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

annotate scripts/linear-algebra/condest.m @ 22826:b7bf2d6d8e55

condest.m: Overhaul function. * condest.m: Rename output 'est' to 'cest' to match documentation. Eliminate unnecessary default_t variable. Use names of bad inuts in error() messages. Reorder code to have input validation first. Add FIXME notes. Add parentheses around conditions in switch statements. Add BIST tests for input validation.

author	Rik <rik@octave.org>
date	Thu, 24 Nov 2016 07:16:17 -0800
parents	c5f496b8352c
children	41a751b19fd2

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
22755 3a2b891d0b33 maint: Standardize Copyright formatting. Rik <rik@octave.org> parents: 22323 diff changeset	8 ## the Free Software Foundation; either version 3 of the License, or
3a2b891d0b33 maint: Standardize Copyright formatting. Rik <rik@octave.org> parents: 22323 diff changeset	9 ## (at your option) any later version.
7189 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
22755 3a2b891d0b33 maint: Standardize Copyright formatting. Rik <rik@octave.org> parents: 22323 diff changeset	13 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
3a2b891d0b33 maint: Standardize Copyright formatting. Rik <rik@octave.org> parents: 22323 diff changeset	14 ## GNU General Public License for more details.
7189 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 --
22824 fb913df7babb doc: Update docstring for condest. Rik <rik@octave.org> parents: 22323 diff changeset	21 ## @deftypefn {} {@var{cest} =} condest (@var{A})
fb913df7babb doc: Update docstring for condest. Rik <rik@octave.org> parents: 22323 diff changeset	22 ## @deftypefnx {} {@var{cest} =} condest (@var{A}, @var{t})
fb913df7babb doc: Update docstring for condest. Rik <rik@octave.org> parents: 22323 diff changeset	23 ## @deftypefnx {} {@var{cest} =} condest (@var{A}, @var{solvefun}, @var{t}, @var{p1}, @var{p2}, @dots{})
fb913df7babb doc: Update docstring for condest. Rik <rik@octave.org> parents: 22323 diff changeset	24 ## @deftypefnx {} {@var{cest} =} condest (@var{Afcn}, @var{solvefun}, @var{t}, @var{p1}, @var{p2}, @dots{})
fb913df7babb doc: Update docstring for condest. Rik <rik@octave.org> parents: 22323 diff changeset	25 ## @deftypefnx {} {[@var{cest}, @var{v}] =} condest (@dots{})
7189 e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	26 ##
22824 fb913df7babb doc: Update docstring for condest. Rik <rik@octave.org> parents: 22323 diff changeset	27 ## Estimate the 1-norm condition number of a square matrix @var{A} using
fb913df7babb doc: Update docstring for condest. Rik <rik@octave.org> parents: 22323 diff changeset	28 ## @var{t} test vectors and a randomized 1-norm estimator.
20160 03b9d17a2d95 doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19700 diff changeset	29 ##
22824 fb913df7babb doc: Update docstring for condest. Rik <rik@octave.org> parents: 22323 diff changeset	30 ## The optional input @var{t} specifies the number of test vectors (default 5).
7189 e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	31 ##
22824 fb913df7babb doc: Update docstring for condest. Rik <rik@octave.org> parents: 22323 diff changeset	32 ## If the matrix is not explicit, e.g., when estimating the condition number of
fb913df7babb doc: Update docstring for condest. Rik <rik@octave.org> parents: 22323 diff changeset	33 ## @var{A} given an LU@tie{}factorization, @code{condest} uses the following
fb913df7babb doc: Update docstring for condest. Rik <rik@octave.org> parents: 22323 diff changeset	34 ## functions:
7189 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
22824 fb913df7babb doc: Update docstring for condest. Rik <rik@octave.org> parents: 22323 diff changeset	37 ## @item @var{Afcn} which must return
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 ##
22824 fb913df7babb doc: Update docstring for condest. Rik <rik@octave.org> parents: 22323 diff changeset	53 ## @item @var{solvefun} which must return
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
22824 fb913df7babb doc: Update docstring for condest. Rik <rik@octave.org> parents: 22323 diff changeset	71 ## @code{@var{Afcn} (@var{flag}, @var{x}, @var{p1}, @var{p2}, @dots{})}
fb913df7babb doc: Update docstring for condest. Rik <rik@octave.org> parents: 22323 diff changeset	72 ## and @code{@var{solvefcn} (@var{flag}, @var{x}, @var{p1}, @var{p2},
22183 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 ##
22824 fb913df7babb doc: Update docstring for condest. Rik <rik@octave.org> parents: 22323 diff changeset	75 ## The principal output is the 1-norm condition number estimate @var{cest}.
