Mercurial > hg > octave-nkf
annotate scripts/general/rat.m @ 20441:83792dd9bcc1
Use in-place operators in m-files where possible.
* scripts/audio/@audioplayer/set.m, scripts/audio/@audiorecorder/set.m,
scripts/audio/mu2lin.m, scripts/elfun/cosd.m, scripts/general/del2.m,
scripts/general/profexplore.m, scripts/general/quadl.m, scripts/general/rat.m,
scripts/general/rotdim.m, scripts/help/get_first_help_sentence.m,
scripts/help/private/__strip_html_tags__.m, scripts/image/cubehelix.m,
scripts/io/textread.m, scripts/linear-algebra/duplication_matrix.m,
scripts/linear-algebra/housh.m, scripts/linear-algebra/krylov.m,
scripts/linear-algebra/logm.m, scripts/linear-algebra/normest.m,
scripts/linear-algebra/onenormest.m, scripts/optimization/fminsearch.m,
scripts/optimization/lsqnonneg.m, scripts/optimization/qp.m,
scripts/plot/appearance/annotation.m, scripts/plot/appearance/axis.m,
scripts/plot/appearance/legend.m, scripts/plot/appearance/specular.m,
scripts/plot/draw/colorbar.m, scripts/plot/draw/hist.m,
scripts/plot/draw/plotmatrix.m, scripts/plot/draw/private/__stem__.m,
scripts/plot/util/__actual_axis_position__.m,
scripts/plot/util/__gnuplot_drawnow__.m, scripts/plot/util/findobj.m,
scripts/plot/util/print.m, scripts/plot/util/private/__go_draw_axes__.m,
scripts/plot/util/private/__print_parse_opts__.m, scripts/plot/util/rotate.m,
scripts/polynomial/pchip.m, scripts/polynomial/polyaffine.m,
scripts/polynomial/polyder.m, scripts/polynomial/private/__splinefit__.m,
scripts/polynomial/residue.m, scripts/signal/arch_fit.m,
scripts/signal/arch_rnd.m, scripts/signal/bartlett.m,
scripts/signal/blackman.m, scripts/signal/freqz.m, scripts/signal/hamming.m,
scripts/signal/hanning.m, scripts/signal/spectral_adf.m,
scripts/signal/spectral_xdf.m, scripts/signal/stft.m,
scripts/sparse/bicgstab.m, scripts/sparse/cgs.m,
scripts/sparse/private/__sprand_impl__.m, scripts/sparse/qmr.m,
scripts/sparse/sprandsym.m, scripts/sparse/svds.m, scripts/specfun/legendre.m,
scripts/special-matrix/gallery.m, scripts/statistics/base/gls.m,
scripts/statistics/models/logistic_regression.m,
scripts/statistics/tests/kruskal_wallis_test.m,
scripts/statistics/tests/manova.m, scripts/statistics/tests/wilcoxon_test.m,
scripts/time/datevec.m:
Use in-place operators in m-files where possible.
| author | Rik <rik@octave.org> |
|---|---|
| date | Tue, 26 May 2015 21:07:42 -0700 |
| parents | 7503499a252b |
| children |
| rev | line source |
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1 ## Copyright (C) 2001-2015 Paul Kienzle |
| 6788 | 2 ## |
| 3 ## This file is part of Octave. | |
| 4 ## | |
| 5 ## Octave is free software; you can redistribute it and/or modify it | |
| 6 ## under the terms of the GNU General Public License as published by | |
| 7016 | 7 ## the Free Software Foundation; either version 3 of the License, or (at |
| 8 ## your option) any later version. | |
| 6788 | 9 ## |
| 10 ## Octave is distributed in the hope that it will be useful, but | |
| 11 ## WITHOUT ANY WARRANTY; without even the implied warranty of | |
| 12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
| 13 ## General Public License for more details. | |
| 14 ## | |
| 15 ## You should have received a copy of the GNU General Public License | |
| 7016 | 16 ## along with Octave; see the file COPYING. If not, see |
| 17 ## <http://www.gnu.org/licenses/>. | |
| 6788 | 18 |
| 19 ## -*- texinfo -*- | |
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20 ## @deftypefn {Function File} {@var{s} =} rat (@var{x}, @var{tol}) |
| 6788 | 21 ## @deftypefnx {Function File} {[@var{n}, @var{d}] =} rat (@var{x}, @var{tol}) |
| 22 ## | |
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23 ## Find a rational approximation to @var{x} within the tolerance defined by |
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24 ## @var{tol} using a continued fraction expansion. |
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25 ## |
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26 ## For example: |
| 6788 | 27 ## |
| 28 ## @example | |
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29 ## @group |
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30 ## rat (pi) = 3 + 1/(7 + 1/16) = 355/113 |
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31 ## rat (e) = 3 + 1/(-4 + 1/(2 + 1/(5 + 1/(-2 + 1/(-7))))) |
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32 ## = 1457/536 |
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33 ## @end group |
| 6788 | 34 ## @end example |
| 35 ## | |
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36 ## When called with two output arguments return the numerator and denominator |
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37 ## separately as two matrices. |
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38 ## @seealso{rats} |
| 6788 | 39 ## @end deftypefn |
| 40 | |
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41 function [n,d] = rat (x,tol) |
| 6788 | 42 |
| 43 if (nargin != [1,2] || nargout > 2) | |
| 44 print_usage (); | |
| 45 endif | |
| 46 | |
| 47 y = x(:); | |
| 48 | |
| 8506 | 49 ## Replace Inf with 0 while calculating ratios. |
| 6788 | 50 y(isinf(y)) = 0; |
| 51 | |
| 52 ## default norm | |
| 53 if (nargin < 2) | |
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54 tol = 1e-6 * norm (y,1); |
