# Computes the marginal matrix A and margins vector m of an estimation problem Given a set of marginal target constraints and the dimension of the array $X$ to wich the targets relate to, this function computes the matrix $A$ of full rank and vector $m$ such that [REMOVE_ME]$$ A^T \pi = (m, 1)^Tt(A) * p = t(c(m, 1)) [REMOVE_ME_2]$$ where vector $m$ contains all components but one of every target and $p$ is a vector of the (unknow) components of $X$. ## Description Given a set of marginal target constraints and the dimension of the array $X$ to wich the targets relate to, this function computes the matrix $A$ of full rank and vector $m$ such that $$ A^T \pi = (m, 1)^Tt(A) * p = t(c(m, 1)) $$ where vector $m$ contains all components but one of every target and $p$ is a vector of the (unknow) components of $X$. ```r ComputeA(dim.arr, target.list, target.data) ``` ## Arguments - `dim.arr`: The dimension of the array $X$ to which the margins are applied. - `target.list`: A list of the target margins provided in target.data. Each component of the list is an array whose cells indicates which dimension the corresponding margin relates to. - `target.data`: A list containing the data of the target margins. Each component of the list is an array storing a margin. The list order must follow the one defined in target.list. Note that the cells of the arrays must be non-negative. ## Returns A list whose elements are defined below. - **marginal.matrix**: The marginal matrix. - **margins**: A vector containing the margins associated with A. - **df**: The degree of freedom of the problem. ## Author(s) Johan Barthelemy Maintainer: Johan Barthelemy . ## See Also `MarginalMatrix`. ## Examples ```r # loading the data data(spnamur, package = "mipfp") # subsetting the data frame, keeping only the first 3 variables spnamur.sub <- subset(spnamur, select = Household.type:Prof.status) # true table true.table <- table(spnamur.sub) # extracting the margins tgt.v1 <- apply(true.table, 1, sum) tgt.v1.v2 <- apply(true.table, c(1,2), sum) tgt.v2.v3 <- apply(true.table, c(2,3), sum) tgt.list.dims <- list(1, c(1,2), c(2,3)) tgt.data <- list(tgt.v1, tgt.v1.v2, tgt.v2.v3) # creating the seed, a 10 pct sample of spnamur seed.df <- spnamur.sub[sample(nrow(spnamur), round(0.10*nrow(spnamur))), ] seed.table <- table(seed.df) # computing the associated marginal matrix and margins vector res.marg <- ComputeA(dim(seed.table), tgt.list.dims, tgt.data) print(res.marg) ```

ComputeA function