7189 e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	76 ##
22824 fb913df7babb doc: Update docstring for condest. Rik <rik@octave.org> parents: 22323 diff changeset	77 ## The optional second output is an approximate null vector when @var{cest} is
fb913df7babb doc: Update docstring for condest. Rik <rik@octave.org> parents: 22323 diff changeset	78 ## large; it satisfies the equation
fb913df7babb doc: Update docstring for condest. Rik <rik@octave.org> parents: 22323 diff changeset	79 ## @code{norm (Av, 1) == norm (A, 1) norm (@var{v}, 1) / @var{est}}.
fb913df7babb doc: Update docstring for condest. Rik <rik@octave.org> parents: 22323 diff changeset	80 ##
fb913df7babb doc: Update docstring for condest. Rik <rik@octave.org> parents: 22323 diff changeset	81 ## Algorithm Note: @code{condest} uses a randomized algorithm to approximate
fb913df7babb doc: Update docstring for condest. Rik <rik@octave.org> parents: 22323 diff changeset	82 ## the 1-norms. Therefore, if consistent results are required, the
fb913df7babb doc: Update docstring for condest. Rik <rik@octave.org> parents: 22323 diff changeset	83 ## @qcode{"state"} of the random generator should be fixed before invoking
fb913df7babb doc: Update docstring for condest. Rik <rik@octave.org> parents: 22323 diff changeset	84 ## @code{condest}.
7189 e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	85 ##
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11523 diff changeset	86 ## References:
16816 12005245b645 doc: Periodic grammarcheck of documentation. Rik <rik@octave.org> parents: 14522 diff changeset	87 ##
7189 e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	88 ## @itemize
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11523 diff changeset	89 ## @item
19040 0850b5212619 doc: Add @nospell macro around proper names in documentation. Rik <rik@octave.org> parents: 17744 diff changeset	90 ## @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	91 ## 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	92 ## Pseudospectra}. SIMAX vol 21, no 4, pp 1185-1201.
7189 e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	93 ## @url{http://dx.doi.org/10.1137/S0895479899356080}
10821 693e22af08ae Grammarcheck documentation of m-files Rik <octave@nomad.inbox5.com> parents: 10793 diff changeset	94 ##
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11523 diff changeset	95 ## @item
19040 0850b5212619 doc: Add @nospell macro around proper names in documentation. Rik <rik@octave.org> parents: 17744 diff changeset	96 ## @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	97 ## 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	98 ## Pseudospectra}. @url{http://citeseer.ist.psu.edu/223007.html}
7189 e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	99 ## @end itemize
e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	100 ##
22824 fb913df7babb doc: Update docstring for condest. Rik <rik@octave.org> parents: 22323 diff changeset	101 ## @seealso{cond, norm, normest1, normest}
7189 e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	102 ## @end deftypefn
e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	103
20194 b0f7ee81d974 doc: Remove extra spaces at start of docstring which show up in Info format. Rik <rik@octave.org> parents: 20160 diff changeset	104 ## Code originally licensed under:
7189 e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	105 ##
20194 b0f7ee81d974 doc: Remove extra spaces at start of docstring which show up in Info format. Rik <rik@octave.org> parents: 20160 diff changeset	106 ## 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	107 ## All rights reserved.
7191 b48a21816f2e [project @ 2007-11-26 21:24:32 by jwe] jwe parents: 7189 diff changeset	108 ##
20194 b0f7ee81d974 doc: Remove extra spaces at start of docstring which show up in Info format. Rik <rik@octave.org> parents: 20160 diff changeset	109 ## 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	110 ## 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	111 ## are met:
7189 e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	112 ##
20194 b0f7ee81d974 doc: Remove extra spaces at start of docstring which show up in Info format. Rik <rik@octave.org> parents: 20160 diff changeset	113 ## * 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	114 ## 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	115 ##
20194 b0f7ee81d974 doc: Remove extra spaces at start of docstring which show up in Info format. Rik <rik@octave.org> parents: 20160 diff changeset	116 ## * 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	117 ## 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	118 ## 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	119 ## with the distribution.
7191 b48a21816f2e [project @ 2007-11-26 21:24:32 by jwe] jwe parents: 7189 diff changeset	120 ##
20194 b0f7ee81d974 doc: Remove extra spaces at start of docstring which show up in Info format. Rik <rik@octave.org> parents: 20160 diff changeset	121 ## * 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	122 ## 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	123 ## 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	124 ## written permission.
