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Use Octave coding conventions in all m-file %!test blocks
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asec.m, asecd.m, asech.m, asind.m, atand.m, cosd.m, cot.m, cotd.m, coth.m,
csc.m, cscd.m, csch.m, sec.m, secd.m, sech.m, sind.m, tand.m, accumarray.m,
accumdim.m, bitcmp.m, bitget.m, bitset.m, blkdiag.m, cart2pol.m, cart2sph.m,
celldisp.m, chop.m, circshift.m, colon.m, common_size.m, cplxpair.m,
cumtrapz.m, curl.m, dblquad.m, deal.m, divergence.m, flipdim.m, fliplr.m,
flipud.m, genvarname.m, gradient.m, idivide.m, int2str.m, interp1.m,
interp1q.m, interp2.m, interp3.m, interpft.m, interpn.m, isa.m, isdir.m,
isequal.m, isequalwithequalnans.m, issquare.m, logspace.m, nargchk.m,
narginchk.m, nargoutchk.m, nextpow2.m, nthargout.m, num2str.m, pol2cart.m,
polyarea.m, postpad.m, prepad.m, profile.m, profshow.m, quadgk.m, quadv.m,
randi.m, rat.m, repmat.m, rot90.m, rotdim.m, shift.m, shiftdim.m, sph2cart.m,
structfun.m, trapz.m, triplequad.m, convhull.m, dsearch.m, dsearchn.m,
griddata3.m, griddatan.m, rectint.m, tsearchn.m, __makeinfo__.m, doc.m,
get_first_help_sentence.m, help.m, type.m, unimplemented.m, which.m, imread.m,
imwrite.m, dlmwrite.m, fileread.m, is_valid_file_id.m, strread.m, textread.m,
textscan.m, commutation_matrix.m, cond.m, condest.m, cross.m,
duplication_matrix.m, expm.m, housh.m, isdefinite.m, ishermitian.m,
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fullfile.m, getfield.m, gzip.m, info.m, inputname.m, isappdata.m, isdeployed.m,
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setappdata.m, setfield.m, substruct.m, symvar.m, ver.m, version.m,
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ishghandle.m, ishold.m, isocolors.m, isonormals.m, isosurface.m, isprop.m,
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statistics.m, std.m, table.m, var.m, zscore.m, betacdf.m, betainv.m, betapdf.m,
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expinv.m, exppdf.m, exprnd.m, fcdf.m, finv.m, fpdf.m, frnd.m, gamcdf.m,
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hygecdf.m, hygeinv.m, hygepdf.m, hygernd.m, kolmogorov_smirnov_cdf.m,
laplace_cdf.m, laplace_inv.m, laplace_pdf.m, laplace_rnd.m, logistic_cdf.m,
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poissrnd.m, stdnormal_cdf.m, stdnormal_inv.m, stdnormal_pdf.m, stdnormal_rnd.m,
tcdf.m, tinv.m, tpdf.m, trnd.m, unidcdf.m, unidinv.m, unidpdf.m, unidrnd.m,
unifcdf.m, unifinv.m, unifpdf.m, unifrnd.m, wblcdf.m, wblinv.m, wblpdf.m,
wblrnd.m, kolmogorov_smirnov_test.m, kruskal_wallis_test.m, base2dec.m,
bin2dec.m, blanks.m, cstrcat.m, deblank.m, dec2base.m, dec2bin.m, dec2hex.m,
findstr.m, hex2dec.m, index.m, isletter.m, mat2str.m, rindex.m, str2num.m,
strcat.m, strjust.m, strmatch.m, strsplit.m, strtok.m, strtrim.m, strtrunc.m,
substr.m, validatestring.m, demo.m, example.m, fail.m, speed.m, addtodate.m,
asctime.m, clock.m, ctime.m, date.m, datenum.m, datetick.m, datevec.m,
eomday.m, etime.m, is_leap_year.m, now.m:
Use Octave coding conventions in all m-file %!test blocks
author | Rik <octave@nomad.inbox5.com> |
---|---|
date | Mon, 13 Feb 2012 07:29:44 -0800 |
parents | 11949c9795a0 |
children | f739e30494c8 |
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## Copyright (C) 2007-2012 Regents of the University of California ## ## This file is part of Octave. ## ## Octave is free software; you can redistribute it and/or modify it ## under the terms of the GNU General Public License as published by ## the Free Software Foundation; either version 3 of the License, or (at ## your option) any later version. ## ## Octave is distributed in the hope that it will be useful, but ## WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with Octave; see the file COPYING. If not, see ## <http://www.gnu.org/licenses/>. ## -*- texinfo -*- ## @deftypefn {Function File} {} condest (@var{A}) ## @deftypefnx {Function File} {} condest (@var{A}, @var{t}) ## @deftypefnx {Function File} {[@var{est}, @var{v}] =} condest (@dots{}) ## @deftypefnx {Function File} {[@var{est}, @var{v}] =} condest (@var{A}, @var{solve}, @var{solve_t}, @var{t}) ## @deftypefnx {Function File} {[@var{est}, @var{v}] =} condest (@var{apply}, @var{apply_t}, @var{solve}, @var{solve_t}, @var{n}, @var{t}) ## ## Estimate the 1-norm condition number of a matrix @var{A} ## using @var{t} test vectors using a randomized 1-norm estimator. ## If @var{t} exceeds 5, then only 5 test vectors are used. ## ## If the matrix is not explicit, e.g., when estimating the condition ## number of @var{A} given an LU@tie{}factorization, @code{condest} uses the ## following functions: ## ## @table @var ## @item apply ## @code{A*x} for a matrix @code{x} of size @var{n} by @var{t}. ## ## @item apply_t ## @code{A'*x} for a matrix @code{x} of size @var{n} by @var{t}. ## ## @item solve ## @code{A \ b} for a matrix @code{b} of size @var{n} by @var{t}. ## ## @item