library("testthat")
d <- 4
A <- matrix(c(
  1, -1, 0, 0,
  0, 1, -1, 0,
  0, 0, 1, -1,
  0, 0, 0, 1
), ncol = d, byrow = TRUE)
b <- c(0, 0, 0, .5)
V <- .5^d / factorial(d)

M <- 50000
X <- matrix(runif(M * d), M)

cntr <- function(X, A, b) {
  sum(apply(X, 1, function(x) all(A %*% x <= b)))
}

set.seed(124356)

test_that("counting methods work", {
  cnt <- multinomineq:::count_samples(X, A, b)
  expect_equal(cnt, cntr(X, A, b))
  expect_equal(cnt / M, V, tol = .005)

  c2 <- count_binom(0, 0, A = A, b = b, M = M)
  expect_equal(attr(c2, "proportion"), V, tol = 5 * attr(c2, "se"))
  c3 <- count_binom(0, 0, A = A, b = b, M = M)
  expect_equal(attr(c3, "proportion"), V, tol = 5 * attr(c3, "se"))

  c4 <- count_binom(0, 0, A = A, b = b, M = 1e5, steps = 2:3)
  c4
  expect_equal(attr(c4, "proportion"), V, tol = 5 * attr(c4, "se"))

  c5 <- count_binom(0, 0, A = A, b = b, M = 1e5, cmin = 1000)
  c5
  expect_equal(attr(c5, "proportion"), V, tol = 5 * attr(c5, "se"))
})

test_that("counting is equivalent for: A/b-method and V-method", {
  skip_on_cran()
  skip_if_not_installed("rPorta")

  A <- matrix(c(
    1, -1, 0,
    0, 1, -1,
    0, 0, 1
  ), ncol = 3, byrow = TRUE)
  b <- c(0, 0, .50)
  V <- matrix(c(
    0, 0, 0,
    0, 0, .5,
    0, .5, .5,
    .5, .5, .5
  ), ncol = 3, byrow = TRUE)

  xin <- c(.1, .2, .45) # inside
  expect_true(inside(xin, A, b))
  expect_true(inside(xin, V = V))
  xout <- c(.4, .1, .55) # outside
  expect_false(inside(xout, A, b))
  expect_false(inside(xout, V = V))
  expect_equal(inside(rbind(xin, xout), A, b), c(TRUE, FALSE))
  expect_equal(inside(rbind(xin, xout), V = V), c(TRUE, FALSE))


  V <- matrix(c(
    1, 0, 0, 0, 0, 1,
    0, 1, 1, 0, 0, 0,
    1, 0, 0, 1, 0, 0,
    1, 1, 1, 1, 1, 0,
    1, 0, 0, 1, 1, 0,
    0, 1, 1, 1, 0, 1,
    0, 0, 1, 1, 1, 1,
    0, 0, 0, 0, 0, 0,
    0, 1, 1, 1, 0, 1,
    1, 1, 1, 1, 1, 1,
    0, 1, 0, 1, 0, 1,
    0, 0, 0, 0, 0, 1
  ), ncol = 6, byrow = TRUE)
  tmp <- V_to_Ab(unique(V))
  A <- tmp$A
  b <- tmp$b

  X <- matrix(runif(2000 * ncol(V)), ncol = ncol(V))
  vertex <- multinomineq:::inside_V(X, V)
  ineq <- apply(X, 1, function(x) all(A %*% x <= b))
  expect_equal(vertex, ineq)
  table(data.frame(vertex, ineq))
})

test_that("transformation of A/b to V representation works", {
  skip_on_cran()
  skip_if_not_installed("rPorta")
})