# umf_lufact

lu factorization of a sparse matrix

## Calling Sequence

    LU_ptr = umf_lufact(A)

## Arguments

A

  a sparse, real or complex, square or rectangular, matrix

LU_ptr

  a pointer to umf lu factors (L,U,p,q,R)

## Description

This function computes a LU factorization of the sparse matrix A () and return at the scilab level, a pointer (LU_ptr) to a handle of the LU factors (L,U,p,q,R) (the memory used for them is "outside" scilab stack).

This function must be used in place of umfpack if you have multiple linear systems with the same matrix to solve when the rhs are not known at the same time (for instance A x1 = b1 and A x2 = b2 but b2 depends on x1, etc...).

When such a factorization have been computed, a linear system must be solved with umf_lusolve (in general x = umf_lusolve(LU_ptr, b) but others options are possible, see umf_lusolve. To free the memory used by the LU factors, use umf_ludel(LU_ptr) (umf_ludel); to retrieve the LU factors at the scilab level (for example to display their sparse patterns), use umf_luget; to get some information (number of non zeros in L and U), use umf_luinfo. To compute an approximation of the condition number use condestsp

## Examples

    // this is the small linear test system from UMFPACK
    // whom solution must be [1;2;3;4;5]
    A = sparse( [ 2  3  0  0  0;
                  3  0  4  0  6;
                  0 -1 -3  2  0;
                  0  0  1  0  0;
                  0  4  2  0  1] );
    b = [8 ; 45; -3; 3; 19];
    Lup = umf_lufact(A);
    x = umf_lusolve(Lup,b)

    // solve now A'x=b
    x = umf_lusolve(Lup,b,"A''x=b")
    norm(A'*x - b)

    // do not forget to clear memory with
    umf_ludel(Lup)

    // a real (but small)  example
    // first load a sparse matrix
    [A] = ReadHBSparse(SCI+"/modules/umfpack/examples/arc130.rua");
    // compute the factorization
    Lup = umf_lufact(A);
    b = rand(size(A,1),1); // a random rhs
    // use umf_lusolve for solving Ax=b
    x = umf_lusolve(Lup,b);
    norm(A*x - b)

    // now the same thing with iterative refiment
    x = umf_lusolve(Lup,b,"Ax=b",A);
    norm(A*x - b)

    // solve now the system A'x=b
    x = umf_lusolve(Lup,b,"A''x=b");  // without refinement
    norm(A'*x - b)
    x = umf_lusolve(Lup,b,"A''x=b",A);  // with refinement
    norm(A'*x - b)

    // do not forget to clear memory
    umf_ludel(Lup)

## See Also

- umfpack
- umf_luget
- umf_lusolve
- umf_ludel
- umf_luinfo
- condestsp