Mercurial > octave-nkf
annotate scripts/statistics/distributions/cauchy_pdf.m @ 20641:c3c052b9192a
Improve performance and error reporting of betainv, gaminv (bug #34363).
* betainv.m: Replace for loop with do-until loop. Shorten max loop cycles to
40, rather than 10,000. Issue warning if algorithm fails.
* gaminv.m: Replace for loop with do-until loop. Shorten max loop cycles to
40, rather than 100. Issue warning if algorithm fails.
author | Rik <rik@octave.org> |
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date | Sun, 11 Oct 2015 16:55:17 -0700 |
parents | d9341b422488 |
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1 ## Copyright (C) 2012 Rik Wehbring |
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2 ## Copyright (C) 1995-2015 Kurt Hornik |
3426 | 3 ## |
3922 | 4 ## This file is part of Octave. |
5 ## | |
6 ## Octave is free software; you can redistribute it and/or modify it | |
7 ## under the terms of the GNU General Public License as published by | |
7016 | 8 ## the Free Software Foundation; either version 3 of the License, or (at |
9 ## your option) any later version. | |
3426 | 10 ## |
3922 | 11 ## Octave is distributed in the hope that it will be useful, but |
3191 | 12 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
13 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
3426 | 14 ## General Public License for more details. |
15 ## | |
3191 | 16 ## You should have received a copy of the GNU General Public License |
7016 | 17 ## along with Octave; see the file COPYING. If not, see |
18 ## <http://www.gnu.org/licenses/>. | |
3191 | 19 |
3456 | 20 ## -*- texinfo -*- |
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21 ## @deftypefn {Function File} {} cauchy_pdf (@var{x}) |
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22 ## @deftypefnx {Function File} {} cauchy_pdf (@var{x}, @var{location}, @var{scale}) |
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23 ## For each element of @var{x}, compute the probability density function (PDF) |
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24 ## at @var{x} of the Cauchy distribution with location parameter |
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25 ## @var{location} and scale parameter @var{scale} > 0. |
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26 ## |
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27 ## Default values are @var{location} = 0, @var{scale} = 1. |
3456 | 28 ## @end deftypefn |
3191 | 29 |
5428 | 30 ## Author: KH <Kurt.Hornik@wu-wien.ac.at> |
3456 | 31 ## Description: PDF of the Cauchy distribution |
3191 | 32 |
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33 function pdf = cauchy_pdf (x, location = 0, scale = 1) |
3426 | 34 |
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35 if (nargin != 1 && nargin != 3) |
6046 | 36 print_usage (); |
3191 | 37 endif |
3426 | 38 |
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39 if (! isscalar (location) || ! isscalar (scale)) |
4854 | 40 [retval, x, location, scale] = common_size (x, location, scale); |
41 if (retval > 0) | |
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42 error ("cauchy_pdf: X, LOCATION, and SCALE must be of common size or scalars"); |
4854 | 43 endif |
3191 | 44 endif |
3426 | 45 |
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46 if (iscomplex (x) || iscomplex (location) || iscomplex (scale)) |
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47 error ("cauchy_pdf: X, LOCATION, and SCALE must not be complex"); |
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48 endif |
3426 | 49 |
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50 if (isa (x, "single") || isa (location, "single") || isa (scale, "single")) |
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51 pdf = NaN (size (x), "single"); |
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52 else |
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53 pdf = NaN (size (x)); |
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54 endif |
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55 |
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56 k = ! isinf (location) & (scale > 0) & (scale < Inf); |
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57 if (isscalar (location) && isscalar (scale)) |
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58 pdf = ((1 ./ (1 + ((x - location) / scale) .^ 2)) |
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59 / pi / scale); |
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60 else |
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61 pdf(k) = ((1 ./ (1 + ((x(k) - location(k)) ./ scale(k)) .^ 2)) |
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62 / pi ./ scale(k)); |
3191 | 63 endif |
3426 | 64 |
3191 | 65 endfunction |
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66 |
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67 |
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68 %!shared x,y |
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69 %! x = [-1 0 0.5 1 2]; |
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70 %! y = 1/pi * ( 2 ./ ((x-1).^2 + 2^2) ); |
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71 %!assert (cauchy_pdf (x, ones (1,5), 2*ones (1,5)), y) |
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72 %!assert (cauchy_pdf (x, 1, 2*ones (1,5)), y) |
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73 %!assert (cauchy_pdf (x, ones (1,5), 2), y) |
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74 %!assert (cauchy_pdf (x, [-Inf 1 NaN 1 Inf], 2), [NaN y(2) NaN y(4) NaN]) |
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75 %!assert (cauchy_pdf (x, 1, 2*[0 1 NaN 1 Inf]), [NaN y(2) NaN y(4) NaN]) |
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76 %!assert (cauchy_pdf ([x, NaN], 1, 2), [y, NaN]) |
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77 |
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78 ## Test class of input preserved |
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79 %!assert (cauchy_pdf (single ([x, NaN]), 1, 2), single ([y, NaN]), eps ("single")) |
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80 %!assert (cauchy_pdf ([x, NaN], single (1), 2), single ([y, NaN]), eps ("single")) |
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81 %!assert (cauchy_pdf ([x, NaN], 1, single (2)), single ([y, NaN]), eps ("single")) |
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82 |
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83 ## Cauchy (0,1) == Student's T distribution with 1 DOF |
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84 %!test |
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85 %! x = rand (10, 1); |
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86 %! assert (cauchy_pdf (x, 0, 1), tpdf (x, 1), eps); |
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87 |
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88 ## Test input validation |
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89 %!error cauchy_pdf () |
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90 %!error cauchy_pdf (1,2) |
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91 %!error cauchy_pdf (1,2,3,4) |
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92 %!error cauchy_pdf (ones (3), ones (2), ones (2)) |
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93 %!error cauchy_pdf (ones (2), ones (3), ones (2)) |
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94 %!error cauchy_pdf (ones (2), ones (2), ones (3)) |
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95 %!error cauchy_pdf (i, 2, 2) |
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96 %!error cauchy_pdf (2, i, 2) |
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97 %!error cauchy_pdf (2, 2, i) |
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98 |