octave: scripts/sparse/spaugment.m annotate

annotate scripts/sparse/spaugment.m @ 27919:1891570abac8

update Octave Project Developers copyright for the new year In files that have the "Octave Project Developers" copyright notice, update for 2020.

author	John W. Eaton <jwe@octave.org>
date	Mon, 06 Jan 2020 22:29:51 -0500
parents	b442ec6dda5c
children	bd51beb6205e

rev	line source
27919 1891570abac8 update Octave Project Developers copyright for the new year John W. Eaton <jwe@octave.org> parents: 27918 diff changeset	1 ## Copyright (C) 2008-2020 The Octave Project Developers
27918 b442ec6dda5c use centralized file for copyright info for individual contributors John W. Eaton <jwe@octave.org> parents: 26376 diff changeset	2 ##
b442ec6dda5c use centralized file for copyright info for individual contributors John W. Eaton <jwe@octave.org> parents: 26376 diff changeset	3 ## See the file COPYRIGHT.md in the top-level directory of this distribution
b442ec6dda5c use centralized file for copyright info for individual contributors John W. Eaton <jwe@octave.org> parents: 26376 diff changeset	4 ## or <https://octave.org/COPYRIGHT.html/>.
b442ec6dda5c use centralized file for copyright info for individual contributors John W. Eaton <jwe@octave.org> parents: 26376 diff changeset	5 ##
7681 b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	6 ##
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	7 ## This file is part of Octave.
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	8 ##
24534 194eb4bd202b maint: Update punctuation for GPL v3 license text. Rik <rik@octave.org> parents: 23220 diff changeset	9 ## Octave is free software: you can redistribute it and/or modify it
7681 b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	10 ## under the terms of the GNU General Public License as published by
24534 194eb4bd202b maint: Update punctuation for GPL v3 license text. Rik <rik@octave.org> parents: 23220 diff changeset	11 ## the Free Software Foundation, either version 3 of the License, or
22755 3a2b891d0b33 maint: Standardize Copyright formatting. Rik <rik@octave.org> parents: 22323 diff changeset	12 ## (at your option) any later version.
7681 b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	13 ##
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	14 ## Octave is distributed in the hope that it will be useful, but
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	15 ## WITHOUT ANY WARRANTY; without even the implied warranty of
22755 3a2b891d0b33 maint: Standardize Copyright formatting. Rik <rik@octave.org> parents: 22323 diff changeset	16 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
3a2b891d0b33 maint: Standardize Copyright formatting. Rik <rik@octave.org> parents: 22323 diff changeset	17 ## GNU General Public License for more details.
7681 b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	18 ##
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	19 ## You should have received a copy of the GNU General Public License
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	20 ## along with Octave; see the file COPYING. If not, see
24534 194eb4bd202b maint: Update punctuation for GPL v3 license text. Rik <rik@octave.org> parents: 23220 diff changeset	21 ## <https://www.gnu.org/licenses/>.
7681 b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	22
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	23 ## -- texinfo --
20852 516bb87ea72e 2015 Code Sprint: remove class of function from docstring for all m-files. Rik <rik@octave.org> parents: 20711 diff changeset	24 ## @deftypefn {} {@var{s} =} spaugment (@var{A}, @var{c})
18809 53af80da6781 doc: Update documentation of sparse functions including seealso links. Rik <rik@octave.org> parents: 17744 diff changeset	25 ## Create the augmented matrix of @var{A}.
53af80da6781 doc: Update documentation of sparse functions including seealso links. Rik <rik@octave.org> parents: 17744 diff changeset	26 ##
53af80da6781 doc: Update documentation of sparse functions including seealso links. Rik <rik@octave.org> parents: 17744 diff changeset	27 ## This is given by
7681 b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	28 ##
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	29 ## @example
9051 1bf0ce0930be Grammar check TexInfo in all .m files Rik <rdrider0-list@yahoo.com> parents: 8920 diff changeset	30 ## @group
14327 4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	31 ## [@var{c} * eye(@var{m}, @var{m}), @var{A};
4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	32 ## @var{A}', zeros(@var{n}, @var{n})]
9051 1bf0ce0930be Grammar check TexInfo in all .m files Rik <rdrider0-list@yahoo.com> parents: 8920 diff changeset	33 ## @end group
7681 b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	34 ## @end example
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	35 ##
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	36 ## @noindent
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11523 diff changeset	37 ## This is related to the least squares solution of
14327 4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	38 ## @code{@var{A} \ @var{b}}, by
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11523 diff changeset	39 ##
7681 b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	40 ## @example
9051 1bf0ce0930be Grammar check TexInfo in all .m files Rik <rdrider0-list@yahoo.com> parents: 8920 diff changeset	41 ## @group
14327 4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	42 ## @var{s} * [ @var{r} / @var{c}; x] = [ @var{b}, zeros(@var{n}, columns(@var{b})) ]
9051 1bf0ce0930be Grammar check TexInfo in all .m files Rik <rdrider0-list@yahoo.com> parents: 8920 diff changeset	43 ## @end group
7681 b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	44 ## @end example
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	45 ##
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	46 ## @noindent
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	47 ## where @var{r} is the residual error
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	48 ##
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	49 ## @example
11471 994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 10549 diff changeset	50 ## @var{r} = @var{b} - @var{A} * @var{x}
7681 b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	51 ## @end example
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	52 ##
20164 df437a52bcaf doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19833 diff changeset	53 ## As the matrix @var{s} is symmetric indefinite it can be factorized with
