annotate scripts/optimization/lsqnonneg.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 b76f0740940e
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rev   line source
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72c96de7a403 maint: update copyright notices for 2012
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1 ## Copyright (C) 2008-2012 Bill Denney
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2 ## Copyright (C) 2008 Jaroslav Hajek
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3 ## Copyright (C) 2009 VZLU Prague
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4 ##
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5 ## This file is part of Octave.
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6 ##
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7 ## Octave is free software; you can redistribute it and/or modify it
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8 ## under the terms of the GNU General Public License as published by
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9 ## the Free Software Foundation; either version 3 of the License, or (at
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10 ## your option) any later version.
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11 ##
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12 ## Octave is distributed in the hope that it will be useful, but
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13 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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14 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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15 ## General Public License for more details.
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16 ##
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17 ## You should have received a copy of the GNU General Public License
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18 ## along with Octave; see the file COPYING. If not, see
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19 ## <http://www.gnu.org/licenses/>.
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20
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21 ## -*- texinfo -*-
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22 ## @deftypefn {Function File} {@var{x} =} lsqnonneg (@var{c}, @var{d})
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23 ## @deftypefnx {Function File} {@var{x} =} lsqnonneg (@var{c}, @var{d}, @var{x0})
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24 ## @deftypefnx {Function File} {[@var{x}, @var{resnorm}] =} lsqnonneg (@dots{})
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25 ## @deftypefnx {Function File} {[@var{x}, @var{resnorm}, @var{residual}] =} lsqnonneg (@dots{})
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26 ## @deftypefnx {Function File} {[@var{x}, @var{resnorm}, @var{residual}, @var{exitflag}] =} lsqnonneg (@dots{})
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27 ## @deftypefnx {Function File} {[@var{x}, @var{resnorm}, @var{residual}, @var{exitflag}, @var{output}] =} lsqnonneg (@dots{})
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28 ## @deftypefnx {Function File} {[@var{x}, @var{resnorm}, @var{residual}, @var{exitflag}, @var{output}, @var{lambda}] =} lsqnonneg (@dots{})
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29 ## Minimize @code{norm (@var{c}*@var{x} - d)} subject to
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30 ## @code{@var{x} >= 0}. @var{c} and @var{d} must be real. @var{x0} is an
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31 ## optional initial guess for @var{x}.
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32 ##
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33 ## Outputs:
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34 ## @itemize @bullet
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35 ## @item resnorm
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36 ##
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37 ## The squared 2-norm of the residual: norm(@var{c}*@var{x}-@var{d})^2
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38 ##
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39 ## @item residual
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40 ##
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41 ## The residual: @var{d}-@var{c}*@var{x}
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42 ##
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43 ## @item exitflag
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44 ##
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45 ## An indicator of convergence. 0 indicates that the iteration count
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46 ## was exceeded, and therefore convergence was not reached; >0 indicates
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47 ## that the algorithm converged. (The algorithm is stable and will
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48 ## converge given enough iterations.)
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49 ##
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50 ## @item output
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51 ##
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52 ## A structure with two fields:
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53 ## @itemize @bullet
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54 ## @item "algorithm": The algorithm used ("nnls")
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55 ##
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56 ## @item "iterations": The number of iterations taken.
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57 ## @end itemize
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58 ##
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59 ## @item lambda
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60 ##
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61 ## Not implemented.
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62 ## @end itemize
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63 ## @seealso{optimset, pqpnonneg}
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64 ## @end deftypefn
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65
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66 ## PKG_ADD: ## Discard result to avoid polluting workspace with ans at startup.
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67 ## PKG_ADD: [~] = __all_opts__ ("lsqnonneg");
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68
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69 ## This is implemented from Lawson and Hanson's 1973 algorithm on page
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70 ## 161 of Solving Least Squares Problems.
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71
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72 function [x, resnorm, residual, exitflag, output, lambda] = lsqnonneg (c, d, x = [], options = struct ())
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73
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74 if (nargin == 1 && ischar (c) && strcmp (c, 'defaults'))
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75 x = optimset ("MaxIter", 1e5);
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76 return
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77 endif
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78
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79 if (! (nargin >= 2 && nargin <= 4 && ismatrix (c) && ismatrix (d) && isstruct (options)))
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80 print_usage ();
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81 endif
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82
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83 ## Lawson-Hanson Step 1 (LH1): initialize the variables.
