1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
|
classdef factorization_chol_sparse < factorization
%FACTORIZATION_CHOL_SPARSE P'*A*P = L*L' where A is sparse and sym. pos. def.
% Copyright 2011-2012, Timothy A. Davis, http://www.suitesparse.com
methods
function F = factorization_chol_sparse (A)
%FACTORIZATION_CHOL_SPARSE : P'*A*P = L*L'
[f.L, g, f.P] = chol (A, 'lower') ;
if (g ~= 0)
error ('MATLAB:posdef', 'Matrix must be positive definite.') ;
end
F.A = A ;
F.Factors = f ;
F.A_rank = size (A,1) ;
F.kind = 'sparse Cholesky factorization: P''*A*P = L*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.L', 1) / norm (F.A, 1) ;
end
function x = mldivide_subclass (F,b)
%MLDIVIDE_SUBCLASS x = A\b using sparse Cholesky
% x = P * (L' \ (L \ (P' * b)))
f = F.Factors ;
x = f.P * (f.L' \ (f.L \ (f.P' * b))) ;
end
function x = mrdivide_subclass (b,F)
%MRDIVIDE_SUBCLASS x = b/A using sparse Cholesky
% x = (P * (L' \ (L \ (P' * b'))))'
x = (mldivide_subclass (F, b'))' ;
end
end
end
|
