octave: scripts/linear-algebra/condest.m annotate

annotate scripts/linear-algebra/condest.m @ 22323:bac0d6f07a3e

maint: Update copyright notices for 2016.

author	John W. Eaton <jwe@octave.org>
date	Wed, 17 Aug 2016 01:05:19 -0400
parents	9fc91bb2aec3
children	3a2b891d0b33 fb913df7babb

rev	line source
22323 bac0d6f07a3e maint: Update copyright notices for 2016. John W. Eaton <jwe@octave.org> parents: 22299 diff changeset	1 ## Copyright (C) 2007-2016 Regents of the University of California
22183 bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	2 ## Copyright (C) 2016 Marco Caliari
7189 e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	3 ##
e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	4 ## This file is part of Octave.
e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	5 ##
e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	6 ## Octave is free software; you can redistribute it and/or modify it
e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	7 ## under the terms of the GNU General Public License as published by
e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	8 ## the Free Software Foundation; either version 3 of the License, or (at
e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	9 ## your option) any later version.
e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	10 ##
e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	11 ## Octave is distributed in the hope that it will be useful, but
e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	12 ## WITHOUT ANY WARRANTY; without even the implied warranty of
e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	13 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	14 ## General Public License for more details.
e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	15 ##
e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	16 ## You should have received a copy of the GNU General Public License
e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	17 ## along with Octave; see the file COPYING. If not, see
e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	18 ## <http://www.gnu.org/licenses/>.
e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	19
e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	20 ## -- texinfo --
20852 516bb87ea72e 2015 Code Sprint: remove class of function from docstring for all m-files. Rik <rik@octave.org> parents: 20194 diff changeset	21 ## @deftypefn {} {} condest (@var{A})
516bb87ea72e 2015 Code Sprint: remove class of function from docstring for all m-files. Rik <rik@octave.org> parents: 20194 diff changeset	22 ## @deftypefnx {} {} condest (@var{A}, @var{t})
516bb87ea72e 2015 Code Sprint: remove class of function from docstring for all m-files. Rik <rik@octave.org> parents: 20194 diff changeset	23 ## @deftypefnx {} {[@var{est}, @var{v}] =} condest (@dots{})
22183 bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	24 ## @deftypefnx {} {[@var{est}, @var{v}] =} condest (@var{A}, @var{solvefun}, @var{t}, @var{p1}, @var{p2}, @dots{})
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	25 ## @deftypefnx {} {[@var{est}, @var{v}] =} condest (@var{afun}, @var{solvefun}, @var{t}, @var{p1}, @var{p2}, @dots{})
7189 e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	26 ##
20160 03b9d17a2d95 doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19700 diff changeset	27 ## Estimate the 1-norm condition number of a matrix @var{A} using @var{t} test
03b9d17a2d95 doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19700 diff changeset	28 ## vectors using a randomized 1-norm estimator.
03b9d17a2d95 doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19700 diff changeset	29 ##
7189 e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	30 ## If @var{t} exceeds 5, then only 5 test vectors are used.
