Balance a matrix to target margins by RAS.

Reconcile a non-negative matrix to prescribed row and column sums using the RAS (biproportional / iterative proportional fitting) algorithm: alternately rescale rows then columns until both margins are matched, preserving the matrix's structure (zero pattern and relative magnitudes). The row and column targets must have equal totals.

Works on dense and sparse (Matrix) inputs, staying in the input representation so it is efficient for both small dense tables and large sparse input-output systems. (The same core also balances the bilateral trade matrices.) For matrices with negative entries the signed GRAS variant is needed and is not implemented here.

Usage

balance_ras(x, target_rows, target_cols, max_iter = 1000L, tol = 1e-09)

Arguments

x

Non-negative matrix (dense or Matrix).

target_rows

Desired row sums, length nrow(x).

target_cols

Desired column sums, length ncol(x).

max_iter

Maximum RAS iterations.

tol

Convergence tolerance on the largest margin deviation, relative to the margin total (so it is scale-free).

Value

The balanced matrix, in the same representation as x (dense in, dense out; sparse in, sparse out).

Examples

m <- matrix(c(1, 2, 3, 4), nrow = 2)
balance_ras(m, target_rows = c(10, 20), target_cols = c(12, 18))
#>          [,1]      [,2]
#> [1,] 3.363083  6.636917
#> [2,] 8.636917 11.363083