7189 e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	125 ##
20194 b0f7ee81d974 doc: Remove extra spaces at start of docstring which show up in Info format. Rik <rik@octave.org> parents: 20160 diff changeset	126 ## 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	127 ## 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	128 ## 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	129 ## 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	130 ## 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	131 ## 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	132 ## 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	133 ## 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	134 ## 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	135 ## 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	136 ## 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	137 ## SUCH DAMAGE.
7189 e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	138
e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	139 ## Author: Jason Riedy <ejr@cs.berkeley.edu>
e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	140 ## Keywords: linear-algebra norm estimation
e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	141 ## Version: 0.2
e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	142
22826 b7bf2d6d8e55 condest.m: Overhaul function. Rik <rik@octave.org> parents: 22825 diff changeset	143 function [cest, v] = condest (varargin)
7191 b48a21816f2e [project @ 2007-11-26 21:24:32 by jwe] jwe parents: 7189 diff changeset	144
7309 26f42a14d4f6 [project @ 2007-12-12 22:05:38 by jwe] jwe parents: 7239 diff changeset	145 if (nargin < 1 \|\| nargin > 6)
7191 b48a21816f2e [project @ 2007-11-26 21:24:32 by jwe] jwe parents: 7189 diff changeset	146 print_usage ();
7189 e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	147 endif
e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	148
22183 bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	149 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	150 \|\| (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	151 && isnumeric (varargin{4})))
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	152 ## onenormest syntax, deprecated in 4.2
22826 b7bf2d6d8e55 condest.m: Overhaul function. Rik <rik@octave.org> parents: 22825 diff changeset	153 [cest, v] = condest_legacy (varargin{:});
b7bf2d6d8e55 condest.m: Overhaul function. Rik <rik@octave.org> parents: 22825 diff changeset	154 return;
22183 bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	155 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	156 ## onenormest syntax, deprecated in 4.2
22826 b7bf2d6d8e55 condest.m: Overhaul function. Rik <rik@octave.org> parents: 22825 diff changeset	157 [cest, v] = condest_legacy (varargin{:});
b7bf2d6d8e55 condest.m: Overhaul function. Rik <rik@octave.org> parents: 22825 diff changeset	158 return;
22183 bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	159 endif
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	160
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	161 have_A = false;
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	162 have_t = false;
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	163 have_apply_normest1 = false;
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	164 have_solve_normest1 = false;
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	165
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	166 if (isnumeric (varargin{1}))
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	167 A = varargin{1};
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	168 if (! issquare (A))
22826 b7bf2d6d8e55 condest.m: Overhaul function. Rik <rik@octave.org> parents: 22825 diff changeset	169 error ("condest: A must be square");
22183 bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	170 endif
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	171 n = rows (A);
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	172 have_A = true;
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	173 if (nargin > 1)
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	174 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	175 solve = varargin{2};
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	176 have_solve_normest1 = true;
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	177 if (nargin > 2)
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	178 t = varargin{3};
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	179 have_t = true;
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	180 endif
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	181 else
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	182 t = varargin{2};
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	183 have_t = true;
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	184 real_op = isreal (A);
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	185 endif
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	186 else
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	187 real_op = isreal (A);
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	188 endif
22826 b7bf2d6d8e55 condest.m: Overhaul function. Rik <rik@octave.org> parents: 22825 diff changeset	189 else # varargin{1} is a function handle
b7bf2d6d8e55 condest.m: Overhaul function. Rik <rik@octave.org> parents: 22825 diff changeset	190 if (nargin == 1)
b7bf2d6d8e55 condest.m: Overhaul function. Rik <rik@octave.org> parents: 22825 diff changeset	191 error("condest: must provide SOLVEFCN when using AFCN");
b7bf2d6d8e55 condest.m: Overhaul function. Rik <rik@octave.org> parents: 22825 diff changeset	192 endif
22183 bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	193 apply = varargin{1};
22826 b7bf2d6d8e55 condest.m: Overhaul function. Rik <rik@octave.org> parents: 22825 diff changeset	194 have_apply_normest1 = true;
