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annotate scripts/linear-algebra/cond.m @ 14363:f3d52523cde1
Use Octave coding conventions in all m-file %!test blocks
* wavread.m, acosd.m, acot.m, acotd.m, acoth.m, acsc.m, acscd.m, acsch.m,
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,
issymmetric.m, logm.m, normest.m, null.m, onenormest.m, orth.m, planerot.m,
qzhess.m, rank.m, rref.m, trace.m, vech.m, ans.m, bincoeff.m, bug_report.m,
bzip2.m, comma.m, compare_versions.m, computer.m, edit.m, fileparts.m,
fullfile.m, getfield.m, gzip.m, info.m, inputname.m, isappdata.m, isdeployed.m,
ismac.m, ispc.m, isunix.m, list_primes.m, ls.m, mexext.m, namelengthmax.m,
news.m, orderfields.m, paren.m, recycle.m, rmappdata.m, semicolon.m,
setappdata.m, setfield.m, substruct.m, symvar.m, ver.m, version.m,
warning_ids.m, xor.m, fminbnd.m, fsolve.m, fzero.m, lsqnonneg.m, optimset.m,
pqpnonneg.m, sqp.m, matlabroot.m, __gnuplot_drawnow__.m,
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colstyle.m, comet3.m, contourc.m, figure.m, gca.m, gcbf.m, gcbo.m, gcf.m,
ginput.m, graphics_toolkit.m, gtext.m, hggroup.m, hist.m, hold.m, isfigure.m,
ishghandle.m, ishold.m, isocolors.m, isonormals.m, isosurface.m, isprop.m,
legend.m, line.m, loglog.m, loglogerr.m, meshgrid.m, ndgrid.m, newplot.m,
orient.m, patch.m, plot3.m, plotyy.m, __print_parse_opts__.m, quiver3.m,
refreshdata.m, ribbon.m, semilogx.m, semilogxerr.m, semilogy.m, stem.m,
stem3.m, subplot.m, title.m, uigetfile.m, view.m, whitebg.m, compan.m, conv.m,
deconv.m, mkpp.m, mpoles.m, pchip.m, poly.m, polyaffine.m, polyder.m,
polyfit.m, polygcd.m, polyint.m, polyout.m, polyval.m, polyvalm.m, ppder.m,
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ismember.m, powerset.m, setdiff.m, setxor.m, union.m, unique.m,
autoreg_matrix.m, bartlett.m, blackman.m, detrend.m, fftconv.m, fftfilt.m,
fftshift.m, freqz.m, hamming.m, hanning.m, ifftshift.m, sinc.m, sinetone.m,
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pcr.m, spaugment.m, spconvert.m, spdiags.m, speye.m, spfun.m, spones.m,
sprand.m, sprandsym.m, spstats.m, spy.m, svds.m, treelayout.m, bessel.m,
beta.m, betaln.m, factor.m, factorial.m, isprime.m, lcm.m, legendre.m,
nchoosek.m, nthroot.m, perms.m, pow2.m, primes.m, reallog.m, realpow.m,
realsqrt.m, hadamard.m, hankel.m, hilb.m, invhilb.m, magic.m, rosser.m,
vander.m, __finish__.m, center.m, cloglog.m, corr.m, cov.m, gls.m, histc.m,
iqr.m, kendall.m, kurtosis.m, logit.m, mahalanobis.m, mean.m, meansq.m,
median.m, mode.m, moment.m, ols.m, ppplot.m, prctile.m, probit.m, quantile.m,
range.m, ranks.m, run_count.m, runlength.m, skewness.m, spearman.m,
statistics.m, std.m, table.m, var.m, zscore.m, betacdf.m, betainv.m, betapdf.m,
betarnd.m, binocdf.m, binoinv.m, binopdf.m, binornd.m, cauchy_cdf.m,
cauchy_inv.m, cauchy_pdf.m, cauchy_rnd.m, chi2cdf.m, chi2inv.m, chi2pdf.m,
chi2rnd.m, discrete_cdf.m, discrete_inv.m, discrete_pdf.m, discrete_rnd.m,
empirical_cdf.m, empirical_inv.m, empirical_pdf.m, empirical_rnd.m, expcdf.m,
expinv.m, exppdf.m, exprnd.m, fcdf.m, finv.m, fpdf.m, frnd.m, gamcdf.m,
gaminv.m, gampdf.m, gamrnd.m, geocdf.m, geoinv.m, geopdf.m, geornd.m,
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,
logistic_inv.m, logistic_pdf.m, logistic_rnd.m, logncdf.m, logninv.m,
lognpdf.m, lognrnd.m, nbincdf.m, nbininv.m, nbinpdf.m, nbinrnd.m, normcdf.m,
norminv.m, normpdf.m, normrnd.m, poisscdf.m, poissinv.m, poisspdf.m,
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> |
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date | Mon, 13 Feb 2012 07:29:44 -0800 |
parents | 72c96de7a403 |
children | 9f50dd7ece60 |
rev | line source |
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1 ## Copyright (C) 1993-2012 John W. Eaton |
2313 | 2 ## |
3 ## This file is part of Octave. | |
4 ## | |
5 ## Octave is free software; you can redistribute it and/or modify it | |
6 ## under the terms of the GNU General Public License as published by | |
7016 | 7 ## the Free Software Foundation; either version 3 of the License, or (at |
8 ## your option) any later version. | |
2313 | 9 ## |
10 ## Octave is distributed in the hope that it will be useful, but | |
11 ## WITHOUT ANY WARRANTY; without even the implied warranty of | |
12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
