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_dense
```classdef factorization_ldl_dense < factorization
%FACTORIZATION_LDL_DENSE P'*A*P = L*D*L' where A is full and symmetric

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

methods

function F = factorization_ldl_dense (A)
%FACTORIZATION_LDL_DENSE : A(p,p) = L*D*L'
if (isempty (A))
f.L = [ ] ;
f.D = [ ] ;
f.p = [ ] ;
else
[f.L, f.D, f.p] = ldl (A, 'vector') ;
end
% D is block diagonal with 2-by-2 blocks, and is best stored as
% a *sparse* matrix, not full.  This saves storage and speeds up
% D\b in the solve phases below.
f.D = sparse (f.D) ;
c = full (condest (f.D)) ;
if (c > 1/(2*eps))
error ('MATLAB:singularMatrix', ...
'Matrix is singular to working precision.') ;
end
n = size (A,1) ;
F.A = A ;
F.Factors = f ;
F.A_rank = n ;
F.A_condest = c ;
F.kind = 'dense LDL factorization: A(p,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.A (f.p, 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 dense LDL
% x = P * (L' \ (D \ (L \ (P' * b))))
f = F.Factors ;
opL.LT = true ;
opLT.LT = true ;
opLT.TRANSA = true ;
y = b (f.p, :) ;
if (issparse (y))
y = full (y) ;
end
x = linsolve (f.L, f.D \ linsolve (f.L, y, opL), opLT) ;
x (f.p, :) = x ;
end

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