LU decomposition of a real square matrix.  The matrix is decomposed as P∙L∙U.

Syntax

P,L,U = LU(M)

Argument

Name

Description

M

A positive definite matrix.

Outputs

Name

Description

P

The permutation matrix.  Same size as M.

L

The lower triangle of the decomposition.  Same size as M.

U

The upper triangle of the decomposition.  Same size as M.

Example

Find the LU decomposition of a square matrix.

Syntax

M = [1.7,0.5,1.2;1.7,-1,-2;-1,0.2,0.8]// Given matrix

P,L,U = LU(M);

Result

Comments

LU decomposition is used for solving linear equations Ax = b.  First, compute the LU decomposition P * A = L * U, then solve Ly = P-1b for y, and finally solve Ux = y for x.  The purpose of P is to increase numerical stability by avoiding small pivots.

LU is based on the LAPACK routines 'dgetrf' for real matrices and 'zgetrf' for the complex case."

See Also:

LSolve

Csky

QR

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