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84 m = rows (c);
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85 n = columns (c);
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86 if (isempty (x))
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87 ## Initial guess is 0s.
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88 x = zeros (n, 1);
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89 else
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90 ## ensure nonnegative guess.
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91 x = max (x, 0);
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92 endif
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93
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94 useqr = m >= n;
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95 max_iter = optimget (options, "MaxIter", 1e5);
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96
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97 ## Initialize P, according to zero pattern of x.
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98 p = find (x > 0).';
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99 if (useqr)
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100 ## Initialize the QR factorization, economized form.
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101 [q, r] = qr (c(:,p), 0);
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102 endif
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103
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104 iter = 0;
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105
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106 ## LH3: test for completion.
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107 while (iter < max_iter)
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108 while (iter < max_iter)
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109 iter++;
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110
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111 ## LH6: compute the positive matrix and find the min norm solution
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112 ## of the positive problem.
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113 if (useqr)
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114 xtmp = r \ q'*d;
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115 else
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116 xtmp = c(:,p) \ d;
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117 endif
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118 idx = find (xtmp < 0);
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119
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120 if (isempty (idx))
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121 ## LH7: tmp solution found, iterate.
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122 x(:) = 0;
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123 x(p) = xtmp;
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124 break;
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125 else
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126 ## LH8, LH9: find the scaling factor.
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127 pidx = p(idx);
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128 sf = x(pidx)./(x(pidx) - xtmp(idx));
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129 alpha = min (sf);
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130 ## LH10: adjust X.
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131 xx = zeros (n, 1);
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132 xx(p) = xtmp;
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133 x += alpha*(xx - x);
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134 ## LH11: move from P to Z all X == 0.
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135 ## This corresponds to those indices where minimum of sf is attained.
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136 idx = idx (sf == alpha);
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137 p(idx) = [];
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138 if (useqr)
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139 ## update the QR factorization.
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140 [q, r] = qrdelete (q, r, idx);
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141 endif
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142 endif
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143 endwhile
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144
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145 ## compute the gradient.
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146 w = c'*(d - c*x);
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147 w(p) = [];
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148 if (! any (w > 0))
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149 if (useqr)
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150 ## verify the solution achieved using qr updating.
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151 ## in the best case, this should only take a single step.
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152 useqr = false;
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153 continue;
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154 else
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155 ## we're finished.
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156 break;
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157 endif
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158 endif
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159
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160 ## find the maximum gradient.
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161 idx = find (w == max (w));
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162 if (numel (idx) > 1)
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163 warning ("lsqnonneg:nonunique",
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164 "a non-unique solution may be returned due to equal gradients");
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165 idx = idx(1);
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166 endif
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167 ## move the index from Z to P. Keep P sorted.
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168 z = [1:n]; z(p) = [];
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169 zidx = z(idx);
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170 jdx = 1 + lookup (p, zidx);
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171 p = [p(1:jdx-1), zidx, p(jdx:end)];
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172 if (useqr)
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173 ## insert the column into the QR factorization.
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174 [q, r] = qrinsert (q, r, jdx, c(:,zidx));
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175 endif
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176
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177 endwhile
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178 ## LH12: complete.
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179
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180 ## Generate the additional output arguments.
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181 if (nargout > 1)
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182 resnorm = norm (c*x - d) ^ 2;
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183 endif
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184 if (nargout > 2)
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185 residual = d - c*x;
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186 endif
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187 exitflag = iter;
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188 if (nargout > 3 && iter >= max_iter)
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189 exitflag = 0;
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190 endif
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191 if (nargout > 4)
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192 output = struct ("algorithm", "nnls", "iterations", iter);
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193 endif
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194 if (nargout > 5)
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195 lambda = zeros (size (x));
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196 lambda(p) = w;
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197 endif
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198
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199 endfunction
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200
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201
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202 %!test
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203 %! C = [1 0;0 1;2 1];
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204 %! d = [1;3;-2];
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205 %! assert (lsqnonneg (C, d), [0;0.5], 100*eps);
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206
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207 %!test
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208 %! C = [0.0372 0.2869;0.6861 0.7071;0.6233 0.6245;0.6344 0.6170];
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209 %! d = [0.8587;0.1781;0.0747;0.8405];
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210 %! xnew = [0;0.6929];
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211 %! assert (lsqnonneg (C, d), xnew, 0.0001);
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212