%FACTORIZE: an object-oriented method for solving linear systems and least
% squares problems. The method provides an efficient way of computing
% mathematical expressions involving the inverse, without actually
% computing the inverse. For example, S=A-B*inverse(D)*C computes the
% Schur complement by computing S=A-B*(D\C) instead.
%
% factorize - an object-oriented method for solving linear systems
% inverse - factorized representation of inv(A) or pinv(A).
%
% The package also includes methods for complete orthogonal decomposition
% of full and sparse matrices:
%
% cod - complete orthogonal decomposition of a full matrix A = U*R*V'
% rq - economy RQ or QL factorization of a full matrix A.
% cod_sparse - complete orthogonal decomposition of a sparse matrix A = U*R*V'
% cod_qmult - computes Q'*X, Q*X, X*Q', or X*Q with Q from COD_SPARSE.
%
% Example
% cd Demo ; fdemo % run the demo
%
% "Don't let that INV go past your eyes; to solve that system, FACTORIZE!"
%
% See also chol, lu, ldl, qr, svd.
% Installation and testing:
%
% To install this package, type "pathtool" in the MATLAB command window. Add
% the directory that contains this Factorize/Contents.m file to the path. Save
% the path for future use. Alternatively, type these commands while in this
% directory:
%
% addpath(pwd)
% savepath
%
% If you do not have the proper file permissions to save your path, create a
% startup.m file that includes the command "addpath(here)" where "here" is the
% directory containing this file. Type "help startup" for more information.
%
% The cod function for sparse matrices requires the SPQR mexFunction from the
% SuiteSparse library. The simplest way to get this is to install all of
% SuiteSparse from http://www.suitesparse.com.
%
% The Test/ subdirectory contains functions that test this package.
%
% The Doc/ subdirectory contains a document that illustrates how to use
% the package (the output of fdemo).
% Object-oriented methods, not meant to be user-callable:
%
% factorization - a generic matrix factorization object
% factorization_chol_dense - A = R'*R where A is full and symmetric pos. def.
% factorization_chol_sparse - P'*A*P = L*L' where A is sparse and sym. pos. def.
% factorization_cod_dense - complete orthogonal factorization: A = U*R*V' where A is full.
% factorization_cod_sparse - complete orthogonal factorization: A = U*R*V' where A is sparse.
% factorization_ldl_dense - A(p,p) = L*D*L' where A is sparse and full
% factorization_ldl_sparse - P'*A*P = L*D*L' where A is sparse and symmetric
% factorization_lu_dense - A(p,:) = L*U where A is square and full.
% factorization_lu_sparse - P*A*Q = L*U where A is square and sparse.
% factorization_qr_dense - A = Q*R where A is full.
% factorization_qr_sparse - (A*P)'*(A*P) = R'*R where A is sparse.
% factorization_qrt_dense - A' = Q*R where A is full.
% factorization_qrt_sparse - (P*A)*(P*A)'=R'*R where A is sparse.
% factorization_svd - A = U*S*V'
% Copyright 2011-2012, Timothy A. Davis, http://www.suitesparse.com