#--- Copula tests ------------------------------------------------------

## library(LocalCop)
## library(TMB)
## library(testthat)

##############
# PDF TEST
##############

test_that("Copula density is same in VineCopula and TMB", {
  nreps <- 20
  test_descr <- expand.grid(family = c(1, 2, 3, 4, 5), # add copula families
                            stringsAsFactors = FALSE)
  n_test <- nrow(test_descr)
  for(ii in 1:n_test) {
    for(jj in 1:nreps) {
      # generate data
      family <- test_descr$family[ii]
      model <- c(`1` = "dgaussian", `2` = "dstudent",
                 `3` = "dclayton",
                 `4` = "dgumbel", `5` = "dfrank")
      model <- model[as.character(family)]
      args <- data_sim(family = family)
      # in R
      ll_r <- VineCopula::BiCopPDF(
        u1 = args$udata[,1],
        u2 = args$udata[,2],
        family = family,
        par = args$epar,
        par2 = args$epar2
      )
      ll_r <- -sum(args$wgt * log(ll_r))
      # in TMB
      parameters <- list(theta = args$epar)
      if(family == 2) {
        parameters <- c(parameters, list(nu = args$epar2))
      }
      cop_adf <- TMB::MakeADFun(
        data = list(
          model = model,
          u1 = args$udata[,1],
          u2 = args$udata[,2],
          weights = args$wgt
        ),
        parameters = parameters,
        silent = TRUE, DLL = "LocalCop_TMBExports")
      ll_tmb <- cop_adf$fn()
      expect_equal(ll_r, ll_tmb)
    }
  }
})


##############
# CDF TEST
##############

test_that("Copula cdf is same in VineCopula and TMB", {
  nreps <- 20
  test_descr <- expand.grid(family = c(3, 4, 5), # add copula families
                            stringsAsFactors = FALSE)
  n_test <- nrow(test_descr)
  for(ii in 1:n_test) {
    for(jj in 1:nreps) {
      # generate data
      family <- test_descr$family[ii]
      model <- c(`1` = "pgaussian", `2` = "pstudent",
                 `3` = "pclayton",
                 `4` = "pgumbel", `5` = "pfrank")
      model <- model[as.character(family)]
      args <- data_sim(family = family)
      # in R
      ll_r <- VineCopula::BiCopCDF(u1 = args$udata[,1], u2 = args$udata[,2],
                                   family = family, par = args$epar, par2 = args$epar2)
      ll_r <- -sum(args$wgt * log(ll_r))
      # in TMB
      cop_adf <- TMB::MakeADFun(
        data = list(
          model = model,
          u1 = args$udata[,1],
          u2 = args$udata[,2],
          weights = args$wgt
        ),
        parameters = list(theta = args$epar),
        silent = TRUE, DLL = "LocalCop_TMBExports")
      ll_tmb <- cop_adf$fn(args$epar)
      expect_equal(ll_r, ll_tmb)
    }
  }
})



############################
# PARTIAL TEST
############################

test_that("Copula partial derivative is same in VineCopula and TMB", {
  nreps <- 20
  test_descr <- expand.grid(family = c(1, 3, 4, 5), # add copula families
                            stringsAsFactors = FALSE)
  n_test <- nrow(test_descr)
  for(ii in 1:n_test) {
    for(jj in 1:nreps) {
      # generate data
      family <- test_descr$family[ii]
      model <- c(`1` = "hgaussian", `2` = "hstudent",
                 `3` = "hclayton",
                 `4` = "hgumbel", `5` = "hfrank")
      model <- model[as.character(family)]
      args <- data_sim(family = family)
      # in R - VineCopula
      ll_r <- VineCopula::BiCopHfunc1(u1 = args$udata[,1], u2 = args$udata[,2],
                                      family = family, par = args$epar, par2 = args$epar2)
      ll_r <- log(ll_r)
      ind <- ll_r > -20  # control the extremely small values in the log scale.
      ll_r <- -sum(args$wgt[ind] * ll_r[ind])
      # in TMB
      cop_adf <- TMB::MakeADFun(
        data = list(
          model = model,
          u1 = args$udata[ind,1],
          u2 = args$udata[ind,2],
          weights = args$wgt[ind]
        ),
        parameters = list(theta = args$epar[ind]),
        silent = TRUE, DLL = "LocalCop_TMBExports")
      ll_tmb <- cop_adf$fn(args$epar[ind])
      expect_equal(ll_r, ll_tmb)
      stopifnot(all.equal(ll_r, ll_tmb))
    }
  }
})