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lu

lu — LU factors of Gaussian elimination

Calling sequence

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

Parameters

A : real or complex matrix (m x n).
L : real or complex matrices (m x min(m,n)).
U : real or complex matrices (min(m,n) x n ).
E : a (n x n) permutation matrix.

Description

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

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.

Examples



a=rand(4,4);
[l,u]=lu(a)
norm(l*u-a)

[h,rk]=lufact(sparse(a))  // lufact fonctionne avec des matrices creuses 
[P,L,U,Q]=luget(h);
ludel(h)
P=full(P);L=full(L);U=full(U);Q=full(Q); 
norm(P*L*U*Q-a) // P,Q sont des matrices de permutation

See also

lufact, luget, lusolve, qr, svd
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