annotate scripts/sparse/sprandsym.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 72c96de7a403
children d00900b3dc4b
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72c96de7a403 maint: update copyright notices for 2012
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1 ## Copyright (C) 2004-2012 David Bateman and Andy Adler
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2 ## Copyright (C) 2012 Jordi Gutiérrez Hermoso
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3 ##
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4 ## This file is part of Octave.
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5 ##
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6 ## Octave is free software; you can redistribute it and/or modify it
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7 ## under the terms of the GNU General Public License as published by
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8 ## the Free Software Foundation; either version 3 of the License, or (at
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9 ## your option) any later version.
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10 ##
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11 ## Octave is distributed in the hope that it will be useful, but
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12 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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13 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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14 ## General Public License for more details.
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15 ##
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16 ## You should have received a copy of the GNU General Public License
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17 ## along with Octave; see the file COPYING. If not, see
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18 ## <http://www.gnu.org/licenses/>.
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19
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20 ## -*- texinfo -*-
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21 ## @deftypefn {Function File} {} sprandsym (@var{n}, @var{d})
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22 ## @deftypefnx {Function File} {} sprandsym (@var{s})
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23 ## Generate a symmetric random sparse matrix. The size of the matrix will be
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24 ## @var{n} by @var{n}, with a density of values given by @var{d}.
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25 ## @var{d} should be between 0 and 1. Values will be normally
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26 ## distributed with mean of zero and variance 1.
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27 ##
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28 ## If called with a single matrix argument, a random sparse matrix is
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29 ## generated wherever the matrix @var{S} is non-zero in its lower
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30 ## triangular part.
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31 ## @seealso{sprand, sprandn}
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32 ## @end deftypefn
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33
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34 function S = sprandsym (n, d)
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35
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36 if (nargin != 1 && nargin != 2)
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37 print_usage ();
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38 endif
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39
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40 if (nargin == 1)
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41 [i, j] = find (tril (n));
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42 [nr, nc] = size (n);
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43 S = sparse (i, j, randn (size (i)), nr, nc);
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44 S = S + tril (S, -1)';
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45 return;
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46 endif
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47
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48 if (!(isscalar (n) && n == fix (n) && n > 0))
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49 error ("sprandsym: N must be an integer greater than 0");
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50 endif
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51
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52 if (d < 0 || d > 1)
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53 error ("sprandsym: density D must be between 0 and 1");
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54 endif
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55
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56 ## Actual number of nonzero entries
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57 k = round (n^2*d);
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58
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59 ## Diagonal nonzero entries, same parity as k
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60 r = pick_rand_diag (n, k);
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61
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62 ## Off diagonal nonzero entries
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63 m = (k - r)/2;
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64
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65 ondiag = randperm (n, r);
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66 offdiag = randperm (n*(n - 1)/2, m);
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67
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68 ## Row index
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69 i = lookup (cumsum (0:n), offdiag - 1) + 1;
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70
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71 ## Column index
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72 j = offdiag - (i - 1).*(i - 2)/2;
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73
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74 diagvals = randn (1, r);
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75 offdiagvals = randn (1, m);
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76
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77 S = sparse ([ondiag, i, j], [ondiag, j, i],
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78 [diagvals, offdiagvals, offdiagvals], n, n);
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79
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80 endfunction
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81
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82 function r = pick_rand_diag (n, k)
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83 ## Pick a random number R of entries for the diagonal of a sparse NxN
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84 ## symmetric square matrix with exactly K nonzero entries, ensuring
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85 ## that this R is chosen uniformly over all such matrices.
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86 ##
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87 ## Let D be the number of diagonal entries and M the number of
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88 ## off-diagonal entries. Then K = D + 2*M. Let A = N*(N-1)/2 be the
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89 ## number of available entries in the upper triangle of the matrix.
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90 ## Then, by a simple counting argument, there is a total of
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91 ##
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92 ## T = nchoosek (N, D) * nchoosek (A, M)
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93 ##
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94 ## symmetric NxN matrices with a total of K nonzero entries and D on
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95 ## the diagonal. Letting D range from mod (K,2) through min (N,K), and
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96 ## dividing by this sum, we obtain the probability P for D to be each
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97 ## of those values.
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98 ##
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99 ## However, we cannot use this form for computation, as the binomial
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100 ## coefficients become unmanageably large. Instead, we use the
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101 ## successive quotients Q(i) = T(i+1)/T(i), which we easily compute to
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102 ## be
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103 ##
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104 ## (N - D)*(N - D - 1)*M
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105 ## Q = -------------------------------
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106 ## (D + 2)*(D + 1)*(A - M + 1)
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107 ##
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108 ## Then, after prepending 1, the cumprod of these quotients is
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109 ##
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110 ## C = [ T(1)/T(1), T(2)/T(1), T(3)/T(1), ..., T(N)/T(1) ]
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111 ##
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112 ## Their sum is thus S = sum (T)/T(1), and then C(i)/S is the desired
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113 ## probability P(i) for i=1:N. The cumsum will finally give the
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114 ## distribution function for computing the random number of entries on
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115 ## the diagonal R.
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116 ##
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117 ## Thanks to Zsbán Ambrus <ambrus@math.bme.hu> for most of the ideas
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118 ## of the implementation here, especially how to do the computation
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119 ## numerically to avoid overflow.
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120
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121 ## Degenerate case
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122 if k == 1
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123 r = 1;
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124 return
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125 endif
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126
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127 ## Compute the stuff described above
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128 a = n*(n - 1)/2;
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129 d = [mod(k,2):2:min(n,k)-2];
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130 m = (k - d)/2;
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131 q = (n - d).*(n - d - 1).*m ./ (d + 2)./(d + 1)./(a - m + 1);
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132
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133 ## Slight modification from discussion above: pivot around the max in
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134 ## order to avoid overflow (underflow is fine, just means effectively
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135 ## zero probabilities).
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136 [~, midx] = max (cumsum (log (q))) ;
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137 midx++;
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138 lc = fliplr (cumprod (1./q(midx-1:-1:1)));
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139 rc = cumprod (q(midx:end));
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140
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141 ## Now c = t(i)/t(midx), so c > 1 == [].
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142 c = [lc, 1, rc];
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143 s = sum (c);
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144 p = c/s;
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145
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146 ## Add final d
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147 d(end+1) = d(end) + 2;
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148
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149 ## Pick a random r using this distribution
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150 r = d(sum (cumsum (p) < rand) + 1);
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151
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152 endfunction
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153
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154
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155 %!test
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156 %! s = sprandsym (10, 0.1);
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157 %! assert (issparse (s));
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158 %! assert (issymmetric (s));
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159 %! assert (size (s), [10, 10]);
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160 %! assert (nnz (s) / numel (s), 0.1, .01);
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161
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162 %% Test 1-input calling form
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163 %!test
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164 %! s = sprandsym (sparse ([1 2 3], [3 2 3], [2 2 2]));
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165 %! [i, j] = find (s);
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166 %! assert (sort (i), [2 3]');
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167 %! assert (sort (j), [2 3]');
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168
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169 %% Test input validation
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170 %!error sprandsym ()
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171 %!error sprandsym (1, 2, 3)
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172 %!error sprandsym (ones (3), 0.5)
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173 %!error sprandsym (3.5, 0.5)
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174 %!error sprandsym (0, 0.5)
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175 %!error sprandsym (3, -1)
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176 %!error sprandsym (3, 2)
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177