solve_t ## @code{A' \ b} for a matrix @code{b} of size @var{n} by @var{t}. ## @end table ## ## The implicit version requires an explicit dimension @var{n}. ## ## @code{condest} uses a randomized algorithm to approximate ## the 1-norms. ## ## @code{condest} returns the 1-norm condition estimate @var{est} and ## a vector @var{v} satisfying @code{norm (A*v, 1) == norm (A, 1) * norm ## (@var{v}, 1) / @var{est}}. When @var{est} is large, @var{v} is an ## approximate null vector. ## ## References: ## @itemize ## @item ## N.J. Higham and F. Tisseur, @cite{A Block Algorithm ## for Matrix 1-Norm Estimation, with an Application to 1-Norm ## Pseudospectra}. SIMAX vol 21, no 4, pp 1185-1201. ## @url{http://dx.doi.org/10.1137/S0895479899356080} ## ## @item ## N.J. Higham and F. Tisseur, @cite{A Block Algorithm ## for Matrix 1-Norm Estimation, with an Application to 1-Norm ## Pseudospectra}. @url{http://citeseer.ist.psu.edu/223007.html} ## @end itemize ## ## @seealso{cond, norm, onenormest} ## @end deftypefn ## Code originally licensed under ## ## Copyright (c) 2007, Regents of the University of California ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions ## are met: ## ## * Redistributions of source code must retain the above copyright ## notice, this list of conditions and the following disclaimer. ## ## * Redistributions in binary form must reproduce the above ## copyright notice, this list of conditions and the following ## disclaimer in the documentation and/or other materials provided ## with the distribution. ## ## * Neither the name of the University of California, Berkeley nor ## the names of its contributors may be used to endorse or promote ## products derived from this software without specific prior ## written permission. ## ## THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED ## TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A ## PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS AND ## CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, ## SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT ## LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF ## USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ## ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT ## OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF ## SUCH DAMAGE. ## Author: Jason Riedy <ejr@cs.berkeley.edu> ## Keywords: linear-algebra norm estimation ## Version: 0.2 function [est, v] = condest (varargin) if (nargin < 1 || nargin > 6) print_usage (); endif default_t = 5; have_A = false; have_t = false; have_solve = false; if (ismatrix (varargin{1})) A = varargin{1}; if (! issquare (A)) error ("condest: matrix must be square"); endif n = rows (A); have_A = true; if (nargin > 1) if (isscalar (varargin{2})) t = varargin{2}; have_t = true; elseif (nargin > 2) solve = varargin{2}; solve_t = varargin{3}; have_solve = true; if (nargin > 3) t = varargin{4}; have_t = true; endif else error ("condest: must supply both SOLVE and SOLVE_T"); endif endif elseif (nargin > 4) apply = varargin{1}; apply_t = varargin{2}; solve = varargin{3}; solve_t = varargin{4}; have_solve = true; n = varargin{5}; if (! isscalar (n)) error ("condest: dimension argument of implicit form must be scalar"); endif if (nargin > 5) t = varargin{6}; have_t = true; endif else error ("condest: implicit form of condest requires at least 5 arguments"); endif if (! have_t) t = min (n, default_t); endif if (! have_solve) if (issparse (A)) [L, U, P, Pc] = lu (A); solve = @(x) Pc' * (U \ (L \ (P * x))); solve_t = @(x) P' * (L' \ (U' \ (Pc * x))); else [L, U, P] = lu (A); solve = @(x) U \ (L \ (P*x)); solve_t = @(x) P' * (L' \ (U' \ x)); endif endif if (have_A) Anorm = norm (A, 1); else Anorm = onenormest (apply, apply_t, n, t); endif [Ainv_norm, v, w] = onenormest (solve, solve_t, n, t); est = Anorm * Ainv_norm; v = w / norm (w, 1); endfunction %!demo %! N = 100; %! A = randn (N) + eye (N); %! condest (A) %! [L,U,P] = lu (A); %! condest (A, @(x) U \ (L \ (P*x)), @(x) P'*(L' \ (U'\x))) %! condest (@(x) A*x, @(x) A'*x, @(x) U \ (L \ (P*x)), @(x) P'*(L' \ (U'\x)), N) %! norm (inv (A), 1) * norm (A, 1) ## Yes, these test bounds are really loose. There's ## enough randomization to trigger odd cases with hilb(). %!test %! N = 6; %! A = hilb (N); %! cA = condest (A); %! cA_test = norm (inv (A), 1) * norm (A, 1); %! assert (cA, cA_test, -2^-8); %!test %! N = 6; %! A = hilb (N); %! solve = @(x) A\x; solve_t = @(x) A'\x; %! cA = condest (A, solve, solve_t); %! cA_test = norm (inv (A), 1) * norm (A, 1); %! assert (cA, cA_test, -2^-8); %!test %! N = 6; %! A = hilb (N); %! apply = @(x) A*x; apply_t = @(x) A'*x; %! solve = @(x) A\x; solve_t = @(x) A'\x; %! cA = condest (apply, apply_t, solve, solve_t, N); %! cA_test = norm (inv (A), 1) * norm (A, 1); %! assert (cA, cA_test, -2^-6); %!test %! N = 12; %! A = hilb (N); %! [rcondA, v] = condest (A); %! x = A*v; %! assert (norm (x, inf), 0, eps);