Code covered by the BSD License
 cheap_condest (d, fail_if...CHEAP_CONDEST checks the diagonal of a triangular matrix
 cod (A, tol)COD complete orthogonal decomposition of a full matrix A = U*R*V'
 cod_qmult (Q, X, method)
 cod_sparse (A, arg)COD_SPARSE complete orthogonal decomposition of a sparse matrix A = U*R*V'
 factorize (A,strategy,bur...FACTORIZE an objectoriented method for solving linear systems
 get_diag (A)GET_DIAG extracts the diagonal of a matrix or vector.
 inverse (A, varargin)INVERSE factorized representation of inv(A) or pinv(A).
 reset_randRESET_RAND resets the state of rand
 rq (A, m, n)RQ economy RQ or QL factorization of a full matrix A.
 test_accuracyTEST_ACCURACY test the accuracy of the factorize object
 test_all (performance)TEST_ALL test the Factorize package (factorize, inverse, and related)
 test_all_codTEST_ALL_COD test the COD factorization
 test_all_svdTEST_ALL_SVD tests the svd factorization method for a range of problems.
 test_cod (A, tol)TEST_COD test the COD, COD_SPARSE and RQ functions
 test_dispTEST_DISP test the display method of the factorize object
 test_errorsTEST_ERRORS tests error handling for the factorize object methods
 test_factorize (A)TEST_FACTORIZE test the accuracy of the factorization object
 test_function (A, strateg...TEST_FUNCTION test various functions applied to a factorize object
 test_functionsTEST_FUNCTIONS test various functions applied to a factorize object
 test_performanceTEST_PERFORMANCE compare performance of factorization/solve methods.
 test_svd (A)
 factorizationFACTORIZATION a generic matrix factorization object
 factorization_chol_denseFACTORIZATION_CHOL_DENSE A = R'*R where A is full and symmetric pos. def.
 factorization_chol_sparse
 factorization_cod_denseFACTORIZATION_COD_DENSE complete orthogonal factorization: A = U*R*V' where A is full.
 factorization_cod_sparseFACTORIZATION_COD_SPARSE complete orthogonal factorization: A = U*R*V' where A is sparse.
 factorization_ldl_denseFACTORIZATION_LDL_DENSE P'*A*P = L*D*L' where A is sparse and full
 factorization_ldl_sparseFACTORIZATION_LDL_SPARSE P'*A*P = L*D*L' where A is sparse and symmetric
 factorization_lu_denseFACTORIZATION_LU_DENSE P*A = L*U where A is square and full.
 factorization_lu_sparseFACTORIZATION_LU_SPARSE P*A*Q = L*U where A is square and sparse.
 factorization_qr_denseFACTORIZATION_QR_DENSE A = Q*R where A is full.
 factorization_qr_sparse
 factorization_qrt_denseFACTORIZATION_QRT_DENSE A' = Q*R where A is full.
 factorization_qrt_sparse
 factorization_svdFACTORIZATION_SVD A = U*S*V'
 Contents.mFACTORIZE: an objectoriented method for solving linear systems and least
 Contents.mTest code for the FACTORIZE object.
 factorize_demo.mTHE FACTORIZE OBJECT for solving linear systems
 fdemo.mRun the factorize demo

View all files
Don't let that INV go past your eyes; to solve that system, FACTORIZE!
by
Tim Davis
14 May 2009
(Updated
06 Sep 2011)
A simpletouse objectoriented method for solving linear systems and leastsquares problems.

factorization_qr_dense 
classdef factorization_qr_dense < factorization
%FACTORIZATION_QR_DENSE A = Q*R where A is full.
% Copyright 2011, Timothy A. Davis, University of Florida.
methods
function F = factorization_qr_dense (A, fail_if_singular)
%FACTORIZATION_QR_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 = n ;
F.kind = 'dense economy QR factorization: A = Q*R' ;
end
function x = mldivide_subclass (F,b)
%MLDIVIDE_SUBLCASS x = A\b using a dense economy QR factorization
% leastsquares solution of an overdetermined problem
% x = R \ (Q' * b)
f = F.Factors ;
opU.UT = true ;
x = linsolve (f.R, f.Q' * full (b), opU) ;
end
function x = mrdivide_subclass (b,F)
%MRDIVIDE_SUBCLASS x = b/A using dense QR of A
% minimum 2norm solution of a underdetermined problem
% x = (Q * (R' \ b'))' ;
f = F.Factors ;
opUT.UT = true ;
opUT.TRANSA = true ;
x = (f.Q * linsolve (f.R, full (b'), opUT))' ;
end
end
end


Contact us