annotate scripts/general/cplxpair.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 11949c9795a0
children 86854d032a37
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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) 2000-2012 Paul Kienzle
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2 ##
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3 ## This file is part of Octave.
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4 ##
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5 ## Octave is free software; you can redistribute it and/or modify it
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6 ## under the terms of the GNU General Public License as published by
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7 ## the Free Software Foundation; either version 3 of the License, or (at
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8 ## your option) any later version.
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9 ##
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10 ## Octave is distributed in the hope that it will be useful, but
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11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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13 ## General Public License for more details.
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14 ##
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15 ## You should have received a copy of the GNU General Public License
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16 ## along with Octave; see the file COPYING. If not, see
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17 ## <http://www.gnu.org/licenses/>.
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18
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19 ## -*- texinfo -*-
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20 ## @deftypefn {Function File} {} cplxpair (@var{z})
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21 ## @deftypefnx {Function File} {} cplxpair (@var{z}, @var{tol})
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22 ## @deftypefnx {Function File} {} cplxpair (@var{z}, @var{tol}, @var{dim})
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23 ## Sort the numbers @var{z} into complex conjugate pairs ordered by
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24 ## increasing real part. Place the negative imaginary complex number
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25 ## first within each pair. Place all the real numbers (those with
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26 ## @code{abs (imag (@var{z}) / @var{z}) < @var{tol})}) after the
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27 ## complex pairs.
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28 ##
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29 ## If @var{tol} is unspecified the default value is 100*@code{eps}.
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30 ##
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31 ## By default the complex pairs are sorted along the first non-singleton
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32 ## dimension of @var{z}. If @var{dim} is specified, then the complex
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33 ## pairs are sorted along this dimension.
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34 ##
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35 ## Signal an error if some complex numbers could not be paired. Signal an
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36 ## error if all complex numbers are not exact conjugates (to within
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37 ## @var{tol}). Note that there is no defined order for pairs with identical
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38 ## real parts but differing imaginary parts.
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39 ## @c Set example in small font to prevent overfull line
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40 ##
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41 ## @smallexample
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42 ## cplxpair (exp(2i*pi*[0:4]'/5)) == exp(2i*pi*[3; 2; 4; 1; 0]/5)
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43 ## @end smallexample
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44 ## @end deftypefn
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45
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46 ## FIXME: subsort returned pairs by imaginary magnitude
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47 ## FIXME: Why doesn't exp(2i*pi*[0:4]'/5) produce exact conjugates. Does
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48 ## FIXME: it in Matlab? The reason is that complex pairs are supposed
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49 ## FIXME: to be exact conjugates, and not rely on a tolerance test.
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50
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51 ## 2006-05-12 David Bateman - Modified for NDArrays
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52
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53 function y = cplxpair (z, tol, dim)
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54
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55 if nargin < 1 || nargin > 3
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56 print_usage ();
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57 endif
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58
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59 if (length (z) == 0)
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60 y = zeros (size (z));
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61 return;
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62 endif
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63
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64 if (nargin < 2 || isempty (tol))
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65 if (isa (z, "single"))
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66 tol = 100 * eps("single");
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67 else
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68 tol = 100*eps;
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69 endif
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70 endif
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71
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72 nd = ndims (z);
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73 orig_dims = size (z);
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74 if (nargin < 3)
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75 ## Find the first singleton dimension.
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76 dim = 0;
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77 while (dim < nd && orig_dims(dim+1) == 1)
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78 dim++;
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79 endwhile
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80 dim++;
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81 if (dim > nd)
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82 dim = 1;
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83 endif
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84 else
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85 dim = floor(dim);
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86 if (dim < 1 || dim > nd)
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87 error ("cplxpair: invalid dimension along which to sort");
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88 endif
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89 endif
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90
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91 ## Move dimension to treat first, and convert to a 2-D matrix.
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92 perm = [dim:nd, 1:dim-1];
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93 z = permute (z, perm);
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94 sz = size (z);
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95 n = sz (1);
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96 m = prod (sz) / n;
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97 z = reshape (z, n, m);
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98
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99 ## Sort the sequence in terms of increasing real values.
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100 [q, idx] = sort (real (z), 1);
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101 z = z(idx + n * ones (n, 1) * [0:m-1]);
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102
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103 ## Put the purely real values at the end of the returned list.
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104 cls = "double";
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105 if (isa (z, "single"))
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106 cls = "single";
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107 endif
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108 [idxi, idxj] = find (abs (imag (z)) ./ (abs (z) + realmin(cls)) < tol);
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109 q = sparse (idxi, idxj, 1, n, m);
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110 nr = sum (q, 1);
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111 [q, idx] = sort (q, 1);
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112 z = z(idx);
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113 y = z;
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114
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115 ## For each remaining z, place the value and its conjugate at the
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116 ## start of the returned list, and remove them from further
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117 ## consideration.
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118 for j = 1:m
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119 p = n - nr(j);
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120 for i = 1:2:p
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121 if (i+1 > p)
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122 error ("cplxpair: could not pair all complex numbers");
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123 endif
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124 [v, idx] = min (abs (z(i+1:p) - conj (z(i))));
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125 if (v > tol)
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126 error ("cplxpair: could not pair all complex numbers");
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127 endif
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128 if (imag (z(i)) < 0)
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129 y([i, i+1]) = z([i, idx+i]);
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130 else
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131 y([i, i+1]) = z([idx+i, i]);
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132 endif
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133 z(idx+i) = z(i+1);
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134 endfor
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135 endfor
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136
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137 ## Reshape the output matrix.
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138 y = ipermute (reshape (y, sz), perm);
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139
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140 endfunction
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141
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142
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143 %!demo
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144 %! [ cplxpair(exp(2i*pi*[0:4]'/5)), exp(2i*pi*[3; 2; 4; 1; 0]/5) ]
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145
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146 %!assert (isempty (cplxpair ([])))
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147 %!assert (cplxpair (1), 1)
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148 %!assert (cplxpair ([1+1i, 1-1i]), [1-1i, 1+1i])
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149 %!assert (cplxpair ([1+1i, 1+1i, 1, 1-1i, 1-1i, 2]), ...
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150 %! [1-1i, 1+1i, 1-1i, 1+1i, 1, 2])
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151 %!assert (cplxpair ([1+1i; 1+1i; 1; 1-1i; 1-1i; 2]), ...
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152 %! [1-1i; 1+1i; 1-1i; 1+1i; 1; 2])
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153 %!assert (cplxpair ([0, 1, 2]), [0, 1, 2])
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154
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155 %!shared z
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156 %! z = exp (2i*pi*[4; 3; 5; 2; 6; 1; 0]/7);
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157 %!assert (cplxpair (z(randperm (7))), z)
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158 %!assert (cplxpair (z(randperm (7))), z)
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159 %!assert (cplxpair (z(randperm (7))), z)
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160 %!assert (cplxpair ([z(randperm(7)),z(randperm(7))]), [z,z])
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161 %!assert (cplxpair ([z(randperm(7)),z(randperm(7))],[],1), [z,z])
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162 %!assert (cplxpair ([z(randperm(7)).';z(randperm(7)).'],[],2), [z.';z.'])
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163
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164 %!## tolerance test
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165 %!assert (cplxpair ([1i, -1i, 1+(1i*eps)],2*eps), [-1i, 1i, 1+(1i*eps)])
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166