Mercurial > octave

annotate scripts/specfun/betainc.m @ 24921:6b33ee8aad0f stable

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
Fixed authors in betainc -- changed libinterp/corefcn/__betainc_lentz__.cc changed scripts/specfun/betainc.m
author Michele Ginesi <michele.ginesi@gmail.com>
date Wed, 21 Feb 2018 23:29:03 +0100
parents ed6f6bbed604
children 40ab8be7d7ec
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
24921
6b33ee8aad0f Fixed authors in betainc
Michele Ginesi <michele.ginesi@gmail.com>
parents: 24919
diff changeset
1 ## Copyright (C) 2018 Stefan Schlögl
6b33ee8aad0f Fixed authors in betainc
Michele Ginesi <michele.ginesi@gmail.com>
parents: 24919
diff changeset
2 ## Copyright (C) 2018 Michele Ginesi
24907
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
3 ##
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
4 ## This file is part of Octave.
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
5 ##
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
6 ## Octave is free software; you can redistribute it and/or modify it
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
7 ## under the terms of the GNU General Public License as published by
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
8 ## the Free Software Foundation; either version 3 of the License, or
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
9 ## (at your option) any later version.
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
10 ##
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
11 ## Octave is distributed in the hope that it will be useful, but
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
12 ## WITHOUT ANY WARRANTY; without even the implied warranty of
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
13 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
14 ## GNU General Public License for more details.
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
15 ##
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
16 ## You should have received a copy of the GNU General Public License
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
17 ## along with Octave; see the file COPYING. If not, see
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
18 ## <http://www.gnu.org/licenses/>.
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
19
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
20 ## Authors: Michele Ginesi <michele.ginesi@gmail.com>
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
21
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
22 ## -*- texinfo -*-
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
23 ## @deftypefn {} {} betainc (@var{x}, @var{a}, @var{b})
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
24 ## @deftypefnx {} {} betainc (@var{x}, @var{a}, @var{b}, @var{tail})
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
25 ## Compute the incomplete beta function ratio.
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
26 ##
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
27 ## This is defined as
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
28 ## @tex
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
29 ## $$
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
30 ## I_x (a, b) = {1 \over {B(a,b)}} \displaystyle{\int_0^x t^{a-1} (1-t)^{b-1} dt}
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
31 ## $$
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
32 ## @end tex
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
33 ## @ifnottex
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
34 ##
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
35 ## @example
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
36 ## @group
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
37 ## x
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
38 ## /
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
39 ## |
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
40 ## I_x (a, b) = | t^(a-1) (1-t)^(b-1) dt
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
41 ## |
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
42 ## /
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
43 ## 0
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
44 ## @end group
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
45 ## @end example
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
46 ##
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
47 ## @end ifnottex
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
48 ##
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
49 ## with @var{x} real in [0,1], @var{a} and @var{b} real and strictly positive.
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
50 ## If one of the input has more than one components, then the others must be
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
51 ## scalar or of compatible dimensions.
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
52 ##
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
53 ## By default or if @var{tail} is @qcode{"lower"} the incomplete beta function
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
54 ## ratio integrated from 0 to @var{x} is computed. If @var{tail} is
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
55 ## @qcode{"upper"} then the complementary function integrated from @var{x} to
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
56 ## 1 is calculated. The two choices are related as
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
57 ##
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
58 ## betainc (@var{x}, @var{a}, @var{b}, @qcode{"lower"}) =
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
59 ## 1 - betainc (@var{x}, @var{a}, @var{b}, @qcode{"upper"}).
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
60 ##
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
61 ## Reference
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
62 ##
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
63 ## @nospell{A. Cuyt, V. Brevik Petersen, B. Verdonk, H. Waadeland, W.B. Jones}
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
64 ## @cite{Handbook of Continued Fractions for Special Functions},
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
65 ## ch. 18.
