 2)), c(4, 3, 3, 4))
  expect_equal(trans$d_inverse(c(-4, -0.5, 0.5, 4)), c(1/3, sqrt(2) / 2, sqrt(2) / 2, 1/3))
  expect_equal(trans$d_transform(x), 1 / trans$d_inverse(trans$transform(x)))
  expect_equal(trans$d_inverse(x), 1 / trans$d_transform(trans$inverse(x)))
})

test_that("transform_yj derivatives work", {
  trans <- transform_yj(p = 0)
  expect_equal(trans$d_transform(c(-2, -1, 1, 2)), c(3, 2, 0.5, 1/3))
  expect_equal(trans$d_inverse(c(-1/2, 1, 2)), c(sqrt(2) / 2, exp(1), exp(2)))
  x <- c(-10:10)
  expect_equal(trans$d_transform(x), 1 / trans$d_inverse(trans$transform(x)))
  expect_equal(trans$d_inverse(x), 1 / trans$d_transform(trans$inverse(x)))

  trans <- transform_yj(p = 3)
  expect_equal(trans$d_transform(c(-2, -1, 1, 2)), c(1/9, 1/4, 4, 9))
  expect_equal(trans$d_inverse(c(-4, -0.5, 1)), c(1/9, 4, (1/16)^(1/3)))
  expect_equal(trans$d_transform(x), 1 / trans$d_inverse(trans$transform(x)))
  expect_equal(trans$d_inverse(0:10), 1 / trans$d_transform(trans$inverse(0:10)))
})

test_that("transform_exp derivatives work", {
  trans <- transform_exp(10)
  expect_equal(trans$d_transform(c(0, 1, 2)), c(1, 10, 100) * log(10))
  expect_equal(trans$d_inverse(c(0.1, 1, 10) / log(10)), c(10, 1, 0.1))
  x <- 1:10
  expect_equal(trans$d_transform(x), 1 / trans$d_inverse(trans$transform(x)))
  expect_equal(trans$d_inverse(x), 1 / trans$d_transform(trans$inverse(x)))
})

test_that("transform_identity derivatives work", {
  trans <- transform_identity()
  expect_equal(trans$d_transform(numeric(0)), numeric(0))
  expect_equal(trans$d_transform(c(0, 1, 2)), c(1, 1, 1))
  expect_equal(trans$d_inverse(numeric(0)), numeric(0))
  expect_equal(trans$d_inverse(c(0, 1, 2)), c(1, 1, 1))
})

test_that("transform_log derivatives work", {
  trans <- transform_log(10)
  expect_equal(trans$d_transform(c(0.1, 1, 10) / log(10)), c(10, 1, 0.1))
  expect_equal(trans$d_inverse(c(0, 1, 2)), c(1, 10, 100) * log(10))
  x <- 1:10
  expect_equal(trans$d_transform(x), 1 / trans$d_inverse(trans$transform(x)))
  expect_equal(trans$d_inverse(x), 1 / trans$d_transform(trans$inverse(x)))
})

test_that("transform_log1p derivatives work", {
  trans <- transform_log1p()
  expect_equal(trans$d_transform(c(0, 1, 2)), c(1, 1/2, 1/3))
  expect_equal(trans$d_inverse(c(0, 1, 2)), exp(c(0, 1, 2)))
  x <- 0:10
  expect_equal(trans$d_transform(x), 1 / trans$d_inverse(trans$transform(x)))
  expect_equal(trans$d_inverse(x), 1 / trans$d_transform(trans$inverse(x)))
})

test_that("transform_pseudo_log derivatives work", {
  trans <- transform_pseudo_log(0.5)
  expect_equal(trans$d_transform(c(0, 1)), c(1, sqrt(2) / 2))
  expect_equal(trans$d_inverse(c(0, 1)), c(1, cosh(1)))
  x <- 1:10
  expect_equal(trans$d_transform(x), 1 / trans$d_inverse(trans$transform(x)))
  expect_equal(trans$d_inverse(x), 1 / trans$d_transform(trans$inverse(x)))
})

test_that("transform_logit derivatives work", {
  trans <- transform_logit()
  expect_equal(trans$d_transform(c(0.1, 0.5, 0.8)), c(100/9, 4, 6.25))
  expect_equal(trans$d_inverse(c(0, 1, 2)), dlogis(c(0, 1, 2)))
  x <- seq(0.1, 0.9, length.out = 10)
  expect_equal(trans$d_transform(x), 1 / trans$d_inverse(trans$transform(x)))
  expect_equal(trans$d_inverse(x), 1 / trans$d_transform(trans$inverse(x)))
})

test_that("transform_reciprocal derivatives work", {
  trans <- transform_reciprocal()
  expect_equal(trans$d_transform(c(0.1, 1, 10)), c(-100, -1, -0.01))
  expect_equal(trans$d_inverse(c(0.1, 1, 10)), c(-100, -1, -0.01))
  x <- (1:20)/10
  expect_equal(trans$d_transform(x), 1 / trans$d_inverse(trans$transform(x)))
  expect_equal(trans$d_inverse(x), 1 / trans$d_transform(trans$inverse(x)))
})

test_that("transform_reverse derivatives work", {
  trans <- transform_reverse()
  expect_equal(trans$d_transform(numeric(0)), numeric(0))
  expect_equal(trans$d_transform(c(-1, 1, 2)), c(-1, -1, -1))
  expect_equal(trans$d_inverse(numeric(0)), numeric(0))
  expect_equal(trans$d_inverse(c(-1, 1, 2)), c(-1, -1, -1))
})

test_that("transform_sqrt derivatives work", {
  trans <- transform_sqrt()
  expect_equal(trans$d_transform(c(1, 4, 9)), c(1/2, 1/4, 1/6))
  expect_equal(trans$d_inverse(c(1, 2, 3)), c(2, 4, 6))
  x <- 1:10
  expect_equal(trans$d_transform(x), 1 / trans$d_inverse(trans$transform(x)))
  expect_equal(trans$d_inverse(x), 1 / trans$d_transform(trans$inverse(x)))
})