1classdef factorization_ldl_dense < factorization
2%FACTORIZATION_LDL_DENSE P'*A*P = L*D*L' where A is full and symmetric
3
4% Copyright 2011-2012, Timothy A. Davis, http://www.suitesparse.com
5
6    methods
7
8        function F = factorization_ldl_dense (A)
9            %FACTORIZATION_LDL_DENSE : A(p,p) = L*D*L'
10            if (isempty (A))
11                f.L = [ ] ;
12                f.D = [ ] ;
13                f.p = [ ] ;
14            else
15                [f.L, f.D, f.p] = ldl (A, 'vector') ;
16            end
17            % D is block diagonal with 2-by-2 blocks, and is best stored as
18            % a *sparse* matrix, not full.  This saves storage and speeds up
19            % D\b in the solve phases below.
20            f.D = sparse (f.D) ;
21            c = full (condest (f.D)) ;
22            if (c > 1/(2*eps))
23                error ('MATLAB:singularMatrix', ...
24                    'Matrix is singular to working precision.') ;
25            end
26            n = size (A,1) ;
27            F.A = A ;
28            F.Factors = f ;
29            F.A_rank = n ;
30            F.A_condest = c ;
31            F.kind = 'dense LDL factorization: A(p,p) = L*D*L''' ;
32        end
33
34        function e = error_check (F)
35            %ERROR_CHECK : return relative 1-norm of error in factorization
36            % meant for testing only
37            f = F.Factors ;
38            e = norm (F.A (f.p, f.p) - f.L*f.D*f.L', 1) / norm (F.A, 1) ;
39        end
40
41        function x = mldivide_subclass (F,b)
42            %MLDIVIDE_SUBCLASS x = A\b using dense LDL
43            % x = P * (L' \ (D \ (L \ (P' * b))))
44            f = F.Factors ;
45            opL.LT = true ;
46            opLT.LT = true ;
47            opLT.TRANSA = true ;
48            y = b (f.p, :) ;
49            if (issparse (y))
50                y = full (y) ;
51            end
52            x = linsolve (f.L, f.D \ linsolve (f.L, y, opL), opLT) ;
53            x (f.p, :) = x ;
54        end
55
56        function x = mrdivide_subclass (b,F)
57            %MRDIVIDE_SUBCLASS x = b/A using dense LDL
58            % x = (P * (L' \ (D \ (L \ (P' * b')))))'
59            x = (mldivide_subclass (F, b'))' ;
60        end
61    end
62end
63