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view scripts/sparse/svds.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,
__plt_get_axis_arg__.m, ancestor.m, cla.m, clf.m, close.m, colorbar.m,
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,
ppint.m, ppjumps.m, ppval.m, residue.m, roots.m, spline.m, intersect.m,
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,
sinewave.m, unwrap.m, bicg.m, bicgstab.m, gmres.m, gplot.m, nonzeros.m, pcg.m,
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> |
---|---|
date | Mon, 13 Feb 2012 07:29:44 -0800 |
parents | 4d917a6a858b |
children | 5d3a684236b0 |
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## Copyright (C) 2006-2012 David Bateman ## ## 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} {@var{s} =} svds (@var{A}) ## @deftypefnx {Function File} {@var{s} =} svds (@var{A}, @var{k}) ## @deftypefnx {Function File} {@var{s} =} svds (@var{A}, @var{k}, @var{sigma}) ## @deftypefnx {Function File} {@var{s} =} svds (@var{A}, @var{k}, @var{sigma}, @var{opts}) ## @deftypefnx {Function File} {[@var{u}, @var{s}, @var{v}] =} svds (@dots{}) ## @deftypefnx {Function File} {[@var{u}, @var{s}, @var{v}, @var{flag}] =} svds (@dots{}) ## ## Find a few singular values of the matrix @var{A}. The singular values ## are calculated using ## ## @example ## @group ## [@var{m}, @var{n}] = size (@var{A}); ## @var{s} = eigs ([sparse(@var{m}, @var{m}), @var{A}; ## @var{A}', sparse(@var{n}, @var{n})]) ## @end group ## @end example ## ## The eigenvalues returned by @code{eigs} correspond to the singular values ## of @var{A}. The number of singular values to calculate is given by @var{k} ## and defaults to 6. ## ## The argument @var{sigma} specifies which singular values to find. When ## @var{sigma} is the string 'L', the default, the largest singular values of ## @var{A} are found. Otherwise, @var{sigma} must be a real scalar and the ## singular values closest to @var{sigma} are found. As a corollary, ## @code{@var{sigma} = 0} finds the smallest singular values. Note that for ## relatively small values of @var{sigma}, there is a chance that the requested ## number of singular values will not be found. In that case @var{sigma} ## should be increased. ## ## @var{opts} is a structure defining options that @code{svds} will pass ## to @code{eigs}. The possible fields of this structure are documented in ## @code{eigs}. By default, @code{svds} sets the following three fields: ## ## @table @code ## @item tol ## The required convergence tolerance for the singular values. The default ## value is 1e-10. @code{eigs} is passed @code{@var{tol} / sqrt(2)}. ## ## @item maxit ## The maximum number of iterations. The default is 300. ## ## @item disp ## The level of diagnostic printout (0|1|2). If @code{disp} is 0 then ## diagnostics are disabled. The default value is 0. ## @end table ## ## If more than one output is requested then @code{svds} will return an ## approximation of the singular value decomposition of @var{A} ## ## @example ## @var{A}_approx = @var{u}*@var{s}*@var{v}' ## @end example ## ## @noindent ## where @var{A}_approx is a matrix of size @var{A} but only rank @var{k}. ## ## @var{flag} returns 0 if the algorithm has succesfully converged, and 1 ## otherwise. The test for convergence is ## ## @example ## @group ## norm (@var{A}*@var{v} - @var{u}*@var{s}, 1) <= @var{tol} * norm (@var{A}, 1) ## @end group ## @end example ## ## @code{svds} is best for finding only a few singular values from a large ## sparse matrix. Otherwise, @code{svd (full(@var{A}))} will likely be more ## efficient. ## @end deftypefn ## @seealso{svd, eigs} function [u, s, v, flag] = svds (A, k, sigma, opts) persistent root2 = sqrt (2); if (nargin < 1 || nargin > 4) print_usage (); endif if (ndims(A) > 2) error ("svds: A must be a 2D matrix"); endif if (nargin < 4) opts.tol = 1e-10 / root2; opts.disp = 0; opts.maxit = 300; else if (!isstruct (opts)) error ("svds: OPTS must be a structure"); endif if (!isfield (opts, "tol")) opts.tol = 1e-10 / root2; else opts.tol = opts.tol / root2; endif if (isfield (opts, "v0")) if (!isvector (opts.v0) || (length (opts.v0) != sum (size (A)))) error ("svds: OPTS.v0 must be a vector with rows(A)+columns(A) entries"); endif endif endif if (nargin < 3 || strcmp (sigma, "L")) if (isreal (A)) sigma = "LA"; else sigma = "LR"; endif elseif (isscalar (sigma) && isnumeric (sigma) && isreal (sigma)) if (sigma < 0) error ("svds: SIGMA must be a positive real value"); endif else error ("svds: SIGMA must be a positive real value or the string 'L'"); endif [m, n] = size (A); max_a = max (abs (A(:))); if (max_a == 0) s = zeros (k, 1); # special case of zero matrix else if (nargin < 2) k = min ([6, m, n]); else k = min ([k, m, n]); endif ## Scale everything by the 1-norm to make things more stable. b = A / max_a; b_opts = opts; ## Call to eigs is always a symmetric matrix by construction b_opts.issym = true; b_opts.tol = opts.tol / max_a; b_sigma = sigma; if (!ischar (b_sigma)) b_sigma = b_sigma / max_a; endif if (b_sigma == 0) ## Find the smallest eigenvalues ## The eigenvalues returns by eigs for sigma=0 are symmetric about 0. ## As we are only interested in the positive eigenvalues, we have to ## double k and then throw out the k negative eigenvalues. ## Separately, if sigma is non-zero, but smaller than the smallest ## singular value, ARPACK may not return k eigenvalues. However, as ## computation scales with k we'd like to avoid doubling k for all ## scalar values of sigma. b_k = 2 * k; else b_k = k; # Normal case, find just the k largest eigenvalues endif if (nargout > 1) [V, s, flag] = eigs ([sparse(m,m), b; b', sparse(n,n)], b_k, b_sigma, b_opts); s = diag (s); else s = eigs ([sparse(m,m), b; b', sparse(n,n)], b_k, b_sigma, b_opts); endif if (ischar (sigma)) norma = max (s); else norma = normest (A); endif ## We wish to exclude all eigenvalues that are less than zero as these ## are artifacts of the way the matrix passed to eigs is formed. There ## is also the possibility that the value of sigma chosen is exactly ## a singular value, and in that case we're dead!! So have to rely on ## the warning from eigs. We exclude the singular values which are ## less than or equal to zero to within some tolerance scaled by the ## norm since if we don't we might end up with too many singular ## values. tol = norma * opts.tol; ind = find(s > tol); if (length (ind) < k) ## Too few eigenvalues returned. Add in any zero eigenvalues of B, ## including the nominally negative ones. zind = find (abs (s) <= tol); p = min (length (zind), k - length (ind)); ind = [ind; zind(1:p)]; elseif (length (ind) > k) ## Too many eigenvalues returned. Select according to criterium. if (b_sigma == 0) ind = ind(end+1-k:end); # smallest eigenvalues else ind = ind(1:k); # largest eigenvalues endif endif s = s(ind); if (length (s) < k) warning ("returning fewer singular values than requested"); if (!ischar (sigma)) warning ("try increasing the value of sigma"); endif endif s = s * max_a; endif if (nargout < 2) u = s; else if (max_a == 0) u = eye (m, k); s = diag (s); v = eye (n, k); else u = root2 * V(1:m,ind); s = diag (s); v = root2 * V(m+1:end,ind); endif if (nargout > 3) flag = norm (A*v - u*s, 1) > root2 * opts.tol * norm (A, 1); endif endif endfunction %!shared n, k, A, u, s, v, opts, rand_state, randn_state %! n = 100; %! k = 7; %! A = sparse ([3:n,1:n,1:(n-2)],[1:(n-2),1:n,3:n],[ones(1,n-2),0.4*n*ones(1,n),ones(1,n-2)]); %! [u,s,v] = svd (full (A)); %! s = diag (s); %! [~, idx] = sort (abs(s)); %! s = s(idx); %! u = u(:, idx); %! v = v(:, idx); %! randn_state = randn ("state"); %! rand_state = rand ("state"); %! randn ("state", 42); % Initialize to make normest function reproducible %! rand ("state", 42); %! opts.v0 = rand (2*n,1); % Initialize eigs ARPACK starting vector %! % to guarantee reproducible results %! %!testif HAVE_ARPACK %! [u2,s2,v2,flag] = svds (A,k); %! s2 = diag (s2); %! assert (flag, !1); %! assert (s2, s(end:-1:end-k+1), 1e-10); %! %!testif HAVE_ARPACK, HAVE_UMFPACK %! [u2,s2,v2,flag] = svds (A,k,0,opts); %! s2 = diag (s2); %! assert (flag, !1); %! assert (s2, s(k:-1:1), 1e-10); %! %!testif HAVE_ARPACK, HAVE_UMFPACK %! idx = floor(n/2); %! % Don't put sigma right on a singular value or there are convergence issues %! sigma = 0.99*s(idx) + 0.01*s(idx+1); %! [u2,s2,v2,flag] = svds (A,k,sigma,opts); %! s2 = diag (s2); %! assert (flag, !1); %! assert (s2, s((idx+floor(k/2)):-1:(idx-floor(k/2))), 1e-10); %! %!testif HAVE_ARPACK %! [u2,s2,v2,flag] = svds (zeros (10), k); %! assert (u2, eye (10, k)); %! assert (s2, zeros (k)); %! assert (v2, eye (10, 7)); %! %!testif HAVE_ARPACK %! s = svds (speye (10)); %! assert (s, ones (6, 1), 2*eps); %!test %! ## Restore random number generator seeds at end of tests %! rand ("state", rand_state); %! randn ("state", randn_state);