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
66 ##
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
67 ## @seealso{beta, betaincinv, betaln}
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
68 ##
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
69 ## @end deftypefn
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
70
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
71 function [y] = betainc (x, a, b, tail = "lower")
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
72
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
73 if (nargin > 4 || nargin < 3)
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
74 print_usage ();
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
75 endif
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
76
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
77 if (! isscalar (x) || ! isscalar (a) || ! isscalar (b))
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
78 [err, x, a, b] = common_size (x, a, b);
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
79 if (err > 0)
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
80 error ("betainc: x, a and b must be of common size or scalars");
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
81 endif
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
82 endif
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
83
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
84 if (iscomplex (x) || iscomplex (a) || iscomplex (b))
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
85 error ("betainc: inputs must be real or integer");
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
86 endif
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
87
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
88 if (any (a <= 0))
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
89 error ("betainc: a must be strictly positive");
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
90 endif
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
91
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
92 if (any (b <= 0))
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
93 error ("betainc: b must be strictly positive");
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
94 endif
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
95
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
96 if (any (x > 1 | x < 0))
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
97 error ("betainc: x must be between 0 and 1");
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
98 endif
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
99
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
100 if (isinteger (x))
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
101 y = double (x);
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
102 endif
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
103
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
104 if (isinteger (a))
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
105 a = double (a);
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
106 endif
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
107
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
108 if (isinteger (b))
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
109 b = double (b);
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
110 endif
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
111
24919
ed6f6bbed604 betainc: vectorized the Lentz's algorithm
Michele Ginesi <michele.ginesi@gmail.com>
parents: 24907
diff changeset
112 sz = size (x);
ed6f6bbed604 betainc: vectorized the Lentz's algorithm
Michele Ginesi <michele.ginesi@gmail.com>
parents: 24907
diff changeset
113 x = x(:);
ed6f6bbed604 betainc: vectorized the Lentz's algorithm
Michele Ginesi <michele.ginesi@gmail.com>
parents: 24907
diff changeset
114 a = a(:);
ed6f6bbed604 betainc: vectorized the Lentz's algorithm
Michele Ginesi <michele.ginesi@gmail.com>
parents: 24907
diff changeset
115 b = b(:);
24907
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
116 y = zeros (size (x));
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
117
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
118 # If any of the argument is single, also the output should be
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
119
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
120 if (strcmpi (class (y), "single") || strcmpi (class (a), "single") || strcmpi (class (b), "single"))
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
121 a = single (a);
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
122 b = single (b);
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
123 x = single (x);
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
124 y = single (y);
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
125 endif
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
126
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
127 # In the following, we use the fact that the continued fraction we will
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
128 # use is more efficient when x <= a / (a+b).
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
129 # Moreover, to compute the upper version, which is defined as
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
130 # I_x(a,b,"upper") = 1 - I_x(a,b) we used the property
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
131 # I_x(a,b) + I_(1-x) (b,a) = 1.
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
132
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
133 if (strcmpi (tail, "upper"))
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
134 flag = (x < a./(a+b));
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
135 x(!flag) = 1 - x(!flag);
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
136 [a(!flag), b(!flag)] = deal (b(!flag), a(!flag));
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
137 elseif (strcmpi (tail, "lower"))
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
138 flag = (x > a./(a+b));
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
139 x (flag) = 1 - x(flag);
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
140 [a(flag), b(flag)] = deal (b(flag), a(flag));
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
141 else
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
142 error ("betainc: invalid value for flag")
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
143 endif
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
144
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
145 f = zeros (size (x), class (x));
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
146
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
147 ## Continued fractions: CPVWJ, formula 18.5.20, modified Lentz algorithm
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
148 ## implemented in a separate .cc file. This particular continued fraction
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
149 ## gives (B(a,b) * I_x(a,b)) / (x^a * (1-x)^b).
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
150
24919
ed6f6bbed604 betainc: vectorized the Lentz's algorithm
Michele Ginesi <michele.ginesi@gmail.com>
parents: 24907
diff changeset
151 f = __betainc_lentz__ (x, a, b, strcmpi (class (x), "single"));
ed6f6bbed604 betainc: vectorized the Lentz's algorithm
Michele Ginesi <michele.ginesi@gmail.com>
parents: 24907
diff changeset
152
24907
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
153 # We divide the continued fraction by B(a,b) / (x^a * (1-x)^b)
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
154 # to obtain I_x(a,b).
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
155 y = a .* log (x) + b .* log1p (-x) + gammaln (a + b) - ...