e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	31 ##
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11523 diff changeset	32 ## If the matrix is not explicit, e.g., when estimating the condition
11593 1577c6f80926 Use non-breaking spaces between certain adjectives and their nouns in docstrings. Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	33 ## number of @var{A} given an LU@tie{}factorization, @code{condest} uses the
7189 e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	34 ## following functions:
e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	35 ##
22183 bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	36 ## @itemize @minus
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	37 ## @item @var{afun} which should returns
22299 9fc91bb2aec3 doc: grammarcheck documentation for 4.2 release. Rik <rik@octave.org> parents: 22183 diff changeset	38 ##
22183 bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	39 ## @itemize @bullet
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	40 ## @item
22299 9fc91bb2aec3 doc: grammarcheck documentation for 4.2 release. Rik <rik@octave.org> parents: 22183 diff changeset	41 ## the dimension @var{n} of @var{a}, if @var{flag} is @qcode{"dim"}
9fc91bb2aec3 doc: grammarcheck documentation for 4.2 release. Rik <rik@octave.org> parents: 22183 diff changeset	42 ##
22183 bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	43 ## @item
22299 9fc91bb2aec3 doc: grammarcheck documentation for 4.2 release. Rik <rik@octave.org> parents: 22183 diff changeset	44 ## true if @var{a} is a real operator, if @var{flag} is @qcode{"real"}
9fc91bb2aec3 doc: grammarcheck documentation for 4.2 release. Rik <rik@octave.org> parents: 22183 diff changeset	45 ##
22183 bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	46 ## @item
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	47 ## the result @code{@var{a} * @var{x}}, if @var{flag} is "notransp"
22299 9fc91bb2aec3 doc: grammarcheck documentation for 4.2 release. Rik <rik@octave.org> parents: 22183 diff changeset	48 ##
22183 bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	49 ## @item
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	50 ## the result @code{@var{a}' * @var{x}}, if @var{flag} is "transp"
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	51 ## @end itemize
22299 9fc91bb2aec3 doc: grammarcheck documentation for 4.2 release. Rik <rik@octave.org> parents: 22183 diff changeset	52 ##
22183 bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	53 ## @item @var{solvefun} which should returns
22299 9fc91bb2aec3 doc: grammarcheck documentation for 4.2 release. Rik <rik@octave.org> parents: 22183 diff changeset	54 ##
22183 bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	55 ## @itemize @bullet
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	56 ## @item
22299 9fc91bb2aec3 doc: grammarcheck documentation for 4.2 release. Rik <rik@octave.org> parents: 22183 diff changeset	57 ## the dimension @var{n} of @var{a}, if @var{flag} is @qcode{"dim"}
9fc91bb2aec3 doc: grammarcheck documentation for 4.2 release. Rik <rik@octave.org> parents: 22183 diff changeset	58 ##
22183 bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	59 ## @item
22299 9fc91bb2aec3 doc: grammarcheck documentation for 4.2 release. Rik <rik@octave.org> parents: 22183 diff changeset	60 ## true if @var{a} is a real operator, if @var{flag} is @qcode{"real"}
9fc91bb2aec3 doc: grammarcheck documentation for 4.2 release. Rik <rik@octave.org> parents: 22183 diff changeset	61 ##
22183 bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	62 ## @item
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	63 ## the result @code{@var{a} \ @var{x}}, if @var{flag} is "notransp"
22299 9fc91bb2aec3 doc: grammarcheck documentation for 4.2 release. Rik <rik@octave.org> parents: 22183 diff changeset	64 ##
22183 bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	65 ## @item
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	66 ## the result @code{@var{a}' \ @var{x}}, if @var{flag} is "transp"
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	67 ## @end itemize
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	68 ## @end itemize
10821 693e22af08ae Grammarcheck documentation of m-files Rik <octave@nomad.inbox5.com> parents: 10793 diff changeset	69 ##
22183 bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	70 ## The parameters @var{p1}, @var{p2}, @dots{} are arguments of
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	71 ## @code{@var{afun} (@var{flag}, @var{x}, @var{p1}, @var{p2}, @dots{})}
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	72 ## and @code{@var{solvefun} (@var{flag}, @var{x}, @var{p1}, @var{p2},
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	73 ## @dots{})}.
10821 693e22af08ae Grammarcheck documentation of m-files Rik <octave@nomad.inbox5.com> parents: 10793 diff changeset	74 ##
22183 bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	75 ## @code{condest} uses a randomized algorithm to approximate the
22299 9fc91bb2aec3 doc: grammarcheck documentation for 4.2 release. Rik <rik@octave.org> parents: 22183 diff changeset	76 ## 1-norms. Therefore, if consistent results are required, the
9fc91bb2aec3 doc: grammarcheck documentation for 4.2 release. Rik <rik@octave.org> parents: 22183 diff changeset	77 ## @qcode{"state"} of the random generator should be fixed before invoking
9fc91bb2aec3 doc: grammarcheck documentation for 4.2 release. Rik <rik@octave.org> parents: 22183 diff changeset	78 ## @code{normest1}.
