Mercurial > hg > octave-nkf
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,
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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,
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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,
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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,
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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 | d00900b3dc4b |
rev | line source |
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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 |
5610 | 3 ## |
7016 | 4 ## This file is part of Octave. |
5610 | 5 ## |
7016 | 6 ## Octave is free software; you can redistribute it and/or modify it |
7 ## under the terms of the GNU General Public License as published by | |
8 ## the Free Software Foundation; either version 3 of the License, or (at | |
9 ## your option) any later version. | |
10 ## | |
11 ## Octave is distributed in the hope that it will be useful, but | |
12 ## WITHOUT ANY WARRANTY; without even the implied warranty of | |
13 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
14 ## General Public License for more details. | |
5610 | 15 ## |
16 ## You should have received a copy of the GNU General Public License | |
7016 | 17 ## along with Octave; see the file COPYING. If not, see |
18 ## <http://www.gnu.org/licenses/>. | |
5610 | 19 |
20 ## -*- texinfo -*- | |
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21 ## @deftypefn {Function File} {} sprandsym (@var{n}, @var{d}) |
5610 | 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 |
5610 | 24 ## @var{n} by @var{n}, with a density of values given by @var{d}. |
25 ## @var{d} should be between 0 and 1. Values will be normally | |
26 ## distributed with mean of zero and variance 1. | |
27 ## | |
28 ## If called with a single matrix argument, a random sparse matrix is | |
29 ## generated wherever the matrix @var{S} is non-zero in its lower | |
30 ## triangular part. | |
5642 | 31 ## @seealso{sprand, sprandn} |
5610 | 32 ## @end deftypefn |
33 | |
6252 | 34 function S = sprandsym (n, d) |
8506 | 35 |
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36 if (nargin != 1 && nargin != 2) |
6046 | 37 print_usage (); |
5610 | 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 |
5610 | 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 |