LU factorization with pivoting
[L,U]= lu(A) [L,U,E]= lu(A)
real or complex matrix (m x n).
real or complex matrices (m x min(m,n)).
real or complex matrices (min(m,n) x n ).
a (n x n) permutation matrix.
[L,U]= lu(A) produces two matrices
U such that
A = L*U with
upper triangular and
L a general matrix without any particular
structure. In fact, the matrix
A is factored as
where the matrix
B is lower triangular
and the matrix
L is computed from
A has rank
U are zero.
[L,U,E]= lu(A) produces three matrices
E such that
E*A = L*U with
U upper triangular and
triangular for a permutation matrix
A is a real matrix, using the function
luget it is possible to obtain
the permutation matrices and also when
A is not full
rank the column compression of the matrix
In the following example, we create the Hilbert matrix of size 4 and factor it with A=LU. Notice that the matrix L is not lower triangular. To get a lower triangular L matrix, we should have given the output argument E to Scilab.
In the following example, we create the Hilbert matrix of size 4 and factor it with EA=LU. Notice that the matrix L is lower triangular.
The following example shows how to use the lufact and luget functions.
lu decompositions are based on the Lapack routines DGETRF for real matrices and ZGETRF for the complex case.