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Справка Scilab >> Linear Algebra > Linear Equations > lu


LU factorization with pivoting


[L,U]= lu(A)
[L,U,E]= lu(A)



real or complex matrix (m x n).


real or complex matrices (m x min(m,n)).


real or complex matrices (min(m,n) x n ).


a (n x n) permutation matrix.


[L,U]= lu(A) produces two matrices L and U such that A = L*U with U upper triangular and L a general matrix without any particular structure. In fact, the matrix A is factored as E*A=B*U where the matrix B is lower triangular and the matrix L is computed from L=E'*B.

If A has rank k, rows k+1 to n of U are zero.

[L,U,E]= lu(A) produces three matrices L, U and E such that E*A = L*U with U upper triangular and E*L lower triangular for a permutation matrix E.

If A is a real matrix, using the function lufact and luget it is possible to obtain the permutation matrices and also when A is not full rank the column compression of the matrix L.

Example #1

In the following example, we create the Hilbert matrix of size 4 and factor it with A=LU. Notice that the matrix L is not lower triangular. To get a lower triangular L matrix, we should have given the output argument E to Scilab.

a = testmatrix("hilb",4);

Example #2

In the following example, we create the Hilbert matrix of size 4 and factor it with EA=LU. Notice that the matrix L is lower triangular.

a = testmatrix("hilb",4);

Example #3

The following example shows how to use the lufact and luget functions.



See also

  • lufact — sparse lu factorization
  • luget — extraction of sparse LU factors
  • lusolve — sparse linear system solver
  • qr — QR decomposition
  • svd — singular value decomposition

Used Functions

lu decompositions are based on the Lapack routines DGETRF for real matrices and ZGETRF for the complex case.

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Last updated:
Tue Feb 25 08:54:54 CET 2020