13 ## General Public License for more details. | |
14 ## | |
15 ## You should have received a copy of the GNU General Public License | |
7016 | 16 ## along with Octave; see the file COPYING. If not, see |
17 ## <http://www.gnu.org/licenses/>. | |
245 | 18 |
3372 | 19 ## -*- texinfo -*- |
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20 ## @deftypefn {Function File} {} cond (@var{A}) |
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21 ## @deftypefnx {Function File} {} cond (@var{A}, @var{p}) |
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22 ## Compute the @var{p}-norm condition number of a matrix. |
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23 ## |
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24 ## @code{cond (@var{A})} is ## defined as |
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25 ## @tex |
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26 ## $ {\parallel A \parallel_p * \parallel A^{-1} \parallel_p .} $ |
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27 ## @end tex |
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28 ## @ifnottex |
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29 ## @code{norm (@var{A}, @var{p}) * norm (inv (@var{A}), @var{p})}. |
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30 ## @end ifnottex |
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31 ## |
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32 ## By default @code{@var{p} = 2} is used which implies a (relatively slow) |
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33 ## singular value decomposition. Other possible selections are |
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34 ## @code{@var{p} = 1, Inf, "fro"} which are generally faster. See |
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35 ## @code{norm} for a full discussion of possible @var{p} values. |
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36 ## @seealso{condest, rcond, norm, svd} |
3372 | 37 ## @end deftypefn |
4 | 38 |
2314 | 39 ## Author: jwe |
40 | |
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41 function retval = cond (A, p) |
4 | 42 |
7484 | 43 if (nargin && nargin < 3) |
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44 if (ndims (A) > 2) |
8664 | 45 error ("cond: only valid on 2-D objects"); |
7484 | 46 endif |
47 | |
48 if (nargin <2) | |
49 p = 2; | |
4890 | 50 endif |
51 | |
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52 if (! ischar (p) && p == 2) |
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53 [nr, nc] = size (A); |
7484 | 54 if (nr == 0 || nc == 0) |
55 retval = 0.0; | |
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56 elseif (any (any (isinf (A) | isnan (A)))) |
7484 | 57 error ("cond: argument must not contain Inf or NaN values"); |
58 else | |
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59 sigma = svd (A); |
7484 | 60 sigma_1 = sigma(1); |
61 sigma_n = sigma(end); | |
62 if (sigma_1 == 0 || sigma_n == 0) | |
63 retval = Inf; | |
64 else | |
65 retval = sigma_1 / sigma_n; | |
66 endif | |
67 endif | |
3250 | 68 else |
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69 retval = norm (A, p) * norm (inv (A), p); |
3250 | 70 endif |
4 | 71 else |
6046 | 72 print_usage (); |
4 | 73 endif |
74 | |
75 endfunction | |
7411 | 76 |
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77 |
7484 | 78 %!test |
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79 %! y = [7, 2, 3; 1, 3, 4; 6, 4, 5]; |
7484 | 80 %! tol = 1e-6; |
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81 %! type = {1, 2, "fro", "inf", inf}; |
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82 %! for n = 1:numel (type) |
7484 | 83 %! rcondition(n) = 1 / cond (y, type{n}); |
84 %! endfor | |
85 %! assert (rcondition, [0.017460, 0.019597, 0.018714, 0.012022, 0.012022], tol); | |
7411 | 86 |
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87 %!assert (cond ([1, 2; 2, 1]), 3, sqrt (eps)) |
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88 %!assert (cond ([1, 2, 3; 4, 5, 6; 7, 8, 9]) > 1.0e+16) |
7411 | 89 |
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90 %!error cond () |
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91 %!error cond (1, 2, 3) |
7411 | 92 |