Mercurial > octave
annotate scripts/specfun/betainc.m @ 27918:b442ec6dda5c
use centralized file for copyright info for individual contributors
* COPYRIGHT.md: New file.
* In most other files, use "Copyright (C) YYYY-YYYY The Octave Project
Developers" instead of tracking individual names in separate source
files. The motivation is to reduce the effort required to update the
notices each year.
Until now, the Octave source files contained copyright notices that
list individual contributors. I adopted these file-scope copyright
notices because that is what everyone was doing 30 years ago in the
days before distributed version control systems. But now, with many
contributors and modern version control systems, having these
file-scope copyright notices causes trouble when we update copyright
years or refactor code.
Over time, the file-scope copyright notices may become outdated as new
contributions are made or code is moved from one file to
another. Sometimes people contribute significant patches but do not
add a line claiming copyright. Other times, people add a copyright
notice for their contribution but then a later refactoring moves part
or all of their contribution to another file and the notice is not
moved with the code. As a practical matter, moving such notices is
difficult -- determining what parts are due to a particular
contributor requires a time-consuming search through the project
history. Even managing the yearly update of copyright years is
problematic. We have some contributors who are no longer
living. Should we update the copyright dates for their contributions
when we release new versions? Probably not, but we do still want to
claim copyright for the project as a whole.
To minimize the difficulty of maintaining the copyright notices, I
would like to change Octave's sources to use what is described here:
https://softwarefreedom.org/resources/2012/ManagingCopyrightInformation.html
in the section "Maintaining centralized copyright notices":
The centralized notice approach consolidates all copyright
notices in a single location, usually a top-level file.
This file should contain all of the copyright notices
provided project contributors, unless the contribution was
clearly insignificant. It may also credit -- without a copyright
notice -- anyone who helped with the project but did not
contribute code or other copyrighted material.
This approach captures less information about contributions
within individual files, recognizing that the DVCS is better
equipped to record those details. As we mentioned before, it
does have one disadvantage as compared to the file-scope
approach: if a single file is separated from the distribution,
the recipient won't see the contributors' copyright notices.
But this can be easily remedied by including a single
copyright notice in each file's header, pointing to the
top-level file:
Copyright YYYY-YYYY The Octave Project Developers
See the COPYRIGHT file at the top-level directory
of this distribution or at https://octave.org/COPYRIGHT.html.
followed by the usual GPL copyright statement.
For more background, see the discussion here:
https://lists.gnu.org/archive/html/octave-maintainers/2020-01/msg00009.html
Most files in the following directories have been skipped intentinally
in this changeset:
doc
libgui/qterminal
liboctave/external
m4
author | John W. Eaton <jwe@octave.org> |
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date | Mon, 06 Jan 2020 15:38:17 -0500 |
parents | 04e5cb5e2cb3 |
children | 1891570abac8 |
rev | line source |
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1 ## Copyright (C) 2018-2019 The Octave Project Developers |
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2 ## |
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3 ## See the file COPYRIGHT.md in the top-level directory of this distribution |
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4 ## or <https://octave.org/COPYRIGHT.html/>. |
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5 ## |
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6 ## |
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7 ## This file is part of Octave. |
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8 ## |
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9 ## Octave is free software: you can redistribute it and/or modify it |
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10 ## under the terms of the GNU General Public License as published by |
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11 ## the Free Software Foundation; either version 3 of the License, or |
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12 ## (at your option) any later version. |
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13 ## |
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14 ## Octave is distributed in the hope that it will be useful, but |
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15 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
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16 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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17 ## GNU General Public License for more details. |
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18 ## |
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19 ## You should have received a copy of the GNU General Public License |
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20 ## along with Octave; see the file COPYING. If not, see |
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21 ## <https://www.gnu.org/licenses/>. |
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22 |
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23 ## -*- texinfo -*- |
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24 ## @deftypefn {} {} betainc (@var{x}, @var{a}, @var{b}) |
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25 ## @deftypefnx {} {} betainc (@var{x}, @var{a}, @var{b}, @var{tail}) |
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26 ## Compute the incomplete beta function. |
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27 ## |
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28 ## This is defined as |
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29 ## @tex |
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30 ## $$ |
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31 ## I_x (a, b) = {1 \over {B(a,b)}} \displaystyle{\int_0^x t^{a-1} (1-t)^{b-1} dt} |
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32 ## $$ |
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33 ## @end tex |
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34 ## @ifnottex |
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35 ## |
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36 ## @example |
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37 ## @group |
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38 ## x |
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39 ## / |
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40 ## | |
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41 ## I_x (a, b) = | t^(a-1) (1-t)^(b-1) dt |
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42 ## | |
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43 ## / |
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44 ## 0 |
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45 ## @end group |
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46 ## @end example |
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47 ## |
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48 ## @end ifnottex |
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49 ## |
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50 ## with real @var{x} in the range [0,1]. The inputs @var{a} and @var{b} must |
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51 ## be real and strictly positive (> 0). If one of the inputs is not a scalar |
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52 ## then the other inputs must be scalar or of compatible dimensions. |
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53 ## |
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54 ## By default, @var{tail} is @qcode{"lower"} and the incomplete beta function |
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55 ## integrated from 0 to @var{x} is computed. If @var{tail} is @qcode{"upper"} |
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56 ## then the complementary function integrated from @var{x} to 1 is calculated. |
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57 ## The two choices are related by |
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58 ## |
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59 ## betainc (@var{x}, @var{a}, @var{b}, @qcode{"upper"}) = |
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60 ## 1 - betainc (@var{x}, @var{a}, @var{b}, @qcode{"lower"}). |
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61 ## |
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62 ## @code{betainc} uses a more sophisticated algorithm than subtraction to |
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63 ## get numerically accurate results when the @qcode{"lower"} value is small. |
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64 ## |
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65 ## Reference: @nospell{A. Cuyt, V. Brevik Petersen, B. Verdonk, H. Waadeland, |
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66 ## W.B. Jones}, @cite{Handbook of Continued Fractions for Special Functions}, |
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67 ## ch.@: 18. |
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68 ## |
