annotate scripts/general/rat.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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72c96de7a403 maint: update copyright notices for 2012
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1 ## Copyright (C) 2001-2012 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} {@var{s} =} rat (@var{x}, @var{tol})
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21 ## @deftypefnx {Function File} {[@var{n}, @var{d}] =} rat (@var{x}, @var{tol})
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22 ##
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23 ## Find a rational approximation to @var{x} within the tolerance defined
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24 ## by @var{tol} using a continued fraction expansion. For example:
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25 ##
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26 ## @example
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27 ## @group
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28 ## rat (pi) = 3 + 1/(7 + 1/16) = 355/113
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29 ## rat (e) = 3 + 1/(-4 + 1/(2 + 1/(5 + 1/(-2 + 1/(-7)))))
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30 ## = 1457/536
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31 ## @end group
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32 ## @end example
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33 ##
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34 ## Called with two arguments returns the numerator and denominator separately
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35 ## as two matrices.
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36 ## @seealso{rats}
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37 ## @end deftypefn
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38
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39 function [n,d] = rat(x,tol)
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40
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41 if (nargin != [1,2] || nargout > 2)
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42 print_usage ();
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43 endif
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44
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45 y = x(:);
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46
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47 ## Replace Inf with 0 while calculating ratios.
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48 y(isinf(y)) = 0;
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49
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50 ## default norm
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51 if (nargin < 2)
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52 tol = 1e-6 * norm(y,1);
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53 endif
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54
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55 ## First step in the approximation is the integer portion
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56
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57 ## First element in the continued fraction.
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58 n = round(y);
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59 d = ones(size(y));
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60 frac = y-n;
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61 lastn = ones(size(y));
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62 lastd = zeros(size(y));
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63
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64 nd = ndims(y);
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65 nsz = numel (y);
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66 steps = zeros([nsz, 0]);
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67
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68 ## Grab new factors until all continued fractions converge.
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69 while (1)
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70 ## Determine which fractions have not yet converged.
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71 idx = find(abs (y-n./d) >= tol);
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72 if (isempty(idx))
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73 if (isempty (steps))
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74 steps = NaN (nsz, 1);
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75 endif
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76 break;
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77 endif
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78
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79 ## Grab the next step in the continued fraction.
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80 flip = 1./frac(idx);
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81 ## Next element in the continued fraction.
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82 step = round(flip);
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83
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84 if (nargout < 2)
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85 tsteps = NaN (nsz, 1);
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86 tsteps (idx) = step;
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87 steps = [steps, tsteps];
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88 endif
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89
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90 frac(idx) = flip-step;
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91
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92 ## Update the numerator/denominator.
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93 nextn = n;
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94 nextd = d;
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95 n(idx) = n(idx).*step + lastn(idx);
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96 d(idx) = d(idx).*step + lastd(idx);
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97 lastn = nextn;
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dbateman
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98 lastd = nextd;
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dbateman
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99 endwhile
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dbateman
parents:
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100
c81a0f3f5a82 [project @ 2007-07-23 22:05:29 by dbateman]
dbateman
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101 if (nargout == 2)
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102 ## Move the minus sign to the top.
6788
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103 n = n.*sign(d);
c81a0f3f5a82 [project @ 2007-07-23 22:05:29 by dbateman]
dbateman
parents:
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104 d = abs(d);
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dbateman
parents:
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105
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diff changeset
106 ## Return the same shape as you receive.
6788
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107 n = reshape(n, size(x));
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dbateman
parents:
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108 d = reshape(d, size(x));
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dbateman
parents:
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109
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diff changeset
110 ## Use 1/0 for Inf.
6788
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111 n(isinf(x)) = sign(x(isinf(x)));
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112 d(isinf(x)) = 0;
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parents:
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113
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114 ## Reshape the output.
