Figure Properties - SERC

2lu
Purpose LU matrix factorization
Syntax [L,U] = lu(X)
[L,U,P] = lu(X)
Y = lu(X)
[L,U,P,Q] = lu(X)
[L,U,P] = lu(X,thresh)
[L,U,P,Q] = lu(X,thresh)
Description The lu function expresses a matrix X as the product of two essentially
triangular matrices, one of them a permutation of a lower triangular matrix
and the other an upper triangular matrix. The factorization is often called the
LU, or sometimes the LR, factorization. X can be rectangular. For a full matrix
X, lu uses the Linear Algebra Package (LAPACK) routines described in
“Algorithm” on page 2-1392.
[L,U] = lu(X) returns an upper triangular matrix in U and a permuted lower
triangular matrix L (that is, a product of lower triangular and permutation
matrices), such that X = L*U.
[L,U,P] = lu(X) returns an upper triangular matrix in U, a lower triangular
matrix L with a unit diagonal, and a permutation matrix P, so that L*U = P*X.
Y = lu(X) returns a matrix Y, which contains the strictly lower triangular L,
i.e., without its unit diagonal, and the upper triangular U as submatrices. That
is, if [L,U,P] = lu(X), then Y = U+L-eye(size(X)). The permutation matrix
P is not returned by Y = lu(X).
[L,U,P,Q] = lu(X) for sparse nonempty X, returns a unit lower triangular
matrix L, an upper triangular matrix U, a row permutation matrix P, and a
column reordering matrix Q, so that P*X*Q = L*U. This syntax uses
UMFPACK and is significantly more time and memory efficient than the other
syntaxes, even when used with colamd. If X is empty or not sparse, lu displays
an error message.
[L,U,P] = lu(X,thresh) controls pivoting in sparse matrices, where thresh
is a pivot threshold in the interval [0,1]. Pivoting occurs when the diagonal
entry in a column has magnitude less than thresh times the magnitude of any
lu
2-1387