context("OptimParams")

naive_f = function(link, M1,M2,M3, p,β,b)
{
  d = length(M1)
  K = length(p)
  λ <- sqrt(colSums(β^2))

  # Compute β x2,3 (self) tensorial products
  β2 = array(0, dim=c(d,d,K))
  β3 = array(0, dim=c(d,d,d,K))
  for (k in 1:K)
  {
    for (i in 1:d)
    {
      for (j in 1:d)
      {
        β2[i,j,k] = β[i,k]*β[j,k]
        for (l in 1:d)
          β3[i,j,l,k] = β[i,k]*β[j,k]*β[l,k]
      }
    }
  }

  res = 0
  for (i in 1:d)
  {
    term = 0
    for (k in 1:K)
      term = term + p[k]*.G(link,1,λ[k],b[k])*β[i,k]
    res = res + (term - M1[i])^2
    for (j in 1:d)
    {
      term = 0
      for (k in 1:K)
        term = term + p[k]*.G(link,2,λ[k],b[k])*β2[i,j,k]
      res = res + (term - M2[i,j])^2
      for (l in 1:d)
      {
        term = 0
        for (k in 1:K)
          term = term + p[k]*.G(link,3,λ[k],b[k])*β3[i,j,l,k]
        res = res + (term - M3[i,j,l])^2
      }
    }
  }
  res
}

test_that("naive computation provides the same result as vectorized computations",
{
  h <- 1e-7 #for finite-difference tests
  tol <- 1e-3 #large tolerance, necessary in some cases... (generally 1e-6 is OK)
  for (dK in list( c(2,2), c(5,3)))
  {
    d = dK[1]
    K = dK[2]

    M1 = runif(d, -1, 1)
    M2 = matrix(runif(d*d,-1,1), ncol=d)
    M3 = array(runif(d*d*d,-1,1), dim=c(d,d,d))

    for (link in c("logit","probit"))
    {
      op = new("OptimParams", "li"=link, "M1"=as.double(M1),
        "M2"=as.double(M2), "M3"=as.double(M3), "K"=as.integer(K))

      for (var in seq_len((2+d)*K-1))
      {
        p = runif(K, 0, 1)
        p = p / sum(p)
        β <- matrix(runif(d*K,-5,5),ncol=K)
        b = runif(K, -5, 5)
        x <- c(p[1:(K-1)],as.double(β),b)

        # Test functions values
        expect_equal( op$f(x), naive_f(link,M1,M2,M3, p,β,b) )

        # Test finite differences ~= gradient values
        dir_h <- rep(0, (2+d)*K-1)
        dir_h[var] = h

        expect_equal( op$grad_f(x)[var], ( op$f(x+dir_h) - op$f(x) ) / h, tol )
      }
    }
  }
})

test_that("W computed in C and in R are the same",
{
  # TODO: provide data X,Y + parameters theta
  dd <- d + d^2 + d^3
  p <- θ$p
  β <- θ$β
  λ <- sqrt(colSums(β^2))
  b <- θ$b
  β2 <- apply(β, 2, function(col) col %o% col)
  β3 <- apply(β, 2, function(col) col %o% col %o% col)
  M <- c(
    β  %*% (p * .G(li,1,λ,b)),
    β2 %*% (p * .G(li,2,λ,b)),
    β3 %*% (p * .G(li,3,λ,b)))
  Id <- as.double(diag(d))
  E <- diag(d)
  v1 <- Y * X
  v2 <- Y * t( apply(X, 1, function(Xi) Xi %o% Xi - Id) )
  v3 <- Y * t( apply(X, 1, function(Xi) { return (Xi %o% Xi %o% Xi
    - Reduce('+', lapply(1:d, function(j) as.double(Xi %o% E[j,] %o% E[j,])), rep(0, d*d*d))
    - Reduce('+', lapply(1:d, function(j) as.double(E[j,] %o% Xi %o% E[j,])), rep(0, d*d*d))
    - Reduce('+', lapply(1:d, function(j) as.double(E[j,] %o% E[j,] %o% Xi)), rep(0, d*d*d))) } ) )
  Omega1 <- matrix(0, nrow=dd, ncol=dd)
  for (i in 1:n)
  {
    gi <- t(as.matrix(c(v1[i,], v2[i,], v3[i,]) - M))
    Omega1 <- Omega1 + t(gi) %*% gi / n
  }
  Omega2 <- matrix( .C("Compute_Omega",
    X=as.double(X), Y=as.double(Y), M=as.double(M),
    pn=as.integer(n), pd=as.integer(d),
    W=as.double(W), PACKAGE="morpheus")$W, nrow=dd, ncol=dd )
  rg <- range(Omega1 - Omega2)
  expect_that(rg[2] - rg[1] <= 1e8)
})