Mercurial > octave
view scripts/linear-algebra/cond.m @ 28886:d8318c12d903
test: remove unnecessary BIST tests in m-files checking for excessive number of inputs.
Remove BIST tests now that interpreter enforces calling function with no more than
the number of arguments defined in the function prototype.
* makeUniqueStrings.m, makeValidName.m, base64decode.m, base64encode.m,
record.m, sound.m, soundsc.m, acosd.m, acot.m, acotd.m, acoth.m, acsc.m,
acscd.m, acsch.m, asec.m, asecd.m, asech.m, asind.m, atan2d.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, accumdim.m, bincoeff.m, bitget.m, bitset.m, cell2mat.m, circshift.m,
cplxpair.m, cumtrapz.m, deg2rad.m, flip.m, fliplr.m, flipud.m, int2str.m,
interpft.m, logspace.m, num2str.m, postpad.m, prepad.m, rad2deg.m, rot90.m,
rotdim.m, shift.m, subsindex.m, trapz.m, rotx.m, roty.m, rotz.m, getappdata.m,
getpixelposition.m, guidata.m, isappdata.m, waitforbuttonpress.m,
__gripe_missing_component__.m, bessel.m, hsv2rgb.m, ind2gray.m, rgb2gray.m,
rgb2hsv.m, rgbplot.m, fileread.m, javachk.m, usejava.m, findstr.m,
genvarname.m, isdir.m, vectorize.m, cond.m, cross.m, duplication_matrix.m,
expm.m, isbanded.m, isdefinite.m, isdiag.m, ishermitian.m, issymmetric.m,
istril.m, istriu.m, trace.m, vech.m, vecnorm.m, cast.m, citation.m,
compare_versions.m, grabcode.m, inputname.m, isfile.m, isfolder.m, ismac.m,
ispc.m, isunix.m, list_primes.m, methods.m, news.m, open.m, run.m, swapbytes.m,
tar.m, verLessThan.m, zip.m, odeget.m, optimget.m, stemleaf.m, allchild.m,
ancestor.m, close.m, groot.m, hgsave.m, isaxes.m, isfigure.m, isgraphics.m,
ishandle.m, isprop.m, linkaxes.m, rotate.m, saveas.m, conv.m, poly.m,
polyint.m, polyreduce.m, ppval.m, roots.m, addpref.m, getpref.m, ispref.m,
rmpref.m, setpref.m, profile.m, profshow.m, powerset.m, autoreg_matrix.m,
bartlett.m, blackman.m, detrend.m, fftconv.m, fftfilt.m, fftshift.m, hamming.m,
hanning.m, ifftshift.m, sinewave.m, spectral_adf.m, spectral_xdf.m, unwrap.m,
nonzeros.m, spconvert.m, sprand.m, sprandn.m, beta.m, betainc.m, betaln.m,
cosint.m, expint.m, factorial.m, legendre.m, nchoosek.m, nthroot.m, perms.m,
pow2.m, primes.m, reallog.m, realpow.m, realsqrt.m, sinint.m, hankel.m, hilb.m,
invhilb.m, magic.m, pascal.m, toeplitz.m, vander.m, wilkinson.m, center.m,
corr.m, cov.m, discrete_cdf.m, discrete_inv.m, discrete_pdf.m, empirical_cdf.m,
empirical_inv.m, empirical_pdf.m, iqr.m, kendall.m, kurtosis.m, mad.m,
meansq.m, median.m, moment.m, prctile.m, quantile.m, range.m, run_count.m,
skewness.m, spearman.m, statistics.m, std.m, var.m, base2dec.m, bin2dec.m,
blanks.m, dec2base.m, dec2bin.m, dec2hex.m, endsWith.m, erase.m, hex2dec.m,
index.m, isletter.m, isstring.m, isstrprop.m, mat2str.m, ostrsplit.m, rindex.m,
startsWith.m, strtrunc.m, substr.m, fail.m, addtodate.m, asctime.m, ctime.m,
date.m, datestr.m, eomday.m, etime.m, is_leap_year.m, now.m:
remove unnecessary BIST tests in m-files checking for excessive number of inputs.
author | Rik <rik@octave.org> |
---|---|
date | Fri, 09 Oct 2020 13:28:53 -0700 |
parents | 28de41192f3c |
children | 6fd6ad758b10 |
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######################################################################## ## ## Copyright (C) 1993-2020 The Octave Project Developers ## ## See the file COPYRIGHT.md in the top-level directory of this ## distribution or <https://octave.org/copyright/>. ## ## 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 ## <https://www.gnu.org/licenses/>. ## ######################################################################## ## -*- texinfo -*- ## @deftypefn {} {} cond (@var{A}) ## @deftypefnx {} {} cond (@var{A}, @var{p}) ## Compute the @var{p}-norm condition number of a matrix with respect to ## inversion. ## ## @code{cond (@var{A})} is defined as ## @tex ## $ {\parallel A \parallel_p * \parallel A^{-1} \parallel_p .} $ ## @end tex ## @ifnottex ## @code{norm (@var{A}, @var{p}) * norm (inv (@var{A}), @var{p})}. ## @end ifnottex ## ## By default, @code{@var{p} = 2} is used which implies a (relatively slow) ## singular value decomposition. Other possible selections are ## @code{@var{p} = 1, Inf, "fro"} which are generally faster. See @code{norm} ## for a full discussion of possible @var{p} values. ## ## The condition number of a matrix quantifies the sensitivity of the matrix ## inversion operation when small changes are made to matrix elements. Ideally ## the condition number will be close to 1. When the number is large this ## indicates small changes (such as underflow or round-off error) will produce ## large changes in the resulting output. In such cases the solution results ## from numerical computing are not likely to be accurate. ## @seealso{condest, rcond, condeig, norm, svd} ## @end deftypefn function retval = cond (A, p = 2) if (nargin < 1) print_usage (); endif if (ndims (A) > 2) error ("cond: A must be a 2-D matrix"); endif if (p == 2) if (isempty (A)) retval = 0.0; elseif (any (! isfinite (A(:)))) error ("cond: A must not contain Inf or NaN values"); else sigma = svd (A); sigma_1 = sigma(1); sigma_n = sigma(end); if (sigma_1 == 0 || sigma_n == 0) retval = Inf; else retval = sigma_1 / sigma_n; endif endif else retval = norm (A, p) * norm (inv (A), p); endif endfunction %!test %! y = [7, 2, 3; 1, 3, 4; 6, 4, 5]; %! tol = 1e-6; %! type = {1, 2, "fro", "inf", inf}; %! for n = 1:numel (type) %! rcondition(n) = 1 / cond (y, type{n}); %! endfor %! assert (rcondition, [0.017460, 0.019597, 0.018714, 0.012022, 0.012022], tol); %!assert (cond ([1, 2; 2, 1]), 3, sqrt (eps)) %!assert (cond ([1, 2, 3; 4, 5, 6; 7, 8, 9]) > 1.0e+16) %!error <Invalid call> cond () %!error <A must be a 2-D matrix> cond (ones (1,3,3)) %!error <A must not contain Inf or NaN value> cond ([1, 2;Inf 4]) %!error <A must not contain Inf or NaN value> cond ([1, 2;NaN 4])