6788
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115 n = reshape (n, size (x));
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116 d = reshape (d, size (x));
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117 else
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118 n = "";
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119 nsteps = size(steps, 2);
c81a0f3f5a82 [project @ 2007-07-23 22:05:29 by dbateman]
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120 for i = 1: nsz
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121 s = [int2str(y(i))," "];
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parents:
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122 j = 1;
c81a0f3f5a82 [project @ 2007-07-23 22:05:29 by dbateman]
dbateman
parents:
diff changeset
123
c81a0f3f5a82 [project @ 2007-07-23 22:05:29 by dbateman]
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parents:
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124 while (true)
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95c3e38098bf Untabify .m scripts
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125 step = steps(i, j++);
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diff changeset
126 if (isnan (step))
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127 break;
95c3e38098bf Untabify .m scripts
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diff changeset
128 endif
95c3e38098bf Untabify .m scripts
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diff changeset
129 if (j > nsteps || isnan (steps(i, j)))
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diff changeset
130 if (step < 0)
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diff changeset
131 s = [s(1:end-1), " + 1/(", int2str(step), ")"];
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diff changeset
132 else
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diff changeset
133 s = [s(1:end-1), " + 1/", int2str(step)];
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diff changeset
134 endif
95c3e38098bf Untabify .m scripts
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parents: 10540
diff changeset
135 break;
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 10540
diff changeset
136 else
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 10540
diff changeset
137 s = [s(1:end-1), " + 1/(", int2str(step), ")"];
6788
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138 endif
c81a0f3f5a82 [project @ 2007-07-23 22:05:29 by dbateman]
dbateman
parents:
diff changeset
139 endwhile
c81a0f3f5a82 [project @ 2007-07-23 22:05:29 by dbateman]
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parents:
diff changeset
140 s = [s, repmat(")", 1, j-2)];
7881
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John W. Eaton <jwe@octave.org>
parents: 7031
diff changeset
141 n_nc = columns (n);
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John W. Eaton <jwe@octave.org>
parents: 7031
diff changeset
142 s_nc = columns (s);
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John W. Eaton <jwe@octave.org>
parents: 7031
diff changeset
143 if (n_nc > s_nc)
11589
b0084095098e missing semicolons in script files
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parents: 11587
diff changeset
144 s(:,s_nc+1:n_nc) = " ";
7881
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John W. Eaton <jwe@octave.org>
parents: 7031
diff changeset
145 elseif (s_nc > n_nc)
10549
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 10540
diff changeset
146 n(:,n_nc+1:s_nc) = " ";
7881
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John W. Eaton <jwe@octave.org>
parents: 7031
diff changeset
147 endif
6788
c81a0f3f5a82 [project @ 2007-07-23 22:05:29 by dbateman]
dbateman
parents:
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148 n = cat (1, n, s);
c81a0f3f5a82 [project @ 2007-07-23 22:05:29 by dbateman]
dbateman
parents:
diff changeset
149 endfor
c81a0f3f5a82 [project @ 2007-07-23 22:05:29 by dbateman]
dbateman
parents:
diff changeset
150 endif
c81a0f3f5a82 [project @ 2007-07-23 22:05:29 by dbateman]
dbateman
parents:
diff changeset
151
c81a0f3f5a82 [project @ 2007-07-23 22:05:29 by dbateman]
dbateman
parents:
diff changeset
152 endfunction
12795
9e7ebbaf69ff codesprint: new tests for files in scripts/general directory
John W. Eaton <jwe@octave.org>
parents: 12185
diff changeset
153
9e7ebbaf69ff codesprint: new tests for files in scripts/general directory
John W. Eaton <jwe@octave.org>
parents: 12185
diff changeset
154
9e7ebbaf69ff codesprint: new tests for files in scripts/general directory
John W. Eaton <jwe@octave.org>
parents: 12185
diff changeset
155 %!test
9e7ebbaf69ff codesprint: new tests for files in scripts/general directory
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parents: 12185
diff changeset
156 %! [n, d] = rat ([0.5, 0.3, 1/3]);
9e7ebbaf69ff codesprint: new tests for files in scripts/general directory
John W. Eaton <jwe@octave.org>
parents: 12185
diff changeset
157 %! assert (n, [1, 3, 1]);
9e7ebbaf69ff codesprint: new tests for files in scripts/general directory
John W. Eaton <jwe@octave.org>
parents: 12185
diff changeset
158 %! assert (d, [2, 10, 3]);
14363
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14327
diff changeset
159
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14327
diff changeset
160 %!error rat ();
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14327
diff changeset
161 %!error rat (1, 2, 3);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14327
diff changeset
162