b7bf2d6d8e55 condest.m: Overhaul function. Rik <rik@octave.org> parents: 22825 diff changeset	195 solve = varargin{2};
b7bf2d6d8e55 condest.m: Overhaul function. Rik <rik@octave.org> parents: 22825 diff changeset	196 have_solve_normest1 = true;
b7bf2d6d8e55 condest.m: Overhaul function. Rik <rik@octave.org> parents: 22825 diff changeset	197 n = apply ("dim", [], varargin{4:end});
b7bf2d6d8e55 condest.m: Overhaul function. Rik <rik@octave.org> parents: 22825 diff changeset	198 if (nargin > 2)
b7bf2d6d8e55 condest.m: Overhaul function. Rik <rik@octave.org> parents: 22825 diff changeset	199 t = varargin{3};
b7bf2d6d8e55 condest.m: Overhaul function. Rik <rik@octave.org> parents: 22825 diff changeset	200 have_t = true;
22183 bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	201 endif
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	202 endif
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	203
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	204 if (! have_t)
22826 b7bf2d6d8e55 condest.m: Overhaul function. Rik <rik@octave.org> parents: 22825 diff changeset	205 t = min (n, 5);
22183 bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	206 endif
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	207
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	208 if (! have_solve_normest1)
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	209 ## 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	210 if (issparse (A))
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	211 [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	212 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	213 else
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	214 [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	215 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	216 endif
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	217 endif
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	218
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	219 if (have_A)
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	220 Anorm = norm (A, 1);
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	221 else
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	222 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	223 endif
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	224 [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	225
22826 b7bf2d6d8e55 condest.m: Overhaul function. Rik <rik@octave.org> parents: 22825 diff changeset	226 cest = Anorm * Ainv_norm;
22183 bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	227 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	228
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	229 endfunction
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 function value = solve_sparse (flag, x, n, real_op, L , U , P , Pc)
22760 c4d80b9d2898 maint: Capitalize variable names appearing in error() messages of m-files. Rik <rik@octave.org> parents: 22755 diff changeset	232 switch (flag)
22183 bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	233 case "dim"
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	234 value = n;
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	235 case "real"
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	236 value = real_op;
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	237 case "notransp"
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	238 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	239 case "transp"
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	240 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	241 endswitch
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	242 endfunction
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	243
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	244 function value = solve_not_sparse (flag, x, n, real_op, L, U, P)
22760 c4d80b9d2898 maint: Capitalize variable names appearing in error() messages of m-files. Rik <rik@octave.org> parents: 22755 diff changeset	245 switch (flag)
22183 bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	246 case "dim"
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	247 value = n;
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	248 case "real"
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	249 value = real_op;
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	250 case "notransp"
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	251 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	252 case "transp"
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	253 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	254 endswitch
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	255 endfunction
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	256
22826 b7bf2d6d8e55 condest.m: Overhaul function. Rik <rik@octave.org> parents: 22825 diff changeset	257 ## FIXME: remove after 4.4
b7bf2d6d8e55 condest.m: Overhaul function. Rik <rik@octave.org> parents: 22825 diff changeset	258 function [cest, v] = condest_legacy (varargin)
22183 bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	259
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	260 persistent warned = false;
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	261 if (! warned)
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	262 warned = true;
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	263 warning ("Octave:deprecated-function",
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	264 "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	265 endif
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	266
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	267 default_t = 5;
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	268
7312 1ebbf0924217 [project @ 2007-12-12 22:19:54 by jwe] jwe parents: 7311 diff changeset	269 have_A = false;
1ebbf0924217 [project @ 2007-12-12 22:19:54 by jwe] jwe parents: 7311 diff changeset	270 have_t = false;
