lu.Matrix: Triangular (LU) Decomposition of a Matrix
Description
Computes the LU decomposition of a matrix.
Usage
lu.Matrix(x, norm.comp = T)
Arguments
x
numeric or complex matrix (does not have to be square). Missing values (NAs)
are not allowed.
norm.comp
a logical vector of length two telling whether or not to compute the
one and/or infinity norm of the matrix, respectively. These norms
should be computed if solve is going to eventually be applied
to the factorization with condit
Value
The LU decomposition of x is returned as an object of class
"lu.Matrix", which is a list with components "l", a unit
lower triangular matrix, "u", an upper triangular matrix, and
"permutation", a row permutation matrix. The one or infinity
norm is included as an attribute, if requested.
and/or infinity norms of the matrix if requested (used for condition
estimation).
Details
This function uses the Lapack subroutine DGETRF to form an LU
factorization of a matrix X.
The factorization has the form
X = P * L * U
where P is a permutation matrix, L is lower triangular
with unit diagonal elements (lower trapezoidal if m > n),
and U is upper triangular (upper trapezoidal if m < n).
References
Anderson, E., et al. (1994).
LAPACK User's Guide,
2nd edition, SIAM, Philadelphia.