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_dense
```classdef factorization_lu_dense < factorization
%FACTORIZATION_LU_DENSE A(p,:) = L*U where A is square and full.

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

methods

function F = factorization_lu_dense (A, fail_if_singular)
%FACTORIZATION_LU_DENSE : A(p,:) = L*U
[m, n] = size (A) ;
if (m ~= n)
error ('FACTORIZE:wrongdim', ...
'LU for rectangular matrices not supported.  Use QR.') ;
end
[f.L, f.U, f.p] = lu (A, 'vector') ;
F.A_condest = cheap_condest (get_diag (f.U), fail_if_singular) ;
F.A = A ;
F.Factors = f ;
F.A_rank = n ;
F.kind = 'dense LU factorization: A(p,:) = 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.A (f.p,:) - f.L*f.U, 1) / norm (F.A, 1) ;
end

function x = mldivide_subclass (F,b)
%MLDIVIDE_SUBCLASS x=A\b using dense LU
% x = U \ (L \ (b (p,:))) ;
f = F.Factors ;
opL.LT = true ;
opU.UT = true ;
y = b (f.p, :) ;
if (issparse (y))
y = full (y) ;
end
x = linsolve (f.U, linsolve (f.L, y, opL), opU) ;
end

function x = mrdivide_subclass (b,F)
%MRDIVIDE_SUBCLASS x = b/A using dense LU
% x (:,p) = (L' \ (U' \ b'))'
f = F.Factors ;
opUT.UT = true ;
opUT.TRANSA = true ;
opLT.LT = true ;
opLT.TRANSA = true ;
y = b' ;
if (issparse (y))
y = full (y) ;
end
x = (linsolve (f.L, linsolve (f.U, y, opUT), opLT))';
x (:, f.p) = x ;
end
end
end
```