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Don't let that INV go past your eyes; to solve that system, FACTORIZE!

Don't let that INV go past your eyes; to solve that system, FACTORIZE!

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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_qrt_dense
classdef factorization_qrt_dense < factorization
%FACTORIZATION_QRT_DENSE A' = Q*R where A is full.

% Copyright 2011, Timothy A. Davis, University of Florida.

    methods

        function F = factorization_qrt_dense (A, fail_if_singular)
            %FACTORIZATION_QRT_DENSE : A' = Q*R
            [m n] = size (A) ;
            if (m >= n)
                error ('FACTORIZE:wrongdim', 'QR(A'') method requires m<n.') ;
            end
            [f.Q f.R] = qr (A',0) ;
            F.A_condest = cheap_condest (get_diag (f.R), fail_if_singular) ;
            F.A = A ;
            F.Factors = f ;
            F.A_rank = m ;
            F.kind = 'dense economy QR factorization: A'' = Q*R' ;
        end

        function x = mldivide_subclass (F,b)
            %MLDIVIDE_SUBCLASS x = A\b using a dense QR factorization of A'
            % minimum 2-norm solution of an underdetermined system
            % x = Q * (R' \ b)
            f = F.Factors ;
            opUT.UT = true ;
            opUT.TRANSA = true ;
            x = f.Q * linsolve (f.R, full (b), opUT) ;
        end

        function x = mrdivide_subclass (b,F)
            %MRDIVIDE_SUBCLASS x = b/A using dense QR of A'
            % least-squares solution of a overdetermined problem
            % x = (R \ (Q' * b'))'
            f = F.Factors ;
            opU.UT = true ;
            x = linsolve (f.R, f.Q' * full (b'), opU)' ;
        end
    end
end

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