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69 ## @seealso{beta, betaincinv, betaln} |
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70 ## @end deftypefn |
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71 |
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72 function y = betainc (x, a, b, tail = "lower") |
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73 |
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74 if (nargin < 3 || nargin > 4) |
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75 print_usage (); |
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76 endif |
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77 |
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78 [err, x, a, b] = common_size (x, a, b); |
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79 if (err > 0) |
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80 error ("betainc: X, A, and B must be of common size or scalars"); |
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81 endif |
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82 |
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83 if (iscomplex (x) || iscomplex (a) || iscomplex (b)) |
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84 error ("betainc: all inputs must be real"); |
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85 endif |
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86 |
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87 ## Remember original shape of data, but convert to column vector for calcs. |
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88 orig_sz = size (x); |
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89 x = x(:); |
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90 a = a(:); |
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91 b = b(:); |
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92 |
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93 if (any ((x < 0) | (x > 1))) |
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94 error ("betainc: X must be in the range [0, 1]"); |
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95 endif |
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96 |
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97 if (any (a <= 0)) |
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98 error ("betainc: A must be strictly positive"); |
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99 endif |
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100 |
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101 if (any (b <= 0)) |
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102 error ("betainc: B must be strictly positive"); |
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103 endif |
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104 |
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105 ## If any of the arguments is single then the output should be as well. |
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106 if (strcmp (class (x), "single") || strcmp (class (a), "single") |
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107 || strcmp (class (b), "single")) |
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108 a = single (a); |
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109 b = single (b); |
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110 x = single (x); |
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111 endif |
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112 |
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113 ## Convert to floating point if necessary |
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114 if (isinteger (x)) |
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115 y = double (x); |
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116 endif |
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117 if (isinteger (a)) |
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118 a = double (a); |
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119 endif |
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120 if (isinteger (b)) |
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121 b = double (b); |
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122 endif |
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123 |
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124 ## Initialize output array |
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125 y = zeros (size (x), class (x)); |
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126 |
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127 ## In the following, we use the fact that the continued fraction Octave uses |
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128 ## is more efficient when x <= a / (a + b). Moreover, to compute the upper |
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129 ## version, which is defined as I_x(a,b,"upper") = 1 - I_x(a,b) we use the |
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130 ## property I_x(a,b) + I_(1-x) (b,a) = 1. |
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131 |
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132 if (strcmpi (tail, "lower")) |
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133 fflag = (x > a./(a+b)); |
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134 x(fflag) = 1 - x(fflag); |
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135 [a(fflag), b(fflag)] = deal (b(fflag), a(fflag)); |
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136 elseif (strcmpi (tail, "upper")) |
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137 fflag = (x < (a ./ (a + b))); |
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138 x(! fflag) = 1 - x(! fflag); |
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139 [a(! fflag), b(! fflag)] = deal (b(! fflag), a(! fflag)); |
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140 else |
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141 error ("betainc: invalid value for TAIL"); |
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142 endif |
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143 |
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144 f = zeros (size (x), class (x)); |
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145 |
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146 ## Continued fractions: CPVWJ, formula 18.5.20, modified Lentz algorithm |
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147 ## implemented in a separate .cc file. This particular continued fraction |
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148 ## gives (B(a,b) * I_x(a,b)) / (x^a * (1-x)^b). |
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149 |
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150 f = __betainc__ (x, a, b); |
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151 |
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152 ## Divide continued fraction by B(a,b) / (x^a * (1-x)^b) to obtain I_x(a,b). |
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153 y = a .* log (x) + b .* log1p (-x) ... |
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154 + (gammaln (a + b) - gammaln (a) - gammaln (b)) + log (f); |
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155 y = real (exp (y)); |
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156 y(fflag) = 1 - y(fflag); |
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157 |
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158 ## Restore original shape |
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159 y = reshape (y, orig_sz); |
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160 |
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161 endfunction |
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162 |
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163 |
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164 ## Double precision |
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165 %!test |
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166 %! a = [1, 1.5, 2, 3]; |
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167 %! b = [4, 3, 2, 1]; |
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168 %! v1 = betainc (1, a, b); |
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169 %! v2 = [1,1,1,1]; |
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170 %! x = [.2, .4, .6, .8]; |
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171 %! v3 = betainc (x, a, b); |
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172 %! v4 = 1 - betainc (1-x, b, a); |
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173 %! assert (v1, v2, sqrt (eps)); |
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174 %! assert (v3, v4, sqrt (eps)); |
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175 |
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176 ## Single precision |
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177 %!test |
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178 %! a = single ([1, 1.5, 2, 3]); |
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179 %! b = single ([4, 3, 2, 1]); |
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180 %! v1 = betainc (1, a, b); |
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181 %! v2 = single ([1,1,1,1]); |
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182 %! x = single ([.2, .4, .6, .8]); |
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183 %! v3 = betainc (x, a, b); |
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184 %! v4 = 1 - betainc (1-x, b, a); |
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185 %! assert (v1, v2, sqrt (eps ("single"))); |
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186 %! assert (v3, v