lu

LU decomposition (with partial pivoting).

Syntax

[L, U]       = lu(A)
[L, U, P]    = lu(A)
[L, U, P, Q] = lu(A)        % sparse only
Y            = lu(A)        % packed compact form

Description

Decomposes A into a lower-triangular L, upper-triangular U, and permutation P such that P*A = L*U. With two outputs, returns L and U such that L*U = A and L is permuted-lower (psychologically lower).

For sparse matrices, an additional column-permutation Q and a row-scaling R may be returned. The single-output form returns the LU factors packed into one matrix (LAPACK packed storage).

Examples

A = [1 2 3; 4 5 6; 7 8 10];
[L, U] = lu(A);
norm(L*U - A)            % near-zero

See also

• chol — Cholesky factorization of a Hermitian positive-definite matrix.
• qr — QR decomposition.
• linsolve — Solve a linear system with optional structure hints.
• inv — Matrix inverse.