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Use Octave coding conventions in all m-file %!test blocks
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Use Octave coding conventions in all m-file %!test blocks
author | Rik <octave@nomad.inbox5.com> |
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date | Mon, 13 Feb 2012 07:29:44 -0800 |
parents | 4d917a6a858b |
children | 5d3a684236b0 |
rev | line source |
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1 ## Copyright (C) 2001-2012 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 |
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24 ## by @var{tol} using a continued fraction expansion. For example: |
6788 | 25 ## |
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 |
6788 | 32 ## @end example |
33 ## | |
7001 | 34 ## Called with two arguments returns the numerator and denominator separately |
6788 | 35 ## as two matrices. |
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36 ## @seealso{rats} |
6788 | 37 ## @end deftypefn |
38 | |
39 function [n,d] = rat(x,tol) | |
40 | |
41 if (nargin != [1,2] || nargout > 2) | |
42 print_usage (); | |
43 endif | |
44 | |
45 y = x(:); | |
46 | |
8506 | 47 ## Replace Inf with 0 while calculating ratios. |
6788 | 48 y(isinf(y)) = 0; |
49 | |
50 ## default norm | |
51 if (nargin < 2) | |
52 tol = 1e-6 * norm(y,1); | |
53 endif | |
54 | |
55 ## First step in the approximation is the integer portion | |
8506 | 56 |
57 ## First element in the continued fraction. | |
58 n = round(y); | |
6788 | 59 d = ones(size(y)); |
60 frac = y-n; | |
61 lastn = ones(size(y)); | |
62 lastd = zeros(size(y)); | |
63 | |
64 nd = ndims(y); | |
6967 | 65 nsz = numel (y); |
6788 | 66 steps = zeros([nsz, 0]); |
67 | |
8506 | 68 ## Grab new factors until all continued fractions converge. |
6788 | 69 while (1) |
8506 | 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)) |
10549 | 74 steps = NaN (nsz, 1); |
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75 endif |
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76 break; |
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77 endif |
6788 | 78 |
8506 | 79 ## Grab the next step in the continued fraction. |
6788 | 80 flip = 1./frac(idx); |
8506 | 81 ## Next element in the continued fraction. |
82 step = round(flip); | |
6788 | 83 |
84 if (nargout < 2) | |
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85 tsteps = NaN (nsz, 1); |
6788 | 86 tsteps (idx) = step; |
87 steps = [steps, tsteps]; | |
88 endif | |
89 | |
90 frac(idx) = flip-step; | |
91 | |
8506 | 92 ## Update the numerator/denominator. |
6788 | 93 nextn = n; |
94 nextd = d; | |
95 n(idx) = n(idx).*step + lastn(idx); | |
96 d(idx) = d(idx).*step + lastd(idx); | |
97 lastn = nextn; | |
98 lastd = nextd; | |
99 endwhile | |
100 | |
101 if (nargout == 2) | |
8506 | 102 ## Move the minus sign to the top. |
6788 | 103 n = n.*sign(d); |
104 d = abs(d); | |
105 | |
8506 | 106 ## Return the same shape as you receive. |
6788 | 107 n = reshape(n, size(x)); |
108 d = reshape(d, size(x)); | |
109 | |
8506 | 110 ## Use 1/0 for Inf. |
6788 | 111 n(isinf(x)) = sign(x(isinf(x))); |
112 d(isinf(x)) = 0; | |
113 | |
8506 | 114 ## Reshape the output. |
6788 | 115 n = reshape (n, size (x)); |
116 d = reshape (d, size (x)); | |
117 else | |
118 n = ""; | |
119 nsteps = size(steps, 2); | |
120 for i = 1: nsz | |
121 s = [int2str(y(i))," "]; | |
122 j = 1; | |
123 | |
124 while (true) | |
10549 | 125 step = steps(i, j++); |
126 if (isnan (step)) | |
127 break; | |
128 endif | |
129 if (j > nsteps || isnan (steps(i, j))) | |
130 if (step < 0) | |
131 s = [s(1:end-1), " + 1/(", int2str(step), ")"]; | |
132 else | |
133 s = [s(1:end-1), " + 1/", int2str(step)]; | |
134 endif | |
135 break; | |
136 else | |
137 s = [s(1:end-1), " + 1/(", int2str(step), ")"]; | |
6788 | 138 endif |
139 endwhile | |
140 s = [s, repmat(")", 1, j-2)]; | |
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141 n_nc = columns (n); |
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142 s_nc = columns (s); |
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143 if (n_nc > s_nc) |
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144 s(:,s_nc+1:n_nc) = " "; |
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145 elseif (s_nc > n_nc) |
10549 | 146 n(:,n_nc+1:s_nc) = " "; |
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147 endif |
6788 | 148 n = cat (1, n, s); |
149 endfor | |
150 endif | |
151 | |
152 endfunction | |
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153 |
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154 |
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155 %!test |
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156 %! [n, d] = rat ([0.5, 0.3, 1/3]); |
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157 %! assert (n, [1, 3, 1]); |
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158 %! assert (d, [2, 10, 3]); |
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160 %!error rat (); |
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161 %!error rat (1, 2, 3); |
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162 |