7189 e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	79 ##
20160 03b9d17a2d95 doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19700 diff changeset	80 ## @code{condest} returns the 1-norm condition estimate @var{est} and a vector
03b9d17a2d95 doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19700 diff changeset	81 ## @var{v} satisfying @code{norm (Av, 1) == norm (A, 1) norm
9051 1bf0ce0930be Grammar check TexInfo in all .m files Rik <rdrider0-list@yahoo.com> parents: 8920 diff changeset	82 ## (@var{v}, 1) / @var{est}}. When @var{est} is large, @var{v} is an
7191 b48a21816f2e [project @ 2007-11-26 21:24:32 by jwe] jwe parents: 7189 diff changeset	83 ## approximate null vector.
7189 e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	84 ##
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11523 diff changeset	85 ## References:
16816 12005245b645 doc: Periodic grammarcheck of documentation. Rik <rik@octave.org> parents: 14522 diff changeset	86 ##
7189 e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	87 ## @itemize
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11523 diff changeset	88 ## @item
19040 0850b5212619 doc: Add @nospell macro around proper names in documentation. Rik <rik@octave.org> parents: 17744 diff changeset	89 ## @nospell{N.J. Higham and F. Tisseur}, @cite{A Block Algorithm
7189 e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	90 ## for Matrix 1-Norm Estimation, with an Application to 1-Norm
10791 3140cb7a05a1 Add spellchecker scripts for Octave and run spellcheck of documentation Rik <octave@nomad.inbox5.com> parents: 10687 diff changeset	91 ## Pseudospectra}. SIMAX vol 21, no 4, pp 1185-1201.
7189 e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	92 ## @url{http://dx.doi.org/10.1137/S0895479899356080}
10821 693e22af08ae Grammarcheck documentation of m-files Rik <octave@nomad.inbox5.com> parents: 10793 diff changeset	93 ##
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11523 diff changeset	94 ## @item
19040 0850b5212619 doc: Add @nospell macro around proper names in documentation. Rik <rik@octave.org> parents: 17744 diff changeset	95 ## @nospell{N.J. Higham and F. Tisseur}, @cite{A Block Algorithm
7189 e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	96 ## for Matrix 1-Norm Estimation, with an Application to 1-Norm
10791 3140cb7a05a1 Add spellchecker scripts for Octave and run spellcheck of documentation Rik <octave@nomad.inbox5.com> parents: 10687 diff changeset	97 ## Pseudospectra}. @url{http://citeseer.ist.psu.edu/223007.html}
7189 e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	98 ## @end itemize
e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	99 ##
22183 bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	100 ## @seealso{cond, norm, normest1}
7189 e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	101 ## @end deftypefn
e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	102
20194 b0f7ee81d974 doc: Remove extra spaces at start of docstring which show up in Info format. Rik <rik@octave.org> parents: 20160 diff changeset	103 ## Code originally licensed under:
7189 e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	104 ##
20194 b0f7ee81d974 doc: Remove extra spaces at start of docstring which show up in Info format. Rik <rik@octave.org> parents: 20160 diff changeset	105 ## Copyright (c) 2007, Regents of the University of California
b0f7ee81d974 doc: Remove extra spaces at start of docstring which show up in Info format. Rik <rik@octave.org> parents: 20160 diff changeset	106 ## All rights reserved.
7191 b48a21816f2e [project @ 2007-11-26 21:24:32 by jwe] jwe parents: 7189 diff changeset	107 ##
20194 b0f7ee81d974 doc: Remove extra spaces at start of docstring which show up in Info format. Rik <rik@octave.org> parents: 20160 diff changeset	108 ## Redistribution and use in source and binary forms, with or without
b0f7ee81d974 doc: Remove extra spaces at start of docstring which show up in Info format. Rik <rik@octave.org> parents: 20160 diff changeset	109 ## modification, are permitted provided that the following conditions
b0f7ee81d974 doc: Remove extra spaces at start of docstring which show up in Info format. Rik <rik@octave.org> parents: 20160 diff changeset	110 ## are met:
7189 e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	111 ##
20194 b0f7ee81d974 doc: Remove extra spaces at start of docstring which show up in Info format. Rik <rik@octave.org> parents: 20160 diff changeset	112 ## * Redistributions of source code must retain the above copyright
b0f7ee81d974 doc: Remove extra spaces at start of docstring which show up in Info format. Rik <rik@octave.org> parents: 20160 diff changeset	113 ## notice, this list of conditions and the following disclaimer.
