Code covered by the BSD License
- 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 object-oriented method for solving linear systems
- 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_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_qrt_denseFACTORIZATION_QRT_DENSE A' = Q*R where A is full.
- factorization_svdFACTORIZATION_SVD A = U*S*V'
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Don't let that INV go past your eyes; to solve that system, FACTORIZE!
14 May 2009
(Updated 06 Sep 2011)
A simple-to-use object-oriented method for solving linear systems and least-squares problems.
classdef factorization_qr_dense < factorization
%FACTORIZATION_QR_DENSE A = Q*R where A is full.
% Copyright 2011, Timothy A. Davis, University of Florida.
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.') ;
[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' ;
function x = mldivide_subclass (F,b)
%MLDIVIDE_SUBLCASS x = A\b using a dense economy QR factorization
% least-squares solution of an overdetermined problem
% x = R \ (Q' * b)
f = F.Factors ;
opU.UT = true ;
x = linsolve (f.R, f.Q' * full (b), opU) ;
function x = mrdivide_subclass (b,F)
%MRDIVIDE_SUBCLASS x = b/A using dense QR of A
% minimum 2-norm 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))' ;