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classdef factorization_cod_dense < factorization
%FACTORIZATION_COD_DENSE complete orthogonal factorization: A = U*R*V' where A is full.
% A fairly accurate estimate of rank is found. double(inverse(F)) is a fairly
% accurate estimate of pinv(A).
% Copyright 2011-2012, Timothy A. Davis, http://www.suitesparse.com
methods
function F = factorization_cod_dense (A)
%FACTORIZATION_COD_DENSE A = U*R*V'
[f.U, f.R, f.V, F.A_rank] = cod (A) ;
F.A = A ;
F.Factors = f ;
F.kind = 'dense COD factorization: A = U*R*V''' ;
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.U*f.R*f.V', 1) / norm (F.A, 1) ;
end
function x = mldivide_subclass (F,b)
%MLDIVIDE_SUBLCASS x = A\b using a dense COD factorization
% x = V * (R \ (U' * b))
f = F.Factors ;
op.UT = true ;
y = f.U' * b ;
if (issparse (y))
y = full (y) ;
end
x = f.V * linsolve (f.R, y, op) ;
end
function x = mrdivide_subclass (b,F)
%MRDIVIDE_SUBCLASS x = b/A using dense COD factorization
% x = ((b * V) / R) * U' = (U * (R' \ (b*V)'))'
f = F.Factors ;
op.UT = true ;
op.TRANSA = true ;
y = (b * f.V)' ;
if (issparse (y))
y = full (y) ;
end
x = (f.U * linsolve (f.R, y, op))' ;
end
end
end
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