test_that("gsDesign2:::hupdate() returns results as expected ", {
  # the design
  gstry <- gsDesign::gsDesign(
    k = 3,
    sfl = gsDesign::sfLDOF,
    delta = 0
  )
  # probabilities calculated based on function gsDesign2:::h1(), IA1 needs to full between low and upper bound
  # in order to continue to IA2
  null.01 <- gsDesign2:::h1(
    theta = gstry$theta[1],
    info = gstry$n.I[1],
    a = gstry$lower$bound[1],
    b = gstry$upper$bound[1]
  )
  # IA2 to reject H0, we integrate from upper bound to Inf
  upper.null.02 <- sum(gsDesign2:::hupdate(
    theta = gstry$theta[1],
    thetam1 = gstry$theta[1],
    info = gstry$n.I[2],
    im1 = gstry$n.I[1],
    gm1 = null.01,
    a = gstry$upper$bound[2],
    b = Inf
  )$h)
  # IA2 to accept H0, we integrate from -Inf to lower bound
  lower.null.02 <- sum(gsDesign2:::hupdate(
    theta = gstry$theta[1],
    thetam1 = gstry$theta[1],
    info = gstry$n.I[2],
    im1 = gstry$n.I[1],
    gm1 = null.01,
    a = -Inf,
    b = gstry$lower$bound[2]
  )$h)

  alt.01 <- gsDesign2:::h1(
    theta = gstry$theta[2],
    info = gstry$n.I[1],
    a = gstry$lower$bound[1],
    b = gstry$upper$bound[1]
  )
  # IA2 to reject H0, we integrate from upper bound to Inf
  upper.alt.02 <- sum(gsDesign2:::hupdate(
    theta = gstry$theta[2],
    thetam1 = gstry$theta[2],
    info = gstry$n.I[2],
    im1 = gstry$n.I[1],
    gm1 = alt.01,
    a = gstry$upper$bound[2],
    b = Inf
  )$h)
  # IA2 to accept H0, we integrate from -Inf to lower bound
  lower.alt.02 <- sum(gsDesign2:::hupdate(
    theta = gstry$theta[2],
    thetam1 = gstry$theta[2],
    info = gstry$n.I[2],
    im1 = gstry$n.I[1],
    gm1 = alt.01,
    a = -Inf,
    b = gstry$lower$bound[2]
  )$h)
  # probabilities calculated based on function gsProbability
  x <- gsDesign::gsProbability(
    k = 3,
    a = gstry$lower$bound,
    b = gstry$upper$bound,
    n.I = gstry$n.I,
    theta = gstry$theta
  )

  expect_equal(object = as.numeric(c(lower.null.02, lower.alt.02)), expected = x$lower$prob[2, ], tolerance = 0.0001)
  expect_equal(object = as.numeric(c(upper.null.02, upper.alt.02)), expected = x$upper$prob[2, ], tolerance = 0.0001)
  # problem with below code on extreme case:
  # gsDesign2:::theta = gstry$theta[1], thetam1= gstry$theta[1],
  #     info=gstry$n.I[1]+0.00000000000001,im1=gstry$n.I[1],gm1=null.01,
  #     a = gstry$upper$bound[2],b=Inf) %>% summarise(p = sum(h))
})

test_that("gsDesign2:::) returns probability almost zero for extreme case", {
  # the design
  gstry <- gsDesign::gsDesign(
    k = 3,
    sfl = gsDesign::sfLDOF,
    delta = 0
  )
  null.01 <- gsDesign2:::h1(
    theta = gstry$theta[1],
    info = gstry$n.I[1],
    a = gstry$lower$bound[1],
    b = gstry$upper$bound[1]
  )
  # IA2 to reject H0, we integrate from upper bound to Inf
  #-8 is an arbitrary extreme case for theta
  poor.02 <- sum(gsDesign2:::hupdate(
    theta = -8,
    thetam1 = gstry$theta[1],
    info = gstry$n.I[2],
    im1 = gstry$n.I[1],
    gm1 = null.01,
    a = gstry$upper$bound[2],
    b = Inf
  )$h)
  # IA2 to accept H0, we integrate from -Inf to lower bound
  #-8 is an arbitrary extreme case for the bound
  high.02 <- sum(gsDesign2:::hupdate(
    theta = gstry$theta[2],
    thetam1 = gstry$theta[2],
    info = gstry$n.I[2],
    im1 = gstry$n.I[1],
    gm1 = null.01,
    a = -Inf,
    b = -8
  )$h)
  expect_equal(object = as.numeric(c(poor.02, high.02)), expected = c(0, 0), tolerance = 0.0001)
})