Command Reference : Function Reference : Function Reference: L
  
 
@lu
LU decomposition of matrix.
Syntax: @lu(M, L, U)
M: matrix
L: matrix
U: matrix
Return: matrix (P)
Performs an LU decomposition with partial (row) pivoting of the matrix M:
if M is a square produce a unit lower triangular matrix, L, an upper triangular matrix, U, and a row permutation matrix, P, such that .
if M is a non-square matrix, if , L will be unit lower trapezoidal (rather than triangular), and if , U will be upper trapezoidal (rather than triangular).
Examples
matrix m = @mnrnd(10, 8)
matrix lmat
matrix umat
matrix pmat = @lu(m, lmat, umat)
generates the random matrix M, then performs the LU decomposition returning PMAT and yielding updated LMAT, UMAT.
The following commands validate the definition
matrix m1 = pmat * lmat * umat
matrix diff = m - m1
since DIFF equals zero.
Cross-references
See also @cholesky, @qr, @svd and @svdfull.