lm_sweep = function(C, pi){
    #
    # Performs the sweep operator:
    #
    # *) http://node101.psych.cornell.edu/Darlington/sweep.htm
    # *) Page 687 of the Hocking book
    #
    # on an input matrix C
    #
    m = dim(C)[1]
    n = dim(C)[2]

    PV = 1./C[pi,pi]

    row_pi = t( as.matrix( C[pi, ] ) )
    col_pi = as.matrix( C[, pi] )

    G = C - ( col_pi %*% row_pi ) * PV # step 2
    G[pi, ] = C[pi, ] * PV # step 3
    G[, pi] = -C[, pi] * PV # step 4
    G[pi, pi] = PV

    G
}


verifty_lm_sweep = function(){
    #
    # Verify the above implementation of the lm_sweep function:
    #
    lines = '9 3 4 -2 5
             3 8 6 5 4
             4 6 7 3 1
             -2 5 3 9 2
             5 4 1 2 8'
    con = textConnection( lines )
    T = read.table( con, header=FALSE )
    close(con)
    colnames(T) = 1:dim(T)[1]
    T = as.matrix( T )

    T1 = lm_sweep(T, 1)
    T2 = lm_sweep(T1, 2)
    T3 = lm_sweep(T2, 3) # <- this matches the matrix found on the Darlington sweep web page mentioned above
    T3
}