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SPDX for MATLAB_Tools
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‎KLU/Doc/KLU_UserGuide.pdf

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‎MATLAB_Tools/Contents.m

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% waitmex % example mexFunction that creates a waitbar
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% find_commponents_example
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%
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% Copyright 2008-2012, Tim Davis, exceot for spqr_rank which is
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% Copyright 2008-2012, Tim Davis, except for spqr_rank which is
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% Copyright by Les Foster (San Jose State Univ) and Tim Davis.
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% See the SPDX license identifier in each package.

‎MATLAB_Tools/Factorize/Contents.m

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% factorization_qrt_sparse - (P*A)*(P*A)'=R'*R where A is sparse.
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% factorization_svd - A = U*S*V'
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% Copyright 2011-2012, Timothy A. Davis, http://www.suitesparse.com
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% Factorize, Copyright (c) 2011-2012, Timothy A Davis. All Rights Reserved.
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% SPDX-License-Identifier: BSD-3-clause

‎MATLAB_Tools/Factorize/Demo/factorize_demo.m

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%% THE FACTORIZE OBJECT for solving linear systems
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%
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% Copyright 2011-2012, Timothy A. Davis, http://www.suitesparse.com
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% Factorize, Copyright (c) 2011-2012, Timothy A Davis. All Rights Reserved.
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% SPDX-License-Identifier: BSD-3-clause
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% [email protected]
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%
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% This is a demonstration of the FACTORIZE object for solving linear

‎MATLAB_Tools/Factorize/Demo/fdemo.m

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% Run the factorize demo
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% Factorize, Copyright (c) 2011-2012, Timothy A Davis. All Rights Reserved.
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% SPDX-License-Identifier: BSD-3-clause
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echodemo ('factorize_demo') ;

‎MATLAB_Tools/Factorize/README.txt

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@@ -12,4 +12,5 @@ without SPQR; in this case, the COD for sparse matrices is not used. This has
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no effect on the use of this method for full-rank matrices, since COD is used
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only for rank-deficient matrices.
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Copyright 2011-2012, Timothy A. Davis, http://www.suitesparse.com
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Factorize, Copyright (c) 2011-2012, Timothy A Davis. All Rights Reserved.
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SPDX-License-Identifier: BSD-3-clause

‎MATLAB_Tools/Factorize/Test/Contents.m

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% test_performance - compare performance of factorization/solve methods.
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% test_svd - test factorize(A,'svd') and factorize(A,'cod') for a given matrix
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% Copyright 2011-2012, Timothy A. Davis, http://www.suitesparse.com
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% Factorize, Copyright (c) 2011-2012, Timothy A Davis. All Rights Reserved.
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% SPDX-License-Identifier: BSD-3-clause

‎MATLAB_Tools/Factorize/Test/README.txt

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@@ -2,3 +2,6 @@ To run all the tests, use test_all.m. The SPQR mexFunction from SuiteSparse is
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required. The output of this test in MATLAB is given in test_all.txt.
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Timothy A. Davis, http://www.suitesparse.com
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Factorize, Copyright (c) 2011-2012, Timothy A Davis. All Rights Reserved.
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SPDX-License-Identifier: BSD-3-clause

‎MATLAB_Tools/Factorize/Test/reset_rand.m

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%
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% See also RandStream, rand, rng
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% Copyright 2011-2012, Timothy A. Davis, http://www.suitesparse.com
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% Factorize, Copyright (c) 2011-2012, Timothy A Davis. All Rights Reserved.
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% SPDX-License-Identifier: BSD-3-clause
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if (verLessThan ('matlab', '7.12'))
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rand ('seed', 0) ; %#ok

‎MATLAB_Tools/Factorize/Test/test_accuracy.m

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%
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% See also test_all, test_factorize.
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% Copyright 2011-2012, Timothy A. Davis, http://www.suitesparse.com
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% Factorize, Copyright (c) 2011-2012, Timothy A Davis. All Rights Reserved.
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% SPDX-License-Identifier: BSD-3-clause
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fprintf ('\nTesting accuracy:\n') ;
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reset_rand ;

‎MATLAB_Tools/Factorize/Test/test_all.m

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% See also factorize, inverse, test_performance, test_accuracy, test_disp,
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% test_errors
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% Copyright 2011-2012, Timothy A. Davis, http://www.suitesparse.com
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% Factorize, Copyright (c) 2011-2012, Timothy A Davis. All Rights Reserved.
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% SPDX-License-Identifier: BSD-3-clause
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if (nargin < 1)
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performance = 1 ;

