# 4D variable (atall: MARG_COMMm x TRAD_COMMi x REGr x REGs), 2 dims fixed
# With MARG_COMMm size=1, reduce_shock picks free_idx=[REGs] (k=1)
#   {REGs}(size-1, factor=3) ties {MARG_COMMm,REGs}(size-2, factor=3) -> smaller size wins
# write_ragged: single-column branch

dat <- ems_data(
  dat_input = dat_input,
  par_input = par_input,
  set_input = set_input,
  REG = "big3",
  PROD_COMM = "macro_sector",
  ENDW_COMM = "labor_agg"
)

model <- ems_model(
  model_file = model_file,
  closure_file = closure_file
)

REG <- c("chn", "usa", "row")
TRAD_COMM <- c("svces", "food", "crops", "mnfcs", "livestock")
MARG_COMM <- "svces"

set.seed(42)

atall_full <- expand.grid(
  MARG_COMMm = MARG_COMM,
  TRAD_COMMi = TRAD_COMM,
  REGr = REG,
  REGs = REG,
  stringsAsFactors = FALSE
)
atall_full$Value <- 0
atall_full <- atall_full[do.call(order, atall_full), ]

# Fix TRAD_COMMi="crops" AND REGr="chn"; free dims MARG_COMMm(1) x REGs(3), n=3
# reduce_shock: {REGs}(factor=3) ties {MARG,REGs}(factor=3) -> k=1, free_idx=[REGs]
atall <- atall_full[
  atall_full$TRAD_COMMi == "crops" & atall_full$REGr == "chn",
]
atall$Value <- runif(nrow(atall))

atall_shk <- ems_custom_shock(var = "atall", input = atall)


cmf_path <- ems_deploy(
  .data = dat,
  model = model,
  shock = atall_shk
)

outputs <- ems_solve(
  cmf_path = cmf_path,
  matrix_method = "LU",
  solution_method = "Johansen"
)

# checks
atall <- merge(atall, atall_full, by = setdiff(colnames(atall), "Value"), all.y = TRUE)
atall$Value.x <- ifelse(is.na(atall$Value.x), atall$Value.y, atall$Value.x)
atall <- atall[, seq_len(ncol(atall) - 1)]
colnames(atall)[ncol(atall)] <- "Value"

check <- all.equal(atall, outputs$dat$atall, check.attributes = FALSE, tolerance = 1e-6)
