Mercurial > octave-antonio
view scripts/sparse/spaugment.m @ 20164:df437a52bcaf stable
doc: Update more docstrings to have one sentence summary as first line.
Reviewed miscellaneous, sparse, strings in scripts directory.
* scripts/miscellaneous/bzip2.m, scripts/miscellaneous/citation.m,
scripts/miscellaneous/compare_versions.m, scripts/miscellaneous/computer.m,
scripts/miscellaneous/debug.m, scripts/miscellaneous/dir.m,
scripts/miscellaneous/edit.m, scripts/miscellaneous/error_ids.m,
scripts/miscellaneous/fileattrib.m, scripts/miscellaneous/fullfile.m,
scripts/miscellaneous/genvarname.m, scripts/miscellaneous/gzip.m,
scripts/miscellaneous/mkoctfile.m, scripts/miscellaneous/news.m,
scripts/miscellaneous/open.m, scripts/miscellaneous/parseparams.m,
scripts/miscellaneous/recycle.m, scripts/miscellaneous/run.m,
scripts/miscellaneous/swapbytes.m, scripts/miscellaneous/tar.m,
scripts/miscellaneous/tmpnam.m, scripts/miscellaneous/unpack.m,
scripts/miscellaneous/what.m, scripts/sparse/bicg.m, scripts/sparse/bicgstab.m,
scripts/sparse/cgs.m, scripts/sparse/colperm.m, scripts/sparse/eigs.m,
scripts/sparse/etreeplot.m, scripts/sparse/gmres.m, scripts/sparse/gplot.m,
scripts/sparse/ichol.m, scripts/sparse/ilu.m, scripts/sparse/pcg.m,
scripts/sparse/pcr.m, scripts/sparse/qmr.m, scripts/sparse/spaugment.m,
scripts/sparse/spconvert.m, scripts/sparse/spdiags.m, scripts/sparse/spfun.m,
scripts/sparse/spones.m, scripts/sparse/sprandsym.m, scripts/sparse/spstats.m,
scripts/sparse/spy.m, scripts/sparse/svds.m, scripts/sparse/treelayout.m,
scripts/sparse/treeplot.m, scripts/strings/base2dec.m,
scripts/strings/bin2dec.m, scripts/strings/blanks.m, scripts/strings/cstrcat.m,
scripts/strings/deblank.m, scripts/strings/dec2base.m,
scripts/strings/dec2bin.m, scripts/strings/dec2hex.m,
scripts/strings/findstr.m, scripts/strings/hex2dec.m, scripts/strings/index.m,
scripts/strings/isletter.m, scripts/strings/isstrprop.m,
scripts/strings/mat2str.m, scripts/strings/ostrsplit.m,
scripts/strings/regexptranslate.m, scripts/strings/rindex.m,
scripts/strings/str2num.m, scripts/strings/strcat.m, scripts/strings/strchr.m,
scripts/strings/strjoin.m, scripts/strings/strjust.m,
scripts/strings/strmatch.m, scripts/strings/strsplit.m,
scripts/strings/strtok.m, scripts/strings/strtrim.m,
scripts/strings/strtrunc.m, scripts/strings/substr.m,
scripts/strings/untabify.m, scripts/time/datenum.m:
Update more docstrings to have one sentence summary as first line.
author | Rik <rik@octave.org> |
---|---|
date | Mon, 04 May 2015 14:22:02 -0700 |
parents | 9fc020886ae9 |
children |
line wrap: on
line source
## Copyright (C) 2008-2015 David Bateman ## ## This file is part of Octave. ## ## Octave is free software; you can redistribute it and/or modify it ## under the terms of the GNU General Public License as published by ## the Free Software Foundation; either version 3 of the License, or (at ## your option) any later version. ## ## Octave is distributed in the hope that it will be useful, but ## WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with Octave; see the file COPYING. If not, see ## <http://www.gnu.org/licenses/>. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{s} =} spaugment (@var{A}, @var{c}) ## Create the augmented matrix of @var{A}. ## ## This is given by ## ## @example ## @group ## [@var{c} * eye(@var{m}, @var{m}), @var{A}; ## @var{A}', zeros(@var{n}, @var{n})] ## @end group ## @end example ## ## @noindent ## This is related to the least squares solution of ## @code{@var{A} \ @var{b}}, by ## ## @example ## @group ## @var{s} * [ @var{r} / @var{c}; x] = [ @var{b}, zeros(@var{n}, columns(@var{b})) ] ## @end group ## @end example ## ## @noindent ## where @var{r} is the residual error ## ## @example ## @var{r} = @var{b} - @var{A} * @var{x} ## @end example ## ## As the matrix @var{s} is symmetric indefinite it can be factorized with ## @code{lu}, and the minimum norm solution can therefore be found without the ## need for a @code{qr} factorization. As the residual error will be ## @code{zeros (@var{m}, @var{m})} for underdetermined problems, and example ## can be ## ## @example ## @group ## m = 11; n = 10; mn = max (m, n); ## A = spdiags ([ones(mn,1), 10*ones(mn,1), -ones(mn,1)], ## [-1, 0, 1], m, n); ## x0 = A \ ones (m,1); ## s = spaugment (A); ## [L, U, P, Q] = lu (s); ## x1 = Q * (U \ (L \ (P * [ones(m,1); zeros(n,1)]))); ## x1 = x1(end - n + 1 : end); ## @end group ## @end example ## ## To find the solution of an overdetermined problem needs an estimate of the ## residual error @var{r} and so it is more complex to formulate a minimum norm ## solution using the @code{spaugment} function. ## ## In general the left division operator is more stable and faster than using ## the @code{spaugment} function. ## @seealso{mldivide} ## @end deftypefn function s = spaugment (A, c) if (nargin < 2) if (issparse (A)) c = max (max (abs (A))) / 1000; else if (ndims (A) != 2) error ("spaugment: expecting 2-dimenisional matrix"); else c = max (abs (A(:))) / 1000; endif endif elseif (! isscalar (c)) error ("spaugment: C must be a scalar"); endif [m, n] = size (A); s = [ c * speye(m, m), A; A', sparse(n, n)]; endfunction %!testif HAVE_UMFPACK %! m = 11; n = 10; mn = max (m ,n); %! A = spdiags ([ones(mn,1), 10*ones(mn,1), -ones(mn,1)],[-1,0,1], m, n); %! x0 = A \ ones (m,1); %! s = spaugment (A); %! [L, U, P, Q] = lu (s); %! x1 = Q * (U \ (L \ (P * [ones(m,1); zeros(n,1)]))); %! x1 = x1(end - n + 1 : end); %! assert (x1, x0, 1e-6);