7191 b48a21816f2e [project @ 2007-11-26 21:24:32 by jwe] jwe parents: 7189 diff changeset	114 ##
20194 b0f7ee81d974 doc: Remove extra spaces at start of docstring which show up in Info format. Rik <rik@octave.org> parents: 20160 diff changeset	115 ## * Redistributions in binary form must reproduce the above
b0f7ee81d974 doc: Remove extra spaces at start of docstring which show up in Info format. Rik <rik@octave.org> parents: 20160 diff changeset	116 ## copyright notice, this list of conditions and the following
b0f7ee81d974 doc: Remove extra spaces at start of docstring which show up in Info format. Rik <rik@octave.org> parents: 20160 diff changeset	117 ## disclaimer in the documentation and/or other materials provided
b0f7ee81d974 doc: Remove extra spaces at start of docstring which show up in Info format. Rik <rik@octave.org> parents: 20160 diff changeset	118 ## with the distribution.
7191 b48a21816f2e [project @ 2007-11-26 21:24:32 by jwe] jwe parents: 7189 diff changeset	119 ##
20194 b0f7ee81d974 doc: Remove extra spaces at start of docstring which show up in Info format. Rik <rik@octave.org> parents: 20160 diff changeset	120 ## * Neither the name of the University of California, Berkeley nor
b0f7ee81d974 doc: Remove extra spaces at start of docstring which show up in Info format. Rik <rik@octave.org> parents: 20160 diff changeset	121 ## the names of its contributors may be used to endorse or promote
b0f7ee81d974 doc: Remove extra spaces at start of docstring which show up in Info format. Rik <rik@octave.org> parents: 20160 diff changeset	122 ## products derived from this software without specific prior
b0f7ee81d974 doc: Remove extra spaces at start of docstring which show up in Info format. Rik <rik@octave.org> parents: 20160 diff changeset	123 ## written permission.
7189 e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	124 ##
20194 b0f7ee81d974 doc: Remove extra spaces at start of docstring which show up in Info format. Rik <rik@octave.org> parents: 20160 diff changeset	125 ## THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS''
b0f7ee81d974 doc: Remove extra spaces at start of docstring which show up in Info format. Rik <rik@octave.org> parents: 20160 diff changeset	126 ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
b0f7ee81d974 doc: Remove extra spaces at start of docstring which show up in Info format. Rik <rik@octave.org> parents: 20160 diff changeset	127 ## TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
b0f7ee81d974 doc: Remove extra spaces at start of docstring which show up in Info format. Rik <rik@octave.org> parents: 20160 diff changeset	128 ## PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS AND
b0f7ee81d974 doc: Remove extra spaces at start of docstring which show up in Info format. Rik <rik@octave.org> parents: 20160 diff changeset	129 ## CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
b0f7ee81d974 doc: Remove extra spaces at start of docstring which show up in Info format. Rik <rik@octave.org> parents: 20160 diff changeset	130 ## SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
b0f7ee81d974 doc: Remove extra spaces at start of docstring which show up in Info format. Rik <rik@octave.org> parents: 20160 diff changeset	131 ## LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF
b0f7ee81d974 doc: Remove extra spaces at start of docstring which show up in Info format. Rik <rik@octave.org> parents: 20160 diff changeset	132 ## USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
b0f7ee81d974 doc: Remove extra spaces at start of docstring which show up in Info format. Rik <rik@octave.org> parents: 20160 diff changeset	133 ## ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
b0f7ee81d974 doc: Remove extra spaces at start of docstring which show up in Info format. Rik <rik@octave.org> parents: 20160 diff changeset	134 ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT
b0f7ee81d974 doc: Remove extra spaces at start of docstring which show up in Info format. Rik <rik@octave.org> parents: 20160 diff changeset	135 ## OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
b0f7ee81d974 doc: Remove extra spaces at start of docstring which show up in Info format. Rik <rik@octave.org> parents: 20160 diff changeset	136 ## SUCH DAMAGE.
