LU | R Documentation |
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.
LU(A, b, tol = sqrt(.Machine$double.eps), verbose = FALSE, ...)
A |
coefficient matrix |
b |
right-hand 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
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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