‎MATLAB_Tools/Factorize/Test/test_all_cod.m

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%
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% See also test_cod
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% Copyright 2011-2012, Timothy A. Davis, http://www.suitesparse.com
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% Factorize, Copyright (c) 2011-2012, Timothy A Davis. All Rights Reserved.
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% SPDX-License-Identifier: BSD-3-clause
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err = 0 ;
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for m = 0:10

‎MATLAB_Tools/Factorize/Test/test_all_svd.m

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%
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% See also test_all.
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% Copyright 2011-2012, Timothy A. Davis, http://www.suitesparse.com
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% Factorize, Copyright (c) 2011-2012, Timothy A Davis. All Rights Reserved.
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% SPDX-License-Identifier: BSD-3-clause
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reset_rand ;
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err = test_svd ;

‎MATLAB_Tools/Factorize/Test/test_cod.m

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%
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% See also test_all_cod, test_all.
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% Copyright 2011-2012, Timothy A. Davis, http://www.suitesparse.com
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% Factorize, Copyright (c) 2011-2012, Timothy A Davis. All Rights Reserved.
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% SPDX-License-Identifier: BSD-3-clause
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if (nargin < 1)
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A = magic (4) ;

‎MATLAB_Tools/Factorize/Test/test_disp.m

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%
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% See also factorize, test_all.
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% Copyright 2011-2012, Timothy A. Davis, http://www.suitesparse.com
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% Factorize, Copyright (c) 2011-2012, Timothy A Davis. All Rights Reserved.
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% SPDX-License-Identifier: BSD-3-clause
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reset_rand ;
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tol = 1e-10 ;

‎MATLAB_Tools/Factorize/Test/test_errors.m

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%
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% See also test_all, factorize.
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% Copyright 2011-2012, Timothy A. Davis, http://www.suitesparse.com
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% Factorize, Copyright (c) 2011-2012, Timothy A Davis. All Rights Reserved.
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% SPDX-License-Identifier: BSD-3-clause
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fprintf ('\nTesting error handling (error messages are expected)\n\n') ;
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reset_rand ;

‎MATLAB_Tools/Factorize/Test/test_factorize.m

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%
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% See also test_all, factorize, inverse, mldivide
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% Copyright 2011-2012, Timothy A. Davis, http://www.suitesparse.com
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% Factorize, Copyright (c) 2011-2012, Timothy A Davis. All Rights Reserved.
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% SPDX-License-Identifier: BSD-3-clause
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reset_rand ;
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if (nargin < 1)

‎MATLAB_Tools/Factorize/Test/test_function.m

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%
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% See also test_all, factorize, inverse, mldivide
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% Copyright 2011-2012, Timothy A. Davis, http://www.suitesparse.com
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% Factorize, Copyright (c) 2011-2012, Timothy A Davis. All Rights Reserved.
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% SPDX-License-Identifier: BSD-3-clause
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reset_rand ;
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‎MATLAB_Tools/Factorize/Test/test_functions.m

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%
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% See also test_all, factorize, inverse, mldivide
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% Copyright 2011-2012, Timothy A. Davis, http://www.suitesparse.com
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% Factorize, Copyright (c) 2011-2012, Timothy A Davis. All Rights Reserved.
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% SPDX-License-Identifier: BSD-3-clause
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fprintf ('\n----- Test functions:\n') ;
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reset_rand ;

‎MATLAB_Tools/Factorize/Test/test_performance.m

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%
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% See also test_all, factorize, inverse, mldivide
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% Copyright 2011-2012, Timothy A. Davis, http://www.suitesparse.com
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% Factorize, Copyright (c) 2011-2012, Timothy A Davis. All Rights Reserved.
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% SPDX-License-Identifier: BSD-3-clause
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fprintf ('\nPerformance comparisons of 4 methods:\n') ;
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fprintf (' backslash: A\\b, or L\\b (and related) for solve times.\n') ;

‎MATLAB_Tools/Factorize/Test/test_svd.m

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%
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% See also test_all
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% Copyright 2011-2012, Timothy A. Davis, http://www.suitesparse.com
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% Factorize, Copyright (c) 2011-2012, Timothy A Davis. All Rights Reserved.
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% SPDX-License-Identifier: BSD-3-clause
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fprintf ('.') ;
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‎MATLAB_Tools/Factorize/cod.m

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%
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% See also qr, svd, rq, spqr, cod_sparse.
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% Copyright 2011-2012, Timothy A. Davis, http://www.suitesparse.com
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% Factorize, Copyright (c) 2011-2012, Timothy A Davis. All Rights Reserved.
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% SPDX-License-Identifier: BSD-3-clause
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if (issparse (A))
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error ('FACTORIZE:cod:sparse', ...

