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_ldl_sparse
```classdef factorization_ldl_sparse < factorization
%FACTORIZATION_LDL_SPARSE P'*A*P = L*D*L' where A is sparse and symmetric

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

methods

function F = factorization_ldl_sparse (A)
%FACTORIZATION_LDL_SPARSE : P'*A*P = L*D*L'
[f.L, f.D, f.P] = ldl (A) ;
c = full (condest (f.D)) ;
if (c > 1/(2*eps))
error ('MATLAB:singularMatrix', ...
'Matrix is singular to working precision.') ;
end
F.A = A ;
F.Factors = f ;
F.A_rank = size (A,1) ;
F.A_condest = c ;
F.kind = 'sparse LDL factorization: P''*A*P = L*D*L''' ;
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.A*f.P - f.L*f.D*f.L', 1) / norm (F.A, 1) ;
end

function x = mldivide_subclass (F,b)
%MLDIVIDE_SUBCLASS x = A\b using sparse LDL
% x = P * (L' \ (L \ (P' * b)))
f = F.Factors ;
x = f.P * (f.L' \ (f.D \ (f.L \ (f.P' * b)))) ;
end

function x = mrdivide_subclass (b,F)
%MRDIVIDE_SUBCLASS x = b/A using sparse LDL
% x = (P * (L' \ (L \ (P' * b'))))'
x = (mldivide_subclass (F,b'))' ;
end
end
end
```