— Loadable Function: [l, u] = splu (a)
— Loadable Function: [l, u, P] = splu (a)
— Loadable Function: [l, u, P, Q] = splu (a)
— Loadable Function: [l, u, P, Q] = splu (..., thres)
— Loadable Function: [l, u, P] = splu (..., Q)

Compute the LU decomposition of the sparse matrix a, using subroutines from UMFPACK. The result is returned in a permuted form, according to the optional return values P and Q.

Called with two or three output arguments and a single input argument, splu is a replacement for lu, and therefore the sparsity preserving column permutations Q are not performed. Called with a fourth output argument, the sparsity preserving column transformation Q is returned, such that P * a * Q = l * u.

An additional input argument thres, that defines the pivoting threshold can be given. Alternatively, the desired sparsity preserving column permutations Q can be passed. Note that Q is assumed to be fixed if three are fewer than four output arguments. Otherwise, the updated column permutations are returned as the fourth argument.

With two output arguments, returns the permuted forms of the upper and lower triangular matrices, such that a = l * u. With two or three output arguments, if a user-defined Q is given, then u * Q' is returned. The matrix is not required to be square.

See also: sparse, spinv, colamd, symamd.