7189 e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	137
e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	138 ## Author: Jason Riedy <ejr@cs.berkeley.edu>
e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	139 ## Keywords: linear-algebra norm estimation
e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	140 ## Version: 0.2
e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	141
e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	142 function [est, v] = condest (varargin)
7191 b48a21816f2e [project @ 2007-11-26 21:24:32 by jwe] jwe parents: 7189 diff changeset	143
7309 26f42a14d4f6 [project @ 2007-12-12 22:05:38 by jwe] jwe parents: 7239 diff changeset	144 if (nargin < 1 \|\| nargin > 6)
7191 b48a21816f2e [project @ 2007-11-26 21:24:32 by jwe] jwe parents: 7189 diff changeset	145 print_usage ();
7189 e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	146 endif
e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	147
e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	148 default_t = 5;
e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	149
22183 bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	150 if ((nargin == 3 && is_function_handle (varargin{3}))
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	151 \|\| (nargin == 4 && is_function_handle (varargin{3})
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	152 && isnumeric (varargin{4})))
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	153 ## onenormest syntax, deprecated in 4.2
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	154 [est, v] = condest_legacy (varargin{:});
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	155 return
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	156 elseif ((nargin >= 5) && is_function_handle (varargin{4}))
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	157 ## onenormest syntax, deprecated in 4.2
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	158 [est, v] = condest_legacy (varargin{:});
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	159 return
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	160 endif
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	161
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	162 have_A = false;
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	163 have_t = false;
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	164 have_apply_normest1 = false;
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	165 have_solve_normest1 = false;
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	166
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	167 if (isnumeric (varargin{1}))
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	168 A = varargin{1};
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	169 if (! issquare (A))
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	170 error ("condest: matrix must be square");
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	171 endif
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	172 n = rows (A);
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	173 have_A = true;
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	174 if (nargin > 1)
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	175 if (is_function_handle (varargin{2}))
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	176 solve = varargin{2};
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	177 have_solve_normest1 = true;
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	178 if (nargin > 2)
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	179 t = varargin{3};
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	180 have_t = true;
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	181 endif
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	182 else
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	183 t = varargin{2};
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	184 have_t = true;
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	185 real_op = isreal (A);
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	186 endif
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	187 else
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	188 real_op = isreal (A);
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	189 endif
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	190 else # varargin{1} is function handle
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	191 apply = varargin{1};
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	192 if (nargin > 1)
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	193 solve = varargin{2};
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	194 have_apply_normest1 = true;
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	195 have_solve_normest1 = true;
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	196 n = apply ("dim", [], varargin{4:end});
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	197 if (nargin > 2)
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	198 t = varargin{3};
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	199 have_t = true;
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	200 endif
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	201 else
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	202 error("condest: wrong number of input parameters");
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	203 endif
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	204 endif
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	205
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	206 if (! have_t)
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	207 t = min (n, default_t);
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	208 endif
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	209
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	210 if (! have_solve_normest1)
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	211 ## prepare solve in normest1 form
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	212 if (issparse (A))