1ebbf0924217 [project @ 2007-12-12 22:19:54 by jwe] jwe parents: 7311 diff changeset	271 have_solve = false;
19700 00e31f316a3a Fix Matlab incompatibility of "ismatrix" (bug #42422). Kai T. Ohlhus <k.ohlhus@gmail.com> parents: 19697 diff changeset	272 if (isnumeric (varargin{1}))
7310 dc9b00ab5aac [project @ 2007-12-12 22:08:58 by jwe] jwe parents: 7309 diff changeset	273 A = varargin{1};
9872 72d6e0de76c7 fix qp, condest and krylov Jaroslav Hajek <highegg@gmail.com> parents: 9307 diff changeset	274 if (! issquare (A))
8664 e07e93c04080 style fixes John W. Eaton <jwe@octave.org> parents: 8347 diff changeset	275 error ("condest: matrix must be square");
7189 e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	276 endif
9872 72d6e0de76c7 fix qp, condest and krylov Jaroslav Hajek <highegg@gmail.com> parents: 9307 diff changeset	277 n = rows (A);
7312 1ebbf0924217 [project @ 2007-12-12 22:19:54 by jwe] jwe parents: 7311 diff changeset	278 have_A = true;
7189 e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	279
7312 1ebbf0924217 [project @ 2007-12-12 22:19:54 by jwe] jwe parents: 7311 diff changeset	280 if (nargin > 1)
14522 f739e30494c8 condest.m: Fix failing %!test. Rik <octave@nomad.inbox5.com> parents: 14363 diff changeset	281 if (! is_function_handle (varargin{2}))
10549 95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 9872 diff changeset	282 t = varargin{2};
95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 9872 diff changeset	283 have_t = true;
7312 1ebbf0924217 [project @ 2007-12-12 22:19:54 by jwe] jwe parents: 7311 diff changeset	284 elseif (nargin > 2)
10549 95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 9872 diff changeset	285 solve = varargin{2};
95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 9872 diff changeset	286 solve_t = varargin{3};
95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 9872 diff changeset	287 have_solve = true;
95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 9872 diff changeset	288 if (nargin > 3)
95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 9872 diff changeset	289 t = varargin{4};
95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 9872 diff changeset	290 have_t = true;
95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 9872 diff changeset	291 endif
7312 1ebbf0924217 [project @ 2007-12-12 22:19:54 by jwe] jwe parents: 7311 diff changeset	292 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	293 error ("condest: must supply both SOLVE and SOLVE_T");
7189 e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	294 endif
e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	295 endif
7311 1b535aed87e2 [project @ 2007-12-12 22:13:43 by jwe] jwe parents: 7310 diff changeset	296 elseif (nargin > 4)
7189 e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	297 apply = varargin{1};
e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	298 apply_t = varargin{2};
e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	299 solve = varargin{3};
e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	300 solve_t = varargin{4};
7312 1ebbf0924217 [project @ 2007-12-12 22:19:54 by jwe] jwe parents: 7311 diff changeset	301 have_solve = true;
7189 e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	302 n = varargin{5};
e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	303 if (! isscalar (n))
8664 e07e93c04080 style fixes John W. Eaton <jwe@octave.org> parents: 8347 diff changeset	304 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	305 endif
7309 26f42a14d4f6 [project @ 2007-12-12 22:05:38 by jwe] jwe parents: 7239 diff changeset	306 if (nargin > 5)
7189 e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	307 t = varargin{6};
7312 1ebbf0924217 [project @ 2007-12-12 22:19:54 by jwe] jwe parents: 7311 diff changeset	308 have_t = true;
7189 e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	309 endif
7311 1b535aed87e2 [project @ 2007-12-12 22:13:43 by jwe] jwe parents: 7310 diff changeset	310 else
8664 e07e93c04080 style fixes John W. Eaton <jwe@octave.org> parents: 8347 diff changeset	311 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	312 endif
e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	313
7312 1ebbf0924217 [project @ 2007-12-12 22:19:54 by jwe] jwe parents: 7311 diff changeset	314 if (! have_t)
7189 e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	315 t = min (n, default_t);
e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	316 endif
e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	317
7312 1ebbf0924217 [project @ 2007-12-12 22:19:54 by jwe] jwe parents: 7311 diff changeset	318 if (! have_solve)
7189 e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	319 if (issparse (A))
8912 57c3155754d6 fix condest Jaroslav Hajek <highegg@gmail.com> parents: 8664 diff changeset	320 [L, U, P, Pc] = lu (A);
7312 1ebbf0924217 [project @ 2007-12-12 22:19:54 by jwe] jwe parents: 7311 diff changeset	321 solve = @(x) Pc' * (U \ (L \ (P * x)));
1ebbf0924217 [project @ 2007-12-12 22:19:54 by jwe] jwe parents: 7311 diff changeset	322 solve_t = @(x) P' * (L' \ (U' \ (Pc * x)));
7189 e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	323 else
e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	324 [L, U, P] = lu (A);
7312 1ebbf0924217 [project @ 2007-12-12 22:19:54 by jwe] jwe parents: 7311 diff changeset	325 solve = @(x) U \ (L \ (P*x));
1ebbf0924217 [project @ 2007-12-12 22:19:54 by jwe] jwe parents: 7311 diff changeset	326 solve_t = @(x) P' * (L' \ (U' \ x));
7189 e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	327 endif
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
22826 b7bf2d6d8e55 condest.m: Overhaul function. Rik <rik@octave.org> parents: 22825 diff changeset	330 ## We already warned about this usage being deprecated.
b7bf2d6d8e55 condest.m: Overhaul function. Rik <rik@octave.org> parents: 22825 diff changeset	331 ## Don't warn again about onenormest.
