Mercurial > octave-nkf
annotate scripts/statistics/distributions/gaminv.m @ 17744:d63878346099
maint: Update copyright notices for release.
author | John W. Eaton <jwe@octave.org> |
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date | Wed, 23 Oct 2013 22:09:27 -0400 |
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1 ## Copyright (C) 2012 Rik Wehbring |
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2 ## Copyright (C) 1995-2013 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} {} gaminv (@var{x}, @var{a}, @var{b}) |
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22 ## For each element of @var{x}, compute the quantile (the inverse of |
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23 ## the CDF) at @var{x} of the Gamma distribution with shape parameter |
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24 ## @var{a} and scale @var{b}. |
5410 | 25 ## @end deftypefn |
26 | |
5428 | 27 ## Author: KH <Kurt.Hornik@wu-wien.ac.at> |
5410 | 28 ## Description: Quantile function of the Gamma distribution |
29 | |
5411 | 30 function inv = gaminv (x, a, b) |
5410 | 31 |
32 if (nargin != 3) | |
6046 | 33 print_usage (); |
5410 | 34 endif |
35 | |
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36 if (!isscalar (a) || !isscalar (b)) |
5410 | 37 [retval, x, a, b] = common_size (x, a, b); |
38 if (retval > 0) | |
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39 error ("gaminv: X, A, and B must be of common size or scalars"); |
5410 | 40 endif |
41 endif | |
42 | |
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43 if (iscomplex (x) || iscomplex (a) || iscomplex (b)) |
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44 error ("gaminv: X, A, and B must not be complex"); |
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45 endif |
5410 | 46 |
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47 if (isa (x, "single") || isa (a, "single") || isa (b, "single")) |
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48 inv = zeros (size (x), "single"); |
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49 else |
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50 inv = zeros (size (x)); |
5410 | 51 endif |
52 | |
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53 k = ((x < 0) | (x > 1) | isnan (x) |
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54 | !(a > 0) | !(a < Inf) | !(b > 0) | !(b < Inf)); |
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55 inv(k) = NaN; |
5410 | 56 |
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57 k = (x == 1) & (a > 0) & (a < Inf) & (b > 0) & (b < Inf); |
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58 inv(k) = Inf; |
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59 |
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60 k = find ((x > 0) & (x < 1) & (a > 0) & (a < Inf) & (b > 0) & (b < Inf)); |
5410 | 61 if (any (k)) |
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62 if (!isscalar (a) || !isscalar (b)) |
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63 a = a(k); |
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64 b = b(k); |
6777 | 65 y = a .* b; |
5410 | 66 else |
6777 | 67 y = a * b * ones (size (k)); |
5410 | 68 endif |
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69 x = x(k); |
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70 |
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71 if (isa (x, "single")) |
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72 myeps = eps ("single"); |
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73 else |
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74 myeps = eps; |
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75 endif |
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76 |
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77 l = find (x < myeps); |
5410 | 78 if (any (l)) |
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79 y(l) = sqrt (myeps) * ones (length (l), 1); |
5410 | 80 endif |
81 | |
82 y_old = y; | |
83 for i = 1 : 100 | |
5411 | 84 h = (gamcdf (y_old, a, b) - x) ./ gampdf (y_old, a, b); |
5410 | 85 y_new = y_old - h; |
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86 ind = find (y_new <= myeps); |
5410 | 87 if (any (ind)) |
88 y_new (ind) = y_old (ind) / 10; | |
89 h = y_old - y_new; | |
90 endif | |
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91 if (max (abs (h)) < sqrt (myeps)) |
5410 | 92 break; |
93 endif | |
94 y_old = y_new; | |
95 endfor | |
96 | |
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97 inv(k) = y_new; |
5410 | 98 endif |
99 | |
100 endfunction | |
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101 |
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102 |
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103 %!shared x |
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104 %! x = [-1 0 0.63212055882855778 1 2]; |
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105 %!assert (gaminv (x, ones (1,5), ones (1,5)), [NaN 0 1 Inf NaN], eps) |
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106 %!assert (gaminv (x, 1, ones (1,5)), [NaN 0 1 Inf NaN], eps) |
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107 %!assert (gaminv (x, ones (1,5), 1), [NaN 0 1 Inf NaN], eps) |
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108 %!assert (gaminv (x, [1 -Inf NaN Inf 1], 1), [NaN NaN NaN NaN NaN]) |
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109 %!assert (gaminv (x, 1, [1 -Inf NaN Inf 1]), [NaN NaN NaN NaN NaN]) |
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110 %!assert (gaminv ([x(1:2) NaN x(4:5)], 1, 1), [NaN 0 NaN Inf NaN]) |
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111 |
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112 %% Test class of input preserved |
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113 %!assert (gaminv ([x, NaN], 1, 1), [NaN 0 1 Inf NaN NaN], eps) |
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114 %!assert (gaminv (single ([x, NaN]), 1, 1), single ([NaN 0 1 Inf NaN NaN]), eps ("single")) |
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115 %!assert (gaminv ([x, NaN], single (1), 1), single ([NaN 0 1 Inf NaN NaN]), eps ("single")) |
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116 %!assert (gaminv ([x, NaN], 1, single (1)), single ([NaN 0 1 Inf NaN NaN]), eps ("single")) |
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117 |
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118 %% Test input validation |
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119 %!error gaminv () |
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120 %!error gaminv (1) |
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121 %!error gaminv (1,2) |
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122 %!error gaminv (1,2,3,4) |
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123 %!error gaminv (ones (3), ones (2), ones (2)) |
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124 %!error gaminv (ones (2), ones (3), ones (2)) |
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125 %!error gaminv (ones (2), ones (2), ones (3)) |
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126 %!error gaminv (i, 2, 2) |
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127 %!error gaminv (2, i, 2) |
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128 %!error gaminv (2, 2, i) |
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129 |