# Helper functions used by test-independent_test_pmvnorm.R

# Bivariate with small variance
pbvnorm <- function(h1, h2, ro) {
  x <- c(0.04691008, 0.23076534, 0.5, 0.76923466, 0.95308992)
  w <- c(0.018854042, 0.038088059, 0.0452707394, 0.038088059, 0.018854042)
  h12 <- (h1 * h1 + h2 * h2) / 2
  bv <- 0
  if (abs(ro) < 0.7) {
    h3 <- h1 * h2
    ror <- ro * x
    ror2 <- 1 - ror * ror
    bv <- ro * w * exp((ror * h3 - h12) / ror2) / sqrt(ror2)
    bvsum <- sum(bv)
    bvfinal <- bvsum + pnorm(h1, lower.tail = TRUE) * pnorm(h2, lower.tail = TRUE)
  } else {
    r2 <- 1 - ro * ro
    r3 <- sqrt(r2)
    if (ro <= 0) {
      h2 <- -h2
    }
    h3 <- h1 * h2
    h7 <- exp(-h3 / 2)
    if (r2 == 0) {
      if (ro > 0) {
        bvfinal <- pnorm(min(h1, h2)) + bv * r3 * h7
      }
      if (ro <= 0) {
        bvfinal <- max(0, pnorm(h1) - pnorm(h2)) - bv * r3 * h7
      }
    } else {
      h6 <- abs(h1 - h2)
      h5 <- h6 * h6 / 2
      h6 <- h6 / r3
      aa <- 0.5 - h3 / 8
      ab <- 3 - 2 * aa * h5
      bv <- 0.13298076 * h6 * ab * pnorm(-h6) - exp(-h5 / r2) * (ab +
        aa * r2) * 0.053051647
      r1 <- r3 * x
      rr <- r1 * r1
      r2 <- sqrt(1 - rr)
      bv1 <- w * exp(-h5 / rr) * (exp(-h3 / (1 + r2)) / r2 / h7 - 1 - aa *
        rr)
      bvsum1 <- sum(bv1)
      bv <- bv - bvsum1
      if (ro > 0) {
        bvfinal <- pnorm(min(h1, h2)) + bv * r3 * h7
      }
      if (ro <= 0) {
        bvfinal <- max(0, pnorm(h1) - pnorm(h2)) - bv * r3 * h7
      }
    }
  }
}

# Bivariate with large variance
pbvnorm2 <- function(h1, h2, ro) {
  x <- c(0.04691008, 0.23076534, 0.5, 0.76923466, 0.95308992)
  w <- c(0.018854042, 0.038088059, 0.0452707394, 0.038088059, 0.018854042)
  h12 <- (h1 * h1 + h2 * h2) / 2
  bv <- 0
  r2 <- 1 - ro * ro
  r3 <- sqrt(r2)
  h3 <- h1 * h2
  h7 <- exp(-h3 / 2)
  h6 <- abs(h1 - h2)
  h5 <- h6 * h6 / 2
  h6 <- h6 / r3
  aa <- 0.5 - h3 / 8
  ab <- 3 - 2 * aa * h5
  bv <- 0.13298076 * h6 * ab * pnorm(h6) - exp(-h5 / r2) * (ab + aa * r2) *
    0.053051647
  r1 <- r3 * x
  rr <- r1 * r1
  r2 <- sqrt(1 - rr)
  bv1 <- w * exp(-h5 / rr) * (exp(-h3 / (1 + r2)) / r2 / h7 - 1 - aa * rr)
  bvsum1 <- sum(bv1)
  bv <- bv - bvsum1
  if (ro > 0) {
    bvfinal <- pnorm(max(h1, h2)) + bv * r3 * h7
  }
  if (ro <= 0) {
    bvfinal <- max(0, pnorm(h1) - pnorm(h2)) - bv * r3 * h7
  }
  bvfinal
}

# Trivariate
ptvnorm <- function(h, r, ro) {
  x <- c(0.0491008, 0.23076534, 0.5, 0.76923466, 0.95308992)
  w <- c(0.018854042, 0.038088059, 0.0452707394, 0.038088059, 0.018854042)

  h1 <- h[1]
  h2 <- h[2]
  h3 <- h[3]
  r12 <- r[1]
  r13 <- r[2]
  r23 <- r[3]

  if ((abs(r23) < abs(r12)) || (abs(r23) < abs(r13))) {
    if (abs(r12) >= abs(r13)) {
      hh <- h1
      h1 <- h3
      h3 <- h2
      h2 <- hh
      rr <- r23
      r23 <- r12
      r12 <- r13
      r13 <- rr
    } else {
      hh <- h1
      h1 <- h2
      h2 <- hh
      rr <- r23
      r23 <- r13
      r13 <- rr
    }
  }
  rh <- c(h1, h2, h3, r12, r13, r23)
  h12 <- h1 * h2
  h13 <- h1 * h3
  h122 <- (h1 * h1 + h2 * h2) / 2
  h132 <- (h1 * h1 + h3 * h3) / 2
  del1 <- 1 - r12 * r12 - r13 * r13 - r23 * r23 + 2 * r12 * r13 * r23

  rr12 <- r12 * x
  rr13 <- r13 * x
  del <- 1 - rr12 * rr12 - rr13 * rr13 - r23 * r23 + 2 * rr12 * rr13 *
    r23
  fac <- sqrt(del)
  rr122 <- 1 - rr12 * rr12
  rr133 <- 1 - rr13 * rr13
  f1 <- rr13 - r23 * rr12
  f2 <- r23 - rr12 * rr13
  f3 <- rr12 - r23 * rr13
  hp1 <- (h3 * rr122 - h1 * f1 - h2 * f2) / fac / sqrt(rr122)
  hp2 <- (h2 * rr133 - h1 * f3 - h3 * f2) / fac / sqrt(rr133)
  TV <- w * exp((rr12 * h12 - h122) / rr122) / sqrt(rr122) * pnorm(hp1) *
    r12 + w * exp((rr13 * h13 - h132) / rr133) / sqrt(rr133) * pnorm(hp2) *
      r13
  TV <- sum(TV)
  rho <- matrix(c(1, r23, r23, 1), 2, 2)
  p2 <- mvtnorm::pmvnorm(-Inf, c(h2, h3), c(0, 0), rho)

  TV <- (TV + pnorm(h1) * p2)
  TV
}