df437a52bcaf doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19833 diff changeset	54 ## @code{lu}, and the minimum norm solution can therefore be found without the
df437a52bcaf doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19833 diff changeset	55 ## need for a @code{qr} factorization. As the residual error will be
df437a52bcaf doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19833 diff changeset	56 ## @code{zeros (@var{m}, @var{m})} for underdetermined problems, and example
df437a52bcaf doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19833 diff changeset	57 ## can be
7681 b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	58 ##
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	59 ## @example
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	60 ## @group
14327 4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	61 ## m = 11; n = 10; mn = max (m, n);
11471 994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 10549 diff changeset	62 ## A = spdiags ([ones(mn,1), 10*ones(mn,1), -ones(mn,1)],
8516 e2a179415bac doc fixes John W. Eaton <jwe@octave.org> parents: 7687 diff changeset	63 ## [-1, 0, 1], m, n);
11471 994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 10549 diff changeset	64 ## x0 = A \ ones (m,1);
994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 10549 diff changeset	65 ## s = spaugment (A);
7681 b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	66 ## [L, U, P, Q] = lu (s);
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	67 ## x1 = Q * (U \ (L \ (P * [ones(m,1); zeros(n,1)])));
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	68 ## x1 = x1(end - n + 1 : end);
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	69 ## @end group
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	70 ## @end example
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	71 ##
20164 df437a52bcaf doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19833 diff changeset	72 ## To find the solution of an overdetermined problem needs an estimate of the
df437a52bcaf doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19833 diff changeset	73 ## residual error @var{r} and so it is more complex to formulate a minimum norm
df437a52bcaf doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19833 diff changeset	74 ## solution using the @code{spaugment} function.
7681 b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	75 ##
20164 df437a52bcaf doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19833 diff changeset	76 ## In general the left division operator is more stable and faster than using
df437a52bcaf doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19833 diff changeset	77 ## the @code{spaugment} function.
18809 53af80da6781 doc: Update documentation of sparse functions including seealso links. Rik <rik@octave.org> parents: 17744 diff changeset	78 ## @seealso{mldivide}
7681 b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	79 ## @end deftypefn
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	80
11471 994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 10549 diff changeset	81 function s = spaugment (A, c)
21758 ffad2baa90f7 maint: Use newlines to make code more readable. Rik <rik@octave.org> parents: 20852 diff changeset	82
7681 b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	83 if (nargin < 2)
11471 994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 10549 diff changeset	84 if (issparse (A))
994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 10549 diff changeset	85 c = max (max (abs (A))) / 1000;
7681 b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	86 else
11471 994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 10549 diff changeset	87 if (ndims (A) != 2)
20711 7b608fadc663 Make error messages more specific about the variable and problem encountered. Rik <rik@octave.org> parents: 20164 diff changeset	88 error ("spaugment: A must be a 2-D matrix");
7681 b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	89 else
11471 994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 10549 diff changeset	90 c = max (abs (A(:))) / 1000;
7681 b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	91 endif
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	92 endif
19833 9fc020886ae9 maint: Clean up m-files to follow Octave coding conventions. Rik <rik@octave.org> parents: 19697 diff changeset	93 elseif (! isscalar (c))
11472 1740012184f9 Use uppercase for variable names in error() strings to match Info documentation. Only m-files done. Rik <octave@nomad.inbox5.com> parents: 11471 diff changeset	94 error ("spaugment: C must be a scalar");
7681 b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	95 endif
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	96
11471 994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 10549 diff changeset	97 [m, n] = size (A);
994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 10549 diff changeset	98 s = [ c * speye(m, m), A; A', sparse(n, n)];
21758 ffad2baa90f7 maint: Use newlines to make code more readable. Rik <rik@octave.org> parents: 20852 diff changeset	99
7681 b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	100 endfunction
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	101
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14327 diff changeset	102
8871 fb1c929dbbb7 tests vs. 64-bit indexing John W. Eaton <jwe@octave.org> parents: 8516 diff changeset	103 %!testif HAVE_UMFPACK
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14327 diff changeset	104 %! m = 11; n = 10; mn = max (m ,n);
11471 994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 10549 diff changeset	105 %! A = spdiags ([ones(mn,1), 10*ones(mn,1), -ones(mn,1)],[-1,0,1], m, n);
994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 10549 diff changeset	106 %! x0 = A \ ones (m,1);
994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 10549 diff changeset	107 %! s = spaugment (A);
7681 b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	108 %! [L, U, P, Q] = lu (s);
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	109 %! x1 = Q * (U \ (L \ (P * [ones(m,1); zeros(n,1)])));
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	110 %! x1 = x1(end - n + 1 : end);
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14327 diff changeset	111 %! assert (x1, x0, 1e-6);

Mercurial > octave

annotate scripts/sparse/spaugment.m @ 27919:1891570abac8