‎MATLAB_Tools/Factorize/cod_qmult.m

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%
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% See also cod_sparse, spqr, spqr_qmult
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% Copyright 2011-2012, Timothy A. Davis, http://www.suitesparse.com
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% Factorize, Copyright (c) 2011-2012, Timothy A Davis. All Rights Reserved.
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% SPDX-License-Identifier: BSD-3-clause
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if (nargin < 3)
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method = 0 ;

‎MATLAB_Tools/Factorize/cod_sparse.m

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%
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% See also qr, cod, cod_qmult, spqr, spqr_qmult.
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% Copyright 2011-2012, Timothy A. Davis, http://www.suitesparse.com
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% Factorize, Copyright (c) 2011-2012, Timothy A Davis. All Rights Reserved.
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% SPDX-License-Identifier: BSD-3-clause
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%-------------------------------------------------------------------------------
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% get the inputs

‎MATLAB_Tools/Factorize/factorization.m

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%
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% See also mldivide, lu, chol, ldl, qr, svd.
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% Copyright 2011-2012, Timothy A. Davis, http://www.suitesparse.com
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% Factorize, Copyright (c) 2011-2012, Timothy A Davis. All Rights Reserved.
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% SPDX-License-Identifier: BSD-3-clause
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properties (SetAccess = protected)
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% The abstract class holds a QR, LU, Cholesky factorization:

‎MATLAB_Tools/Factorize/factorization_chol_dense.m

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%FACTORIZATION_CHOL_DENSE A = R'*R where A is full and symmetric pos. def.
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% Adds an extra method, cholupdate, which acts just like the builtin cholupdate.
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% Copyright 2011-2012, Timothy A. Davis, http://www.suitesparse.com
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% Factorize, Copyright (c) 2011-2012, Timothy A Davis. All Rights Reserved.
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% SPDX-License-Identifier: BSD-3-clause
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methods
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‎MATLAB_Tools/Factorize/factorization_chol_sparse.m

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classdef factorization_chol_sparse < factorization
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%FACTORIZATION_CHOL_SPARSE P'*A*P = L*L' where A is sparse and sym. pos. def.
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% Copyright 2011-2012, Timothy A. Davis, http://www.suitesparse.com
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% Factorize, Copyright (c) 2011-2012, Timothy A Davis. All Rights Reserved.
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% SPDX-License-Identifier: BSD-3-clause
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‎MATLAB_Tools/Factorize/factorization_cod_dense.m

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% A fairly accurate estimate of rank is found. double(inverse(F)) is a fairly
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% accurate estimate of pinv(A).
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% Copyright 2011-2012, Timothy A. Davis, http://www.suitesparse.com
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% Factorize, Copyright (c) 2011-2012, Timothy A Davis. All Rights Reserved.
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% SPDX-License-Identifier: BSD-3-clause
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methods
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‎MATLAB_Tools/Factorize/factorization_cod_sparse.m

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% A fairly accurate estimate of rank is found. double(inverse(F)) is a fairly
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% accurate estimate of pinv(A).
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% Copyright 2011-2012, Timothy A. Davis, http://www.suitesparse.com
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% Factorize, Copyright (c) 2011-2012, Timothy A Davis. All Rights Reserved.
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% SPDX-License-Identifier: BSD-3-clause
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‎MATLAB_Tools/Factorize/factorization_ldl_dense.m

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classdef factorization_ldl_dense < factorization
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%FACTORIZATION_LDL_DENSE P'*A*P = L*D*L' where A is full and symmetric
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% Copyright 2011-2012, Timothy A. Davis, http://www.suitesparse.com
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% Factorize, Copyright (c) 2011-2012, Timothy A Davis. All Rights Reserved.
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% SPDX-License-Identifier: BSD-3-clause
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‎MATLAB_Tools/Factorize/factorization_ldl_sparse.m

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classdef factorization_ldl_sparse < factorization
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%FACTORIZATION_LDL_SPARSE P'*A*P = L*D*L' where A is sparse and symmetric
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% Copyright 2011-2012, Timothy A. Davis, http://www.suitesparse.com
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% Factorize, Copyright (c) 2011-2012, Timothy A Davis. All Rights Reserved.
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% SPDX-License-Identifier: BSD-3-clause
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‎MATLAB_Tools/Factorize/factorization_lu_dense.m

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classdef factorization_lu_dense < factorization
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%FACTORIZATION_LU_DENSE A(p,:) = L*U where A is square and full.
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% Copyright 2011-2012, Timothy A. Davis, http://www.suitesparse.com
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% Factorize, Copyright (c) 2011-2012, Timothy A Davis. All Rights Reserved.
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% SPDX-License-Identifier: BSD-3-clause
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‎MATLAB_Tools/Factorize/factorization_lu_sparse.m

