octave-antonio: scripts/sparse/spaugment.m annotate

annotate scripts/sparse/spaugment.m @ 14327:4d917a6a858b stable

doc: Use Octave coding conventions in @example blocks of docstrings. * accumarray.m, accumdim.m, bar.m, base2dec.m, bincoeff.m, bitcmp.m, bitset.m, celldisp.m, chop.m, clabel.m, cloglog.m, colon.m, compass.m, computer.m, contour3.m, contourc.m, corr.m, cstrcat.m, ctime.m, cylinder.m, date.m, dec2base.m, demo.m, dir.m, dlmwrite.m, expm.m, ezcontourf.m, ezcontour.m, ezmeshc.m, ezmesh.m, ezplot.m, ezsurfc.m, ezsurf.m, feather.m, findobj.m, flipdim.m, fplot.m, genvarname.m, getfield.m, hankel.m, hilb.m, hist.m, idivide.m, index.m, int2str.m, interp1.m, is_leap_year.m, ismember.m, isocolors.m, isonormals.m, isosurface.m, kurtosis.m, legendre.m, linkprop.m, logit.m, logm.m, __makeinfo__.m, __marching_cube__.m, median.m, mkoctfile.m, moment.m, mpoles.m, orderfields.m, pcg.m, pcr.m, plot3.m, plotmatrix.m, polyaffine.m, polygcd.m, poly.m, polyout.m, print.m, qp.m, quadgk.m, qzhess.m, randi.m, rat.m, refreshdata.m, residue.m, rose.m, rot90.m, saveas.m, saveobj.m, shiftdim.m, skewness.m, spaugment.m, spdiags.m, sqp.m, stem.m, str2num.m, strcat.m, strjust.m, strread.m, strsplit.m, structfun.m, subplot.m, subsindex.m, substruct.m, surfl.m, surfnorm.m, svds.m, uimenu.m, union.m, voronoi.m, warning_ids.m, wblpdf.m: Use Octave coding conventions in @example blocks of docstrings.

author	Rik <octave@nomad.inbox5.com>
date	Sat, 04 Feb 2012 22:12:50 -0800
parents	72c96de7a403
children	f3d52523cde1

rev	line source
14138 72c96de7a403 maint: update copyright notices for 2012 John W. Eaton <jwe@octave.org> parents: 12575 diff changeset	1 ## Copyright (C) 2008-2012 David Bateman
7681 b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	2 ##
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	3 ## This file is part of Octave.
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	4 ##
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	5 ## Octave is free software; you can redistribute it and/or modify it
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	6 ## under the terms of the GNU General Public License as published by
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	7 ## the Free Software Foundation; either version 3 of the License, or (at
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	8 ## your option) any later version.
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	9 ##
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	10 ## 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	11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	13 ## General Public License for more details.
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	14 ##
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	15 ## 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	16 ## along with Octave; see the file COPYING. If not, see
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	17 ## <http://www.gnu.org/licenses/>.
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 ## -- texinfo --
11471 994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 10549 diff changeset	20 ## @deftypefn {Function File} {@var{s} =} spaugment (@var{A}, @var{c})
12575 d0b799dafede Grammarcheck files for 3.4.1 release. Rik <octave@nomad.inbox5.com> parents: 11589 diff changeset	21 ## Create the augmented matrix of @var{A}. This is given by
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 ## @example
9051 1bf0ce0930be Grammar check TexInfo in all .m files Rik <rdrider0-list@yahoo.com> parents: 8920 diff changeset	24 ## @group
14327 4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	25 ## [@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	26 ## @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	27 ## @end group
7681 b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	28 ## @end example
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	29 ##
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	30 ## @noindent
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11523 diff changeset	31 ## 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	32 ## @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	33 ##
7681 b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	34 ## @example
9051 1bf0ce0930be Grammar check TexInfo in all .m files Rik <rdrider0-list@yahoo.com> parents: 8920 diff changeset	35 ## @group
14327 4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	36 ## @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	37 ## @end group
7681 b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	38 ## @end example
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	39 ##
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	40 ## @noindent
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	41 ## where @var{r} is the residual error
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	42 ##
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	43 ## @example
11471 994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 10549 diff changeset	44 ## @var{r} = @var{b} - @var{A} * @var{x}
7681 b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	45 ## @end example
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	46 ##
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	47 ## As the matrix @var{s} is symmetric indefinite it can be factorized
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	48 ## with @code{lu}, and the minimum norm solution can therefore be found
9051 1bf0ce0930be Grammar check TexInfo in all .m files Rik <rdrider0-list@yahoo.com> parents: 8920 diff changeset	49 ## without the need for a @code{qr} factorization. As the residual
7681 b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	50 ## error will be @code{zeros (@var{m}, @var{m})} for under determined
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11523 diff changeset	51 ## problems, and example can be
7681 b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	52 ##
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	53 ## @example
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	54 ## @group
14327 4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	55 ## 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	56 ## 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	57 ## [-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	58 ## 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	59 ## s = spaugment (A);
7681 b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	60 ## [L, U, P, Q] = lu (s);
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	61 ## x1 = Q * (U \ (L \ (P * [ones(m,1); zeros(n,1)])));
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	62 ## x1 = x1(end - n + 1 : end);
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	63 ## @end group
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	64 ## @end example
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	65 ##
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	66 ## To find the solution of an overdetermined problem needs an estimate
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	67 ## of the residual error @var{r} and so it is more complex to formulate
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	68 ## a minimum norm solution using the @code{spaugment} function.
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	69 ##
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	70 ## In general the left division operator is more stable and faster than
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	71 ## using the @code{spaugment} function.
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	72 ## @end deftypefn
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	73
11471 994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 10549 diff changeset	74 function s = spaugment (A, c)
7681 b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	75 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	76 if (issparse (A))
994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 10549 diff changeset	77 c = max (max (abs (A))) / 1000;
7681 b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	78 else
11471 994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 10549 diff changeset	79 if (ndims (A) != 2)
11589 b0084095098e missing semicolons in script files John W. Eaton <jwe@octave.org> parents: 11587 diff changeset	80 error ("spaugment: expecting 2-dimenisional matrix");
7681 b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	81 else
11471 994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 10549 diff changeset	82 c = max (abs (A(:))) / 1000;
7681 b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	83 endif
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	84 endif
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	85 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	86 error ("spaugment: C must be a scalar");
7681 b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	87 endif
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	88
11471 994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 10549 diff changeset	89 [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	90 s = [ c * speye(m, m), A; A', sparse(n, n)];
7681 b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	91 endfunction
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	92
8871 fb1c929dbbb7 tests vs. 64-bit indexing John W. Eaton <jwe@octave.org> parents: 8516 diff changeset	93 %!testif HAVE_UMFPACK
7681 b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	94 %! 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	95 %! 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	96 %! 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	97 %! s = spaugment (A);
7681 b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	98 %! [L, U, P, Q] = lu (s);
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	99 %! x1 = Q * (U \ (L \ (P * [ones(m,1); zeros(n,1)])));
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	100 %! x1 = x1(end - n + 1 : end);
7687 795be0215bf7 spaugment: reduce test script tolerance Ben Abbott <bpabbott@mac.com> parents: 7681 diff changeset	101 %! assert (x1, x0, 1e-6)

Mercurial > octave-antonio

annotate scripts/sparse/spaugment.m @ 14327:4d917a6a858b stable