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#' @name idcond_check
#' @description Check the identifiability conditions C1-C2 of Park and Oh (2015).
#' @title Check the identifiability conditions
#' @usage idCond_check(P)
#' @param P source composition matrix in multivariate receptor model
#' @return idCond TRUE if all the conditions are satisfied, FALSE otherwise
#'
idCond_check = function(P){
q = base::nrow(P)
idCond_1 = 1
idCond_2 = 1
for (k in 1:q){
idCol = base::which(P[k,]==0)
idCond_1 = idCond_1*(base::length(idCol) >= q-1) # Condition C1
idRow = base::c(1:q)[-k]
P_k = P[idRow, idCol]
idCond_2 = idCond_2*(base::qr(P_k)$rank == q-1) # Condition C2
}
idCond = idCond_1 * idCond_2
return(idCond) # if all the conditions are satisfied, it is TRUE (1).
}
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