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	213 [L, U, P, Pc] = lu (A);
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	214 solve = @(flag, x) solve_sparse (flag, x, n, real_op, L, U, P, Pc);
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	215 else
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	216 [L, U, P] = lu (A);
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	217 solve = @(flag, x) solve_not_sparse (flag, x, n, real_op, L, U, P);
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	218 endif
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	219 endif
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	220
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	221 if (have_A)
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	222 Anorm = norm (A, 1);
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	223 else
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	224 Anorm = normest1 (apply, t, [], varargin{4:end});
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	225 endif
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	226 [Ainv_norm, v, w] = normest1 (solve, t, [], varargin{4:end});
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	227
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	228 est = Anorm * Ainv_norm;
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	229 v = w / norm (w, 1);
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	230
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	231 endfunction
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	232
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	233 function value = solve_sparse (flag, x, n, real_op, L , U , P , Pc)
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	234 switch flag
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	235 case "dim"
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	236 value = n;
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	237 case "real"
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	238 value = real_op;
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	239 case "notransp"
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	240 value = P' * (L' \ (U' \ (Pc * x)));
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	241 case "transp"
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	242 value = Pc' * (U \ (L \ (P * x)));
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	243 endswitch
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	244 endfunction
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	245
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	246 function value = solve_not_sparse (flag, x, n, real_op, L, U, P)
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	247 switch flag
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	248 case "dim"
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	249 value = n;
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	250 case "real"
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	251 value = real_op;
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	252 case "notransp"
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	253 value = P' * (L' \ (U' \ x));
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	254 case "transp"
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	255 value = U \ (L \ (P * x));
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	256 endswitch
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	257 endfunction
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	258
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	259 function [est, v] = condest_legacy (varargin) # to be removed after 4.2
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	260
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	261 persistent warned = false;
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	262 if (! warned)
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	263 warned = true;
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	264 warning ("Octave:deprecated-function",
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	265 "condest: this syntax is deprecated, call condest (A, SOLVEFUN, T, P1, P2, ...) instead.");
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	266 endif
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	267
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	268 default_t = 5;
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	269
7312 1ebbf0924217 [project @ 2007-12-12 22:19:54 by jwe] jwe parents: 7311 diff changeset	270 have_A = false;
1ebbf0924217 [project @ 2007-12-12 22:19:54 by jwe] jwe parents: 7311 diff changeset	271 have_t = false;
1ebbf0924217 [project @ 2007-12-12 22:19:54 by jwe] jwe parents: 7311 diff changeset	272 have_solve = false;
19700 00e31f316a3a Fix Matlab incompatibility of "ismatrix" (bug #42422). Kai T. Ohlhus <k.ohlhus@gmail.com> parents: 19697 diff changeset	273 if (isnumeric (varargin{1}))
7310 dc9b00ab5aac [project @ 2007-12-12 22:08:58 by jwe] jwe parents: 7309 diff changeset	274 A = varargin{1};
9872 72d6e0de76c7 fix qp, condest and krylov Jaroslav Hajek <highegg@gmail.com> parents: 9307 diff changeset	275 if (! issquare (A))
8664 e07e93c04080 style fixes John W. Eaton <jwe@octave.org> parents: 8347 diff changeset	276 error ("condest: matrix must be square");
7189 e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	277 endif
9872 72d6e0de76c7 fix qp, condest and krylov Jaroslav Hajek <highegg@gmail.com> parents: 9307 diff changeset	278 n = rows (A);
7312 1ebbf0924217 [project @ 2007-12-12 22:19:54 by jwe] jwe parents: 7311 diff changeset	279 have_A = true;
7189 e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	280
7312 1ebbf0924217 [project @ 2007-12-12 22:19:54 by jwe] jwe parents: 7311 diff changeset	281 if (nargin > 1)
14522 f739e30494c8 condest.m: Fix failing %!test. Rik <octave@nomad.inbox5.com> parents: 14363 diff changeset	282 if (! is_function_handle (varargin{2}))
10549 95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 9872 diff changeset	283 t = varargin{2};
