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

annotate scripts/sparse/spaugment.m @ 18725:54a1e95365e1

Overhaul sprand, sprandn functions. * __sprand_impl__: Rename variable "funname" to "fcnname". Add comments to Reciprocal Condition number calculation. Rename "mynnz" to "k" to match rest of code. Add input validation test that RC is scalar or vector. Use double quotes instead of single quotes per Octave guidelines. Check for special case of output vector to avoid problems. Use randperm to replace do/until loop for speed. Pre-calculate speye() value instead of doing per loop iteration. * sprand.m: Improve docstring. Match function output variable name to documentation. Add check string to %!error tests. * sprandn.m: Improve docstring. Match function output variable name to documentation. Add check string to %!error tests.

author	Rik <rik@octave.org>
date	Sun, 23 Mar 2014 20:35:22 -0700
parents	d63878346099
children	53af80da6781

rev	line source
17744 d63878346099 maint: Update copyright notices for release. John W. Eaton <jwe@octave.org> parents: 14363 diff changeset	1 ## Copyright (C) 2008-2013 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
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14327 diff changeset	93
8871 fb1c929dbbb7 tests vs. 64-bit indexing John W. Eaton <jwe@octave.org> parents: 8516 diff changeset	94 %!testif HAVE_UMFPACK
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14327 diff changeset	95 %! 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	96 %! 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	97 %! 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	98 %! s = spaugment (A);
7681 b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	99 %! [L, U, P, Q] = lu (s);
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	100 %! x1 = Q * (U \ (L \ (P * [ones(m,1); zeros(n,1)])));
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	101 %! 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	102 %! assert (x1, x0, 1e-6);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14327 diff changeset	103

Mercurial > hg > octave-nkf

annotate scripts/sparse/spaugment.m @ 18725:54a1e95365e1