Code covered by the BSD License

# Don't let that INV go past your eyes; to solve that system, FACTORIZE!

### Tim Davis (view profile)

14 May 2009 (Updated )

A simple-to-use object-oriented method for solving linear systems and least-squares problems.

### Editor's Notes:

This file was selected as MATLAB Central Pick of the Week

factorization_lu_sparse
```classdef factorization_lu_sparse < factorization
%FACTORIZATION_LU_SPARSE P*A*Q = L*U where A is square and sparse.

% Copyright 2011-2012, Timothy A. Davis, http://www.suitesparse.com

methods

function F = factorization_lu_sparse (A, fail_if_singular)
%FACTORIZATION_LU_SPARSE : P*(R\A)*Q = L*U
[m, n] = size (A) ;
if (m ~= n)
error ('FACTORIZE:wrongdim', ...
'LU for rectangular matrices not supported.  Use QR.') ;
end
if (n == 0)
nil = sparse ([ ]) ;
f.L = nil ;
f.U = nil ;
f.P = nil ;
f.Q = nil ;
f.R = nil ;
F.A_condest = 1 ;
else
[f.L, f.U, f.P, f.Q, f.R] = lu (A) ;
F.A_condest = cheap_condest (get_diag (f.U), fail_if_singular) ;
end
F.A = A ;
F.Factors = f ;
F.A_rank = n ;
F.kind = 'sparse LU factorization: P*(R\A)*Q = L*U' ;
end

function e = error_check (F)
%ERROR_CHECK : return relative 1-norm of error in factorization
% meant for testing only
f = F.Factors ;
e = norm (f.P*(f.R\F.A)*f.Q - f.L*f.U, 1) / norm (F.A, 1) ;
end

function x = mldivide_subclass (F,b)
%MLDIVIDE_SUBCLASS x = A\b using sparse LU
% x = Q * (U \ (L \ (P * (R \ b))))
f = F.Factors ;
x = f.Q * (f.U \ (f.L \ (f.P * (f.R \ b)))) ;
end

function x = mrdivide_subclass (b,F)
%MRDIVIDE_SUBCLASS x = b/A using sparse LU
% x = ((((b * Q) / U) / L) * P) / R ;
f = F.Factors ;
x = ((((b * f.Q) / f.U) / f.L) * f.P) / f.R ;
end
end
end
```