R : Copyright 2005, The R Foundation for Statistical Computing
Version 2.1.1  (2005-06-20), ISBN 3-900051-07-0

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[Previously saved workspace restored]

>  # sweepex.r                    J F Monahan September 2007
>  #
>  # sweep operator -- function and example
>  #
>   A <- matrix( c(3,1,0,1,4,2,0,2,6), 3, 3)
>  #  write it out
>   A
     [,1] [,2] [,3]
[1,]    3    1    0
[2,]    1    4    2
[3,]    0    2    6
>  #  define function
>    regsweep <- function(A,k) {
+               d <- A[k,k]               # sweep out row k, col k
+               A[k,] <- A[k,]/d
+               b <- A[,k]
+               b[k] <- 0                 # don't change row k here
+               A <- A - outer(b,A[k,])   # main operation
+               A[,k] <- -b/d             # fix col k
+               A[k,k] <- 1/d             # diagonal element & done
+               regsweep <- A     }
>  # 
>  #  write it out
>   A <- regsweep(A,2)                    # sweep second row/col
>   A
      [,1]  [,2] [,3]
[1,]  2.75 -0.25 -0.5
[2,]  0.25  0.25  0.5
[3,] -0.50 -0.50  5.0
>   A <- regsweep(A,3)                    # sweep third row/col
>   A
     [,1] [,2] [,3]
[1,]  2.7 -0.3  0.1
[2,]  0.3  0.3 -0.1
[3,] -0.1 -0.1  0.2
>   A <- regsweep(A,2)                    # sweep second row/col
>   A
     [,1]      [,2]       [,3]
[1,]    3 1.0000000  0.0000000
[2,]    1 3.3333333 -0.3333333
[3,]    0 0.3333333  0.1666667
>   A <- regsweep(A,1)                    # sweep first row/col
>   A
           [,1]      [,2]       [,3]
[1,]  0.3333333 0.3333333  0.0000000
[2,] -0.3333333 3.0000000 -0.3333333
[3,]  0.0000000 0.3333333  0.1666667
>  rm(list=ls())                # clean up
> 

>  # regsweep.r                    J F Monahan September 2007
>  #
>  # sweep operator -- function and example
>  #                  response vector
>   y <-c( 4.5, 5.5, 6.5, 8, 10, 12)
>  #                  design matrix -- intercept, linear, quadratic
>   X <- matrix(1,6,3)          # get shape and intercept, fix later
>   X[,2] <- 1:6
>   X[,3] <- (1:6)*(1:6)
>  #                  put X and y together for easy printing
>   Xy <- cbind(X,y)  # put them together
>   Xy                # write it out
               y
[1,] 1 1  1  4.5
[2,] 1 2  4  5.5
[3,] 1 3  9  6.5
[4,] 1 4 16  8.0
[5,] 1 5 25 10.0
[6,] 1 6 36 12.0
>  #
>  #  construct inner product matrix
>   A <- crossprod(Xy,Xy)
>  #  write it out
>   A
                     y
   6.0  21   91  46.50
  21.0  91  441 189.00
  91.0 441 2275 895.00
y 46.5 189  895 400.75
>  #  define function
>    regsweep <- function(A,k) {
+               d <- A[k,k]               # sweep out row k, col k
+               A[k,] <- A[k,]/d
+               b <- A[,k]
+               b[k] <- 0                 # don't change row k here
+               A <- A - outer(b,A[k,])   # main operation
+               A[,k] <- -b/d             # fix col k
+               A[k,k] <- 1/d             # diagonal element & done
+               regsweep <- A     }
>  # 
>  #  sweep first row/col to get means, css for X and y
>   A <- regsweep(A,1)     # sweep first row/col
>   A
                                     y
    0.1666667   3.50  15.16667   7.750
   -3.5000000  17.50 122.50000  26.250
  -15.1666667 122.50 894.83333 189.750
y  -7.7500000  26.25 189.75000  40.375
>   A <- regsweep(A,2)                    # sweep linear row/col
>   A
                                     y
   0.8666667 -0.20000000 -9.333333 2.5
  -0.2000000  0.05714286  7.000000 1.5
   9.3333333 -7.00000000 37.333333 6.0
y -2.5000000 -1.50000000  6.000000 1.0
>   A <- regsweep(A,3)                    # sweep quadratic row/col
>   A
                                       y
   3.20 -1.950000  0.25000000 4.00000000
  -1.95  1.369643 -0.18750000 0.37500000
   0.25 -0.187500  0.02678571 0.16071429
y -4.00 -0.375000 -0.16071429 0.03571429
>   A <- regsweep(A,3)                    # second sweep restores
>   A
                                     y
   0.8666667 -0.20000000 -9.333333 2.5
  -0.2000000  0.05714286  7.000000 1.5
   9.3333333 -7.00000000 37.333333 6.0
y -2.5000000 -1.50000000  6.000000 1.0