95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 9872 diff changeset	284 have_t = true;
7312 1ebbf0924217 [project @ 2007-12-12 22:19:54 by jwe] jwe parents: 7311 diff changeset	285 elseif (nargin > 2)
10549 95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 9872 diff changeset	286 solve = varargin{2};
95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 9872 diff changeset	287 solve_t = varargin{3};
95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 9872 diff changeset	288 have_solve = true;
95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 9872 diff changeset	289 if (nargin > 3)
95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 9872 diff changeset	290 t = varargin{4};
95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 9872 diff changeset	291 have_t = true;
95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 9872 diff changeset	292 endif
7312 1ebbf0924217 [project @ 2007-12-12 22:19:54 by jwe] jwe parents: 7311 diff changeset	293 else
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	294 error ("condest: must supply both SOLVE and SOLVE_T");
7189 e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	295 endif
e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	296 endif
7311 1b535aed87e2 [project @ 2007-12-12 22:13:43 by jwe] jwe parents: 7310 diff changeset	297 elseif (nargin > 4)
7189 e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	298 apply = varargin{1};
e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	299 apply_t = varargin{2};
e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	300 solve = varargin{3};
e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	301 solve_t = varargin{4};
7312 1ebbf0924217 [project @ 2007-12-12 22:19:54 by jwe] jwe parents: 7311 diff changeset	302 have_solve = true;
7189 e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	303 n = varargin{5};
e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	304 if (! isscalar (n))
8664 e07e93c04080 style fixes John W. Eaton <jwe@octave.org> parents: 8347 diff changeset	305 error ("condest: dimension argument of implicit form must be scalar");
7189 e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	306 endif
7309 26f42a14d4f6 [project @ 2007-12-12 22:05:38 by jwe] jwe parents: 7239 diff changeset	307 if (nargin > 5)
7189 e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	308 t = varargin{6};
7312 1ebbf0924217 [project @ 2007-12-12 22:19:54 by jwe] jwe parents: 7311 diff changeset	309 have_t = true;
7189 e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	310 endif
7311 1b535aed87e2 [project @ 2007-12-12 22:13:43 by jwe] jwe parents: 7310 diff changeset	311 else
8664 e07e93c04080 style fixes John W. Eaton <jwe@octave.org> parents: 8347 diff changeset	312 error ("condest: implicit form of condest requires at least 5 arguments");
7189 e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	313 endif
e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	314
7312 1ebbf0924217 [project @ 2007-12-12 22:19:54 by jwe] jwe parents: 7311 diff changeset	315 if (! have_t)
7189 e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	316 t = min (n, default_t);
e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	317 endif
e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	318
7312 1ebbf0924217 [project @ 2007-12-12 22:19:54 by jwe] jwe parents: 7311 diff changeset	319 if (! have_solve)
7189 e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	320 if (issparse (A))
8912 57c3155754d6 fix condest Jaroslav Hajek <highegg@gmail.com> parents: 8664 diff changeset	321 [L, U, P, Pc] = lu (A);
7312 1ebbf0924217 [project @ 2007-12-12 22:19:54 by jwe] jwe parents: 7311 diff changeset	322 solve = @(x) Pc' * (U \ (L \ (P * x)));
1ebbf0924217 [project @ 2007-12-12 22:19:54 by jwe] jwe parents: 7311 diff changeset	323 solve_t = @(x) P' * (L' \ (U' \ (Pc * x)));
7189 e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	324 else
e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	325 [L, U, P] = lu (A);
7312 1ebbf0924217 [project @ 2007-12-12 22:19:54 by jwe] jwe parents: 7311 diff changeset	326 solve = @(x) U \ (L \ (P*x));
1ebbf0924217 [project @ 2007-12-12 22:19:54 by jwe] jwe parents: 7311 diff changeset	327 solve_t = @(x) P' * (L' \ (U' \ x));
7189 e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	328 endif
e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	329 endif
e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	330
22183 bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	331 ## We already warned about this usage being deprecated. Don't
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	332 ## warn again about onenormest.
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	333 warning ("off", "Octave:deprecated-function", "local");
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	334
7312 1ebbf0924217 [project @ 2007-12-12 22:19:54 by jwe] jwe parents: 7311 diff changeset	335 if (have_A)
7189 e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	336 Anorm = norm (A, 1);
e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	337 else
e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	338 Anorm = onenormest (apply, apply_t, n, t);
e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	339 endif
e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	340
e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	341 [Ainv_norm, v, w] = onenormest (solve, solve_t, n, t);
e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	342
e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	343 est = Anorm * Ainv_norm;
e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	344 v = w / norm (w, 1);
e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	345
e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	346 endfunction
e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	347
e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	348 ## Yes, these test bounds are really loose. There's
e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	349 ## enough randomization to trigger odd cases with hilb().