22183 bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	332 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	333
7312 1ebbf0924217 [project @ 2007-12-12 22:19:54 by jwe] jwe parents: 7311 diff changeset	334 if (have_A)
7189 e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	335 Anorm = norm (A, 1);
e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	336 else
e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	337 Anorm = onenormest (apply, apply_t, n, t);
e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	338 endif
e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	339
e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	340 [Ainv_norm, v, w] = onenormest (solve, solve_t, n, t);
e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	341
22826 b7bf2d6d8e55 condest.m: Overhaul function. Rik <rik@octave.org> parents: 22825 diff changeset	342 cest = Anorm * Ainv_norm;
7189 e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	343 v = w / norm (w, 1);
e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	344
e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	345 endfunction
e8d953d03f6a [project @ 2007-11-26 20:42:09 by dbateman] dbateman parents: diff changeset	346
22826 b7bf2d6d8e55 condest.m: Overhaul function. Rik <rik@octave.org> parents: 22825 diff changeset	347
b7bf2d6d8e55 condest.m: Overhaul function. Rik <rik@octave.org> parents: 22825 diff changeset	348 ## Note: These test bounds are very loose. There is enough randomization to
b7bf2d6d8e55 condest.m: Overhaul function. Rik <rik@octave.org> parents: 22825 diff changeset	349 ## trigger odd cases with hilb().
7189 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
22826 b7bf2d6d8e55 condest.m: Overhaul function. Rik <rik@octave.org> parents: 22825 diff changeset	355 %! switch (flag)
22183 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
22826 b7bf2d6d8e55 condest.m: Overhaul function. Rik <rik@octave.org> parents: 22825 diff changeset	370 %! switch (flag)
22183 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
22826 b7bf2d6d8e55 condest.m: Overhaul function. Rik <rik@octave.org> parents: 22825 diff changeset	389 %!test # to be removed after 4.4
22183 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
22826 b7bf2d6d8e55 condest.m: Overhaul function. Rik <rik@octave.org> parents: 22825 diff changeset	398 %!test # to be removed after 4.4
22183 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
22826 b7bf2d6d8e55 condest.m: Overhaul function. Rik <rik@octave.org> parents: 22825 diff changeset	408 %!test # to be removed after 4.4
22183 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);
22826 b7bf2d6d8e55 condest.m: Overhaul function. Rik <rik@octave.org> parents: 22825 diff changeset	422 %! [~, v] = condest (A);
14237 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);
22826 b7bf2d6d8e55 condest.m: Overhaul function. Rik <rik@octave.org> parents: 22825 diff changeset	433
22183 bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	434 %!test
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	435 %! N = 6;
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	436 %! A = hilb (N);
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	437 %! 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	438 %! 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	439 %! cA = condest (apply, solve);
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	440 %! 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	441 %! 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	442
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	443 %!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	444 %! N = 6;
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	445 %! A = hilb (N);
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	446 %! m = 2;
bfb1b089c230 New function normest1 as replacement for onenormest (patch #8837) Marco Caliari <marco.caliari@univr.it> parents: 20852 diff changeset	447 %! 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	448 %! 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	449 %! assert (cA, cA_test, -2^-6);
22826 b7bf2d6d8e55 condest.m: Overhaul function. Rik <rik@octave.org> parents: 22825 diff changeset	450
b7bf2d6d8e55 condest.m: Overhaul function. Rik <rik@octave.org> parents: 22825 diff changeset	451 ## Test input validation
b7bf2d6d8e55 condest.m: Overhaul function. Rik <rik@octave.org> parents: 22825 diff changeset	452 %!error condest ()
b7bf2d6d8e55 condest.m: Overhaul function. Rik <rik@octave.org> parents: 22825 diff changeset	453 %!error condest (1,2,3,4,5,6,7)
b7bf2d6d8e55 condest.m: Overhaul function. Rik <rik@octave.org> parents: 22825 diff changeset	454 %!error <A must be square> condest ([1 2])
b7bf2d6d8e55 condest.m: Overhaul function. Rik <rik@octave.org> parents: 22825 diff changeset	455 %!error <must provide SOLVEFCN when using AFCN> condest (@sin)
b7bf2d6d8e55 condest.m: Overhaul function. Rik <rik@octave.org> parents: 22825 diff changeset	456