| 6788 | 55 endif |
| 56 | |
| 57 ## First step in the approximation is the integer portion | |
| 8506 | 58 |
| 59 ## First element in the continued fraction. | |
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60 n = round (y); |
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61 d = ones (size (y)); |
| 6788 | 62 frac = y-n; |
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63 lastn = ones (size (y)); |
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64 lastd = zeros (size (y)); |
| 6788 | 65 |
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66 nd = ndims (y); |
| 6967 | 67 nsz = numel (y); |
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68 steps = zeros ([nsz, 0]); |
| 6788 | 69 |
| 8506 | 70 ## Grab new factors until all continued fractions converge. |
| 6788 | 71 while (1) |
| 8506 | 72 ## Determine which fractions have not yet converged. |
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73 idx = find (abs (y-n./d) >= tol); |
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74 if (isempty (idx)) |
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75 if (isempty (steps)) |
| 10549 | 76 steps = NaN (nsz, 1); |
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77 endif |
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78 break; |
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79 endif |
| 6788 | 80 |
| 8506 | 81 ## Grab the next step in the continued fraction. |
| 6788 | 82 flip = 1./frac(idx); |
| 8506 | 83 ## Next element in the continued fraction. |
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84 step = round (flip); |
| 6788 | 85 |
| 86 if (nargout < 2) | |
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87 tsteps = NaN (nsz, 1); |
| 6788 | 88 tsteps (idx) = step; |
| 89 steps = [steps, tsteps]; | |
| 90 endif | |
| 91 | |
| 92 frac(idx) = flip-step; | |
| 93 | |
| 8506 | 94 ## Update the numerator/denominator. |
| 6788 | 95 nextn = n; |
| 96 nextd = d; | |
| 97 n(idx) = n(idx).*step + lastn(idx); | |
| 98 d(idx) = d(idx).*step + lastd(idx); | |
| 99 lastn = nextn; | |
| 100 lastd = nextd; | |
| 101 endwhile | |
| 102 | |
| 103 if (nargout == 2) | |
| 8506 | 104 ## Move the minus sign to the top. |
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105 n .*= sign (d); |
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106 d = abs (d); |
| 6788 | 107 |
| 8506 | 108 ## Return the same shape as you receive. |
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109 n = reshape (n, size (x)); |
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110 d = reshape (d, size (x)); |
| 6788 | 111 |
| 8506 | 112 ## Use 1/0 for Inf. |
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113 n(isinf (x)) = sign (x(isinf (x))); |
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114 d(isinf (x)) = 0; |
| 6788 | 115 |
| 8506 | 116 ## Reshape the output. |
| 6788 | 117 n = reshape (n, size (x)); |
| 118 d = reshape (d, size (x)); | |
| 119 else | |
| 120 n = ""; | |
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121 nsteps = columns (steps); |
| 6788 | 122 for i = 1: nsz |
| 123 s = [int2str(y(i))," "]; | |
| 124 j = 1; | |
| 125 | |
| 126 while (true) | |
| 10549 | 127 step = steps(i, j++); |
| 128 if (isnan (step)) | |
| 129 break; | |
| 130 endif | |
| 131 if (j > nsteps || isnan (steps(i, j))) | |
| 132 if (step < 0) | |
| 133 s = [s(1:end-1), " + 1/(", int2str(step), ")"]; | |
| 134 else | |
| 135 s = [s(1:end-1), " + 1/", int2str(step)]; | |
| 136 endif | |
| 137 break; | |
| 138 else | |
| 139 s = [s(1:end-1), " + 1/(", int2str(step), ")"]; | |
| 6788 | 140 endif |
| 141 endwhile | |
| 142 s = [s, repmat(")", 1, j-2)]; | |
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143 n_nc = columns (n); |
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144 s_nc = columns (s); |
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145 if (n_nc > s_nc) |
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146 s(:,s_nc+1:n_nc) = " "; |
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147 elseif (s_nc > n_nc && n_nc != 0) |
| 10549 | 148 n(:,n_nc+1:s_nc) = " "; |
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149 endif |
| 6788 | 150 n = cat (1, n, s); |
| 151 endfor | |
| 152 endif | |
| 153 | |
| 154 endfunction | |
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155 |
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156 |
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157 %!test |
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158 %! [n, d] = rat ([0.5, 0.3, 1/3]); |
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159 %! assert (n, [1, 3, 1]); |
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160 %! assert (d, [2, 10, 3]); |
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161 |
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162 ## bug #43374 |
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163 %!assert (eval (rat (0.75)), [0.75]) |
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164 |
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165 %!error rat (); |
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166 %!error rat (1, 2, 3); |
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167 |