Handling zero values in IOT

[WesIngwersen]

Division by zero is invalid - this applies to matrix inversion as well when either rows or columns of a matrix contain all zero values.
In useeior, the primary function for normalizing Make and Use tables is normalizeIOtransactions.
normalizeIOtransactions has built in code to change 0 values to 0.001 in both the transactions matrix (e.g. Make or Use body) and the output vector.

normalizeIOTransactions <- function (IO_transactions_df, IO_output_df) {
  # Replace 0 in IO_transactions_df and IO_output_df with 1E-3 to avoid errors in solve(x_hat)
  for (s in names(IO_output_df[IO_output_df == 0])){
    IO_transactions_df[s, s] <- 1E-3    
  }
  IO_output_df[IO_output_df == 0] <- 1E-3
  Z <- as.matrix(IO_transactions_df)
  x <- unname(unlist(IO_output_df))
  x_hat <- diag(x, length(x), length(x))
  A <- Z %*% solve(x_hat)
  dimnames(A) <- dimnames(Z)

Is this fully necessary (for instance can only output be adjusted which is the one that is inverted?
Is this done in CEDA?

RESOLVED: Use CEDA approach as described below.

[MoLi7]

CEDA does not pre-replace zeros with small values. Instead, it handles zeros after division using .fillna(0), see example 1 and example 2.

This means for normalization, e.g. deriving $A$ matrix, when $q=0$, the division $U/q$ produces NaN (or inf), which gets converted to 0. This is mathematically equivalent to saying "if a commodity has no output, it has no economic contribution to direct requirements," which is a reasonable assumption.