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
156 gammaln (a) - gammaln (b) + log (f);
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
157 y = real (exp (y));
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
158 y(flag) = 1 - y(flag);
24919
ed6f6bbed604 betainc: vectorized the Lentz's algorithm
Michele Ginesi <michele.ginesi@gmail.com>
parents: 24907
diff changeset
159 y = reshape (y, sz);
24907
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
160
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
161 endfunction
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
162
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
163 ## Tests from betainc.cc
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
164
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
165 # Double precision
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
166 %!test
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
167 %! a = [1, 1.5, 2, 3];
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
168 %! b = [4, 3, 2, 1];
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
169 %! v1 = betainc (1,a,b);
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
170 %! v2 = [1,1,1,1];
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
171 %! x = [.2, .4, .6, .8];
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
172 %! v3 = betainc (x, a, b);
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
173 %! v4 = 1 - betainc (1.-x, b, a);
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
174 %! assert (v1, v2, sqrt (eps));
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
175 %! assert (v3, v4, sqrt (eps));
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
176
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
177 # Single precision
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
178 %!test
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
179 %! a = single ([1, 1.5, 2, 3]);
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
180 %! b = single ([4, 3, 2, 1]);
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
181 %! v1 = betainc (1,a,b);
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
182 %! v2 = single ([1,1,1,1]);
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
183 %! x = single ([.2, .4, .6, .8]);
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
184 %! v3 = betainc (x, a, b);
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
185 %! v4 = 1 - betainc (1.-x, b, a);
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
186 %! assert (v1, v2, sqrt (eps ("single")));
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
187 %! assert (v3, v4, sqrt (eps ("single")));
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
188
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
189 # Mixed double/single precision
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
190 %!test
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
191 %! a = single ([1, 1.5, 2, 3]);
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
192 %! b = [4, 3, 2, 1];
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
193 %! v1 = betainc (1,a,b);
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
194 %! v2 = single ([1,1,1,1]);
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
195 %! x = [.2, .4, .6, .8];
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
196 %! v3 = betainc (x, a, b);
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
197 %! v4 = 1-betainc (1.-x, b, a);
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
198 %! assert (v1, v2, sqrt (eps ("single")));
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
199 %! assert (v3, v4, sqrt (eps ("single")));
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
200
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
201 ## New test
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
202
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
203 %!test #<51157>
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
204 %! y = betainc([0.00780;0.00782;0.00784],250.005,49750.995);
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
205 %! y_ex = [0.999999999999989; 0.999999999999992; 0.999999999999995];
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
206 %! assert (y, y_ex, -1e-14);
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
207
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
208 %!assert (betainc (0.001, 20, 30), 2.750687665855991e-47, -3e-14);
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
209 %!assert (betainc (0.0001, 20, 30), 2.819953178893307e-67, -3e-14);
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
210 %!assert (betainc (0.99, 20, 30, "upper"), 1.5671643161872703e-47, -3e-14);
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
211 %!assert (betainc (0.999, 20, 30, "upper"), 1.850806276141535e-77, -3e-14);
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
212 %!assert (betainc (0.5, 200, 300), 0.9999964565197356, -1e-15);
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
213 %!assert (betainc (0.5, 200, 300, "upper"), 3.54348026439253e-06, -1e-13);
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
214
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
215 # Test trivial values
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
216
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
217 %!test
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
218 %! [a,b] = ndgrid (linspace(1e-4, 100, 20), linspace(1e-4, 100, 20));
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
219 %! assert (betainc (0,a,b), zeros(20));
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
220 %! assert (betainc (1,a,b), ones(20));
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
221
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
222 ## Test input validation
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
223
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
224 %!error betainc ()
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
225 %!error betainc (1)
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
226 %!error betainc (1,2)
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
227 %!error betainc (1.1,1,1)
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
228 %!error betainc (-0.1,1,1)
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
229 %!error betainc (0.5,0,1)
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
230 %!error betainc (0.5,1,0)
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
231 %!error betainc (1,2,3,4)
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
232 %!error betainc (1,2)
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
233 %!error betainc (1,2,3,4,5)
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
234 %!error betainc (0.5i, 1, 2)
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
235 %!error betainc (0, 1i, 1)
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
236 %!error betainc (0, 1, 1i)