Recover the history of the row operations that have been performed. This function combines the transformation matrices into a single transformation matrix representing all row operations or may optionally print all the individual operations which have been performed.
a matrix A, joined with a vector of constants, b, that has been passed to
gaussianElimination or the row operator matrix functions
logical; print individual transformation ies?
additional arguments
the transformation matrix or a list of individual transformation matrices
A <- matrix(c(2, 1, -1,
-3, -1, 2,
-2, 1, 2), 3, 3, byrow=TRUE)
b <- c(8, -11, -3)
# using row operations to reduce below diagonal to 0
Abt <- Ab <- cbind(A, b)
Abt <- rowadd(Abt, 1, 2, 3/2)
Abt <- rowadd(Abt, 1, 3, 1)
Abt <- rowadd(Abt, 2, 3, -4)
Abt
#> b
#> [1,] 2 1.0 -1.0 8
#> [2,] 0 0.5 0.5 1
#> [3,] 0 0.0 -1.0 1
# build T matrix and multiply by original form
(T <- buildTmat(Abt))
#> [,1] [,2] [,3]
#> [1,] 1.0 0 0
#> [2,] 1.5 1 0
#> [3,] -5.0 -4 1
T %*% Ab # same as Abt
#> b
#> [1,] 2 1.0 -1.0 8
#> [2,] 0 0.5 0.5 1
#> [3,] 0 0.0 -1.0 1
# print all transformation matrices
buildTmat(Abt, TRUE)
#> $T1
#> [,1] [,2] [,3]
#> [1,] 1.0 0 0
#> [2,] 1.5 1 0
#> [3,] 0.0 0 1
#>
#> $T2
#> [,1] [,2] [,3]
#> [1,] 1 0 0
#> [2,] 0 1 0
#> [3,] 1 0 1
#>
#> $T3
#> [,1] [,2] [,3]
#> [1,] 1 0 0
#> [2,] 0 1 0
#> [3,] 0 -4 1
#>
# invert transformation matrix to reverse operations
inv(T) %*% Abt
#> b
#> [1,] 2 1 -1 8
#> [2,] -3 -1 2 -11
#> [3,] -2 1 2 -3
# gaussian elimination
(soln <- gaussianElimination(A, b))
#> [,1] [,2] [,3] [,4]
#> [1,] 1 0 0 2
#> [2,] 0 1 0 3
#> [3,] 0 0 1 -1
T <- buildTmat(soln)
inv(T) %*% soln
#> [,1] [,2] [,3] [,4]
#> [1,] 2 1 -1 8
#> [2,] -3 -1 2 -11
#> [3,] -2 1 2 -3