annotate scripts/general/rat.m @ 21581:6fab85c1538f

maint: Follow Octave conventions for use of semicolon in BIST tests. * testfun.txi: Document Octave conventions for use of semicolon in BIST tests. * cellfun.cc, ellipj.cc, file-io.cc, gcd.cc, hash.cc, nproc.cc, utils.cc, fftw.cc, ov-usr-fcn.cc, oct-parse.in.yy, md5sum.m, wavread.m, wavwrite.m, cplxpair.m, rat.m, im2double.m, rref.m, stem3.m, rotate.m, pchip.m, blackman.m, hamming.m, hanning.m, spectral_adf.m, spectral_xdf.m, assert.m, fail.m, etime.m, build-sparse-tests.sh, classes.tst, ctor-vs-method.tst, index.tst, io.tst, struct.tst: Follow Octave conventions for use of semicolon in BIST tests.
author Rik <rik@octave.org>
date Fri, 01 Apr 2016 18:16:01 -0700
parents 516bb87ea72e
children bac0d6f07a3e
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
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1 ## Copyright (C) 2001-2015 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 {} {@var{s} =} rat (@var{x}, @var{tol})
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21 ## @deftypefnx {} {[@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 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:
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27 ##
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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
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34 ## @end example
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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}
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39 ## @end deftypefn
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40
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41 function [n,d] = rat (x,tol)
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42
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43 if (nargin != [1,2] || nargout > 2)
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44 print_usage ();
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45 endif
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46
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47 y = x(:);
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48
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49 ## Replace Inf with 0 while calculating ratios.
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50 y(isinf(y)) = 0;
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51
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52 ## default norm
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53 if (nargin < 2)
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54 tol = 1e-6 * norm (y,1);
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55 endif
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56
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57 ## First step in the approximation is the integer portion
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58
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59 ## First element in the continued fraction.
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60 n = round (y);
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61 d = ones (size (y));
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62 frac = y-n;
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63 lastn = ones (size (y));
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64 lastd = zeros (size (y));
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65
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66 nd = ndims (y);
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67 nsz = numel (y);
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68 steps = zeros ([nsz, 0]);
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69
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70 ## Grab new factors until all continued fractions converge.
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71 while (1)
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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))
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76 steps = NaN (nsz, 1);
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77 endif
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78 break;
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79 endif
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80
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81 ## Grab the next step in the continued fraction.
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82 flip = 1./frac(idx);
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83 ## Next element in the continued fraction.
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84 step = round (flip);
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85
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86 if (nargout < 2)
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87 tsteps = NaN (nsz, 1);
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88 tsteps (idx) = step;
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89 steps = [steps, tsteps];
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90 endif
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91
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92 frac(idx) = flip-step;
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93
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94 ## Update the numerator/denominator.
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95 nextn = n;
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96 nextd = d;
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97 n(idx) = n(idx).*step + lastn(idx);
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98 d(idx) = d(idx).*step + lastd(idx);
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99 lastn = nextn;
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100 lastd = nextd;
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101 endwhile
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102
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103 if (nargout == 2)
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104 ## Move the minus sign to the top.
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105 n .*= sign (d);
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106 d = abs (d);
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107
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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));
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111
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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;
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115
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116 ## Reshape the output.
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117 n = reshape (n, size (x));
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118 d = reshape (d, size (x));
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119 else
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120 n = "";
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121 nsteps = columns (steps);
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122 for i = 1: nsz
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123 s = [int2str(y(i))," "];
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124 j = 1;
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125
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126 while (true)
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127 step = steps(i, j++);
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128 if (isnan (step))
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129 break;
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130 endif
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131 if (j > nsteps || isnan (steps(i, j)))
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132 if (step < 0)
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133 s = [s(1:end-1), " + 1/(", int2str(step), ")"];
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134 else
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135 s = [s(1:end-1), " + 1/", int2str(step)];
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136 endif
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137 break;
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138 else
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139 s = [s(1:end-1), " + 1/(", int2str(step), ")"];
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140 endif
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141 endwhile
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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)
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148 n(:,n_nc+1:s_nc) = " ";
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149 endif
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150 n = cat (1, n, s);
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151 endfor
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152 endif
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153
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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