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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 | LU LU LU Decomposition for Matrices
Usage
Computes the LU decomposition for a matrix. The form of the
command depends on the type of the argument. For full (non-sparse)
matrices, the primary form for lu is
[L,U,P] = lu(A),
where L is lower triangular, U is upper triangular, and
P is a permutation matrix such that L*U = P*A. The second form is
[V,U] = lu(A),
where V is P'*L (a row-permuted lower triangular matrix),
and U is upper triangular. For sparse, square matrices,
the LU decomposition has the following form:
[L,U,P,Q,R] = lu(A),
where A is a sparse matrix of either double or dcomplex type.
The matrices are such that L*U=P*R*A*Q, where L is a lower triangular
matrix, U is upper triangular, P and Q are permutation vectors
and R is a diagonal matrix of row scaling factors. The decomposition
is computed using UMFPACK for sparse matrices, and LAPACK for dense
matrices.
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