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classdef factorization_lu_sparse < factorization
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%FACTORIZATION_LU_SPARSE P*A*Q = L*U where A is square and sparse.
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% Copyright 2011-2012, Timothy A. Davis, http://www.suitesparse.com
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% Factorize, Copyright (c) 2011-2012, Timothy A Davis. All Rights Reserved.
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% SPDX-License-Identifier: BSD-3-clause
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‎MATLAB_Tools/Factorize/factorization_qr_dense.m

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classdef factorization_qr_dense < factorization
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%FACTORIZATION_QR_DENSE A = Q*R where A is full.
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% Copyright 2011-2012, Timothy A. Davis, http://www.suitesparse.com
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% Factorize, Copyright (c) 2011-2012, Timothy A Davis. All Rights Reserved.
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% SPDX-License-Identifier: BSD-3-clause
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‎MATLAB_Tools/Factorize/factorization_qr_sparse.m

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classdef factorization_qr_sparse < factorization
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%FACTORIZATION_QR_SPARSE (A*P)'*(A*P) = R'*R where A is sparse.
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% Copyright 2011-2012, Timothy A. Davis, http://www.suitesparse.com
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% Factorize, Copyright (c) 2011-2012, Timothy A Davis. All Rights Reserved.
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% SPDX-License-Identifier: BSD-3-clause
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‎MATLAB_Tools/Factorize/factorization_qrt_dense.m

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classdef factorization_qrt_dense < factorization
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%FACTORIZATION_QRT_DENSE A' = Q*R where A is full.
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% Copyright 2011-2012, Timothy A. Davis, http://www.suitesparse.com
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% Factorize, Copyright (c) 2011-2012, Timothy A Davis. All Rights Reserved.
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% SPDX-License-Identifier: BSD-3-clause
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‎MATLAB_Tools/Factorize/factorization_qrt_sparse.m

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classdef factorization_qrt_sparse < factorization
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%FACTORIZATION_QRT_SPARSE (P*A)*(P*A)'=R'*R where A is sparse.
33

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% Copyright 2011-2012, Timothy A. Davis, http://www.suitesparse.com
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% Factorize, Copyright (c) 2011-2012, Timothy A Davis. All Rights Reserved.
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% SPDX-License-Identifier: BSD-3-clause
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‎MATLAB_Tools/Factorize/factorization_svd.m

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% C = pinv (F) the pseudo-inverse, V'*(S\V).
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% [U,S,V] = svd (F) SVD of A or pinv(A), regular, economy, or rank-sized
1616

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% Copyright 2011-2012, Timothy A. Davis, http://www.suitesparse.com
17+
% Factorize, Copyright (c) 2011-2012, Timothy A Davis. All Rights Reserved.
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% SPDX-License-Identifier: BSD-3-clause
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‎MATLAB_Tools/Factorize/factorize.m

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%
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% See also inverse, slash, linsolve, spqr.
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% Copyright 2011-2012, Timothy A. Davis, http://www.suitesparse.com
86+
% Factorize, Copyright (c) 2011-2012, Timothy A Davis. All Rights Reserved.
87+
% SPDX-License-Identifier: BSD-3-clause
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8889
assert (ndims (A) == 2, 'Matrix must be 2D.') ;
8990

‎MATLAB_Tools/Factorize/inverse.m

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%
3737
% See also factorize, slash, inv, pinv.
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% Copyright 2011-2012, Timothy A. Davis, http://www.suitesparse.com
39+
% Factorize, Copyright (c) 2011-2012, Timothy A Davis. All Rights Reserved.
40+
% SPDX-License-Identifier: BSD-3-clause
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% This function is only called when A is a matrix. If A is a factorize
4243
% object, then factorize.inverse is called instead.

‎MATLAB_Tools/Factorize/private/cheap_condest.m

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function c = cheap_condest (d, fail_if_singular)
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%CHEAP_CONDEST checks the diagonal of a triangular matrix
33

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% Copyright 2011-2012, Timothy A. Davis, http://www.suitesparse.com
4+
% Factorize, Copyright (c) 2011-2012, Timothy A Davis. All Rights Reserved.
5+
% SPDX-License-Identifier: BSD-3-clause
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if (isempty (d))
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dmin = 1 ;

‎MATLAB_Tools/Factorize/private/get_diag.m

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function d = get_diag (A)
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%GET_DIAG extracts the diagonal of a matrix or vector.
33

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% Copyright 2011-2012, Timothy A. Davis, http://www.suitesparse.com
4+
% Factorize, Copyright (c) 2011-2012, Timothy A Davis. All Rights Reserved.
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% SPDX-License-Identifier: BSD-3-clause
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if (isempty (A))
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d = [ ] ;

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