context("test-g01-monotonicity")

CONSTANT <- "CONSTANT"
AFFINE <- "AFFINE"
CONVEX <- "CONVEX"
CONCAVE <- "CONCAVE"
UNKNOWN <- "UNKNOWN"

test_that("Test application of DCP composition rules to determine curvature", {
  skip_on_cran()
  expr <- 1 + exp(Variable())
  expect_equal(curvature(expr), CONVEX)

  expr <- Parameter() * Variable(nonneg = TRUE)
  expect_equal(curvature(expr), AFFINE)

  f <- function(x) { x^2 + x^0.5 }
  expr <- f(Constant(2))
  expect_equal(curvature(expr), CONSTANT)

  expr <- exp(Variable())^2
  expect_equal(curvature(expr), CONVEX)

  expr <- 1 - sqrt(Variable())
  expect_equal(curvature(expr), CONVEX)

  expr <- log(sqrt(Variable()))
  expect_equal(curvature(expr), CONCAVE)

  expr <- -(exp(Variable()))^2
  expect_equal(curvature(expr), CONCAVE)

  expr <- log(exp(Variable()))
  expect_false(is_dcp(expr))

  expr <- entr(Variable(nonneg = TRUE))
  expect_equal(curvature(expr), CONCAVE)

  expr <- ((Variable()^2)^0.5)^0
  expect_equal(curvature(expr), CONSTANT)
})

test_that("Test DCP composition rules with signed monotonicity", {
  skip_on_cran()
  # Convex argument
  expr <- abs(1 + exp(Variable()))
  expect_equal(curvature(expr), CONVEX)

  expr <- abs(-entr(Variable()))
  expect_equal(curvature(expr), UNKNOWN)

  expr <- abs(-log(Variable()))
  expect_equal(curvature(expr), UNKNOWN)

  # Concave argument
  expr <- abs(log(Variable()))
  expect_equal(curvature(expr), UNKNOWN)

  expr <- abs(Variable()^2)
  expect_equal(curvature(expr), CONVEX)

  expr <- abs(entr(Variable()))
  expect_equal(curvature(expr), UNKNOWN)

  # Affine argument
  expr <- abs(Variable(nonneg = TRUE))
  expect_equal(curvature(expr), CONVEX)

  expr <- abs(-Variable(nonneg = TRUE))
  expect_equal(curvature(expr), CONVEX)

  expr <- abs(Variable())
  expect_equal(curvature(expr), CONVEX)
})