e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	350
22183 bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	351 %!function value = apply_fun (flag, x, A, m)
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	352 %! if (nargin == 3)
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	353 %! m = 1;
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	354 %! endif
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	355 %! switch flag
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	356 %! case "dim"
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	357 %! value = length (A);
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	358 %! case "real"
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	359 %! value = isreal (A);
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	360 %! case "notransp"
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	361 %! value = x; for i = 1:m, value = A * value;, endfor
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	362 %! case "transp"
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	363 %! value = x; for i = 1:m, value = A' * value;, endfor
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	364 %! endswitch
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	365 %!endfunction
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	366 %!function value = solve_fun (flag, x, A, m)
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	367 %! if (nargin == 3)
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	368 %! m = 1;
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	369 %! endif
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	370 %! switch flag
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	371 %! case "dim"
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	372 %! value = length (A);
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	373 %! case "real"
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	374 %! value = isreal (A);
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	375 %! case "notransp"
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	376 %! value = x; for i = 1:m, value = A \ value;, endfor;
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	377 %! case "transp"
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	378 %! value = x; for i = 1:m, value = A' \ value;, endfor;
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	379 %! endswitch
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	380 %!endfunction
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	381
7189 e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	382 %!test
14237 11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	383 %! N = 6;
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	384 %! A = hilb (N);
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	385 %! cA = condest (A);
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	386 %! cA_test = norm (inv (A), 1) * norm (A, 1);
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	387 %! assert (cA, cA_test, -2^-8);
7189 e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	388
22183 bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	389 %!test # to be removed after 4.2
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	390 %! warning ("off", "Octave:deprecated-function", "local");
14237 11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	391 %! N = 6;
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	392 %! A = hilb (N);
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	393 %! solve = @(x) A\x; solve_t = @(x) A'\x;
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	394 %! cA = condest (A, solve, solve_t);
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	395 %! cA_test = norm (inv (A), 1) * norm (A, 1);
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	396 %! assert (cA, cA_test, -2^-8);
7189 e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	397
22183 bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	398 %!test # to be removed after 4.2
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	399 %! warning ("off", "Octave:deprecated-function", "local");
14237 11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	400 %! N = 6;
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	401 %! A = hilb (N);
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	402 %! apply = @(x) Ax; apply_t = @(x) A'x;
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	403 %! solve = @(x) A\x; solve_t = @(x) A'\x;
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	404 %! cA = condest (apply, apply_t, solve, solve_t, N);
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	405 %! cA_test = norm (inv (A), 1) * norm (A, 1);
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	406 %! assert (cA, cA_test, -2^-6);
7189 e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	407
22183 bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	408 %!test # to be removed after 4.2
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	409 %! warning ("off", "Octave:deprecated-function", "local");
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	410 %! N = 6;
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	411 %! A = hilb (N);
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	412 %! apply = @(x) Ax; apply_t = @(x) A'x;
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	413 %! solve = @(x) A\x; solve_t = @(x) A'\x;
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	414 %! cA = condest (apply, apply_t, solve, solve_t, N, 2);
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	415 %! cA_test = norm (inv (A), 1) * norm (A, 1);
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	416 %! assert (cA, cA_test, -2^-6);
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	417
7189 e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	418 %!test
19670 e5facc6eec13 Silence warning messages in %!test code. Rik <rik@octave.org> parents: 19040 diff changeset	419 %! warning ("off", "Octave:nearly-singular-matrix", "local");
14237 11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	420 %! N = 12;
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	421 %! A = hilb (N);
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	422 %! [rcondA, v] = condest (A);
11949c9795a0 Revamp %!demos in m-files to use Octave coding conventions on spacing, etc. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	423 %! x = A*v;
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14237 diff changeset	424 %! assert (norm (x, inf), 0, eps);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14237 diff changeset	425
22183 bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	426 %!test
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	427 %! N = 6;
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	428 %! A = hilb (N);
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	429 %! solve = @(flag, x) solve_fun (flag, x, A);
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	430 %! cA = condest (A, solve);
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	431 %! cA_test = norm (inv (A), 1) * norm (A, 1);
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	432 %! assert (cA, cA_test, -2^-6);
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	433 %!test
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	434 %! N = 6;
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	435 %! A = hilb (N);
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	436 %! apply = @(flag, x) apply_fun (flag, x, A);
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	437 %! solve = @(flag, x) solve_fun (flag, x, A);
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	438 %! cA = condest (apply, solve);
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	439 %! cA_test = norm (inv (A), 1) * norm (A, 1);
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	440 %! assert (cA, cA_test, -2^-6);
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	441
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	442 %!test # parameters for apply and solve functions
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	443 %! N = 6;
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	444 %! A = hilb (N);
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	445 %! m = 2;
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	446 %! cA = condest (@apply_fun, @solve_fun, [], A, m);
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	447 %! cA_test = norm (inv (A^2), 1) * norm (A^2, 1);
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	448 %! assert (cA, cA_test, -2^-6);