lu

LU matrix factorization.

📝 Syntax

• [L, U] = lu(A)

• [L, U, P] = lu(A)

📥 Input argument

• A - a matrix: square, finite single or double.

📤 Output argument

• L - Lower triangular factor: matrix (same type A)

• U - Upper triangular factor: matrix (same type A).

• P - Row permutation: matrix (same type A).

📄 Description

[L, U] = lu(A) function decomposes a full matrixA into two matrices: an upper triangular matrixU and a permuted lower triangular matrix L.

This factorization satisfies the equation A = L * U.

[L, U, P] = lu(A) function, when used with three output arguments, provides a permutation matrixP in addition to the unit lower triangular matrixL and the upper triangular matrix U.

This factorization is expressed as A = P'LU, where L is unit lower triangular, and U is upper triangular.

Used function(s)

LAPACKE_dgetrf, LAPACKE_sgetrf, LAPACKE_zgetrf, LAPACKE_cgetrf

💡 Examples

A = magic(5)
[L, U] = lu(A)
L * U

A = magic(5)
[L, U, P] = lu(A);
subplot(1, 2, 1)
spy(L)
title(_('L factor'))
subplot(1, 2, 2)
spy(U)
title(_('U factor'))

🔗 See also

cond.

🕔 History

Version	📄 Description
1.1.0	initial version