Description Usage Arguments Details Value Author(s) Examples
LU
computes the LU decomposition of a matrix, A, such that P A = L U,
where L is a lower triangle matrix, U is an upper triangle, and P is a
permutation matrix.
1 
A 
coefficient matrix 
b 
righthand side vector. When supplied the returned object will also contain the solved
d and 
tol 
tolerance for checking for 0 pivot 
verbose 
logical; if 
... 
additional arguments passed to 
The LU decomposition is used to solve the equation A x = b by calculating L(Ux  d) = 0, where Ld = b. If row exchanges are necessary for A then the permutation matrix P will be required to exchange the rows in A; otherwise, P will be an identity matrix and the LU equation will be simplified to A = L U.
A list of matrix components of the solution, P
, L
and U
. If b
is supplied, the vectors d and x
are also returned.
Phil Chalmers
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19  A < matrix(c(2, 1, 1,
3, 1, 2,
2, 1, 2), 3, 3, byrow=TRUE)
b < c(8, 11, 3)
(ret < LU(A)) # P is an identity; no row swapping
with(ret, L %*% U) # check that A = L * U
LU(A, b)
LU(A, b, verbose=TRUE)
LU(A, b, verbose=TRUE, fractions=TRUE)
# permutations required in this example
A < matrix(c(1, 1, 1,
2, 2, 4,
1, 1, 1), 3, 3, byrow=TRUE)
b < c(1, 2, 9)
(ret < LU(A, b))
with(ret, P %*% A)
with(ret, L %*% U)

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