Mercurial > octave-nkf
annotate scripts/statistics/distributions/betainv.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 |
children | 4e307c55a2b5 |
rev | line source |
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1 ## Copyright (C) 2012 Rik Wehbring |
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2 ## Copyright (C) 1995-2015 Kurt Hornik |
5410 | 3 ## |
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. | |
5410 | 10 ## |
11 ## Octave is distributed in the hope that it will be useful, but | |
12 ## WITHOUT ANY WARRANTY; without even the implied warranty of | |
13 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
14 ## General Public License for more details. | |
15 ## | |
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/>. | |
5410 | 19 |
20 ## -*- texinfo -*- | |
5411 | 21 ## @deftypefn {Function File} {} betainv (@var{x}, @var{a}, @var{b}) |
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22 ## For each element of @var{x}, compute the quantile (the inverse of the CDF) |
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23 ## at @var{x} of the Beta distribution with parameters @var{a} and @var{b}. |
5410 | 24 ## @end deftypefn |
25 | |
5428 | 26 ## Author: KH <Kurt.Hornik@wu-wien.ac.at> |
5410 | 27 ## Description: Quantile function of the Beta distribution |
28 | |
5411 | 29 function inv = betainv (x, a, b) |
5410 | 30 |
31 if (nargin != 3) | |
6046 | 32 print_usage (); |
5410 | 33 endif |
34 | |
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35 if (! isscalar (a) || ! isscalar (b)) |
5410 | 36 [retval, x, a, b] = common_size (x, a, b); |
37 if (retval > 0) | |
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38 error ("betainv: X, A, and B must be of common size or scalars"); |
5410 | 39 endif |
40 endif | |
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41 |
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42 if (iscomplex (x) || iscomplex (a) || iscomplex (b)) |
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43 error ("betainv: X, A, and B must not be complex"); |
5410 | 44 endif |
45 | |
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46 if (isa (x, "single") || isa (a, "single") || isa (b, "single")) |
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47 inv = zeros (size (x), "single"); |
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48 else |
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49 inv = zeros (size (x)); |
5410 | 50 endif |
51 | |
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52 k = (x < 0) | (x > 1) | !(a > 0) | !(b > 0) | isnan (x); |
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53 inv(k) = NaN; |
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54 |
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55 k = (x == 1) & (a > 0) & (b > 0); |
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56 inv(k) = 1; |
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57 |
5410 | 58 k = find ((x > 0) & (x < 1) & (a > 0) & (b > 0)); |
59 if (any (k)) | |
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60 if (! isscalar (a) || ! isscalar (b)) |
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61 a = a(k); |
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62 b = b(k); |
5410 | 63 y = a ./ (a + b); |
64 else | |
65 y = a / (a + b) * ones (size (k)); | |
66 endif | |
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67 x = x(k); |
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68 |
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69 if (isa (y, "single")) |
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70 myeps = eps ("single"); |
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71 else |
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72 myeps = eps; |
5410 | 73 endif |
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74 |
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75 l = find (y < myeps); |
5410 | 76 if (any (l)) |
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77 y(l) = sqrt (myeps) * ones (length (l), 1); |
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78 endif |
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79 l = find (y > 1 - myeps); |
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80 if (any (l)) |
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81 y(l) = 1 - sqrt (myeps) * ones (length (l), 1); |
5410 | 82 endif |
83 | |
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84 y_new = y; |
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85 loopcnt = 0; |
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86 do |
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87 y_old = y_new; |
5411 | 88 h = (betacdf (y_old, a, b) - x) ./ betapdf (y_old, a, b); |
5410 | 89 y_new = y_old - h; |
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90 ind = find (y_new <= myeps); |
5410 | 91 if (any (ind)) |
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92 y_new(ind) = y_old(ind) / 10; |
5410 | 93 endif |
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94 ind = find (y_new >= 1 - myeps); |
5410 | 95 if (any (ind)) |
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96 y_new(ind) = 1 - (1 - y_old(ind)) / 10; |
5410 | 97 endif |
98 h = y_old - y_new; | |
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99 until (max (abs (h)) < sqrt (myeps) || ++loopcnt == 40) |
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100 |
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101 if (loopcnt == 40) |
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102 warning ("betainv: calculation failed to converge for some values"); |
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103 endif |
5410 | 104 |
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105 inv(k) = y_new; |
5410 | 106 endif |
107 | |
108 endfunction | |
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109 |
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110 |
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111 %!shared x |
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112 %! x = [-1 0 0.75 1 2]; |
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113 %!assert (betainv (x, ones (1,5), 2*ones (1,5)), [NaN 0 0.5 1 NaN]) |
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114 %!assert (betainv (x, 1, 2*ones (1,5)), [NaN 0 0.5 1 NaN]) |
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115 %!assert (betainv (x, ones (1,5), 2), [NaN 0 0.5 1 NaN]) |
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116 %!assert (betainv (x, [1 0 NaN 1 1], 2), [NaN NaN NaN 1 NaN]) |
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117 %!assert (betainv (x, 1, 2*[1 0 NaN 1 1]), [NaN NaN NaN 1 NaN]) |
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118 %!assert (betainv ([x(1:2) NaN x(4:5)], 1, 2), [NaN 0 NaN 1 NaN]) |
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119 |
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120 ## Test class of input preserved |
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121 %!assert (betainv ([x, NaN], 1, 2), [NaN 0 0.5 1 NaN NaN]) |
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122 %!assert (betainv (single ([x, NaN]), 1, 2), single ([NaN 0 0.5 1 NaN NaN])) |
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123 %!assert (betainv ([x, NaN], single (1), 2), single ([NaN 0 0.5 1 NaN NaN])) |
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124 %!assert (betainv ([x, NaN], 1, single (2)), single ([NaN 0 0.5 1 NaN NaN])) |
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125 |
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126 ## Test input validation |
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127 %!error betainv () |
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128 %!error betainv (1) |
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129 %!error betainv (1,2) |
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130 %!error betainv (1,2,3,4) |
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131 %!error betainv (ones (3), ones (2), ones (2)) |
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132 %!error betainv (ones (2), ones (3), ones (2)) |
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133 %!error betainv (ones (2), ones (2), ones (3)) |
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134 %!error betainv (i, 2, 2) |
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135 %!error betainv (2, i, 2) |
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136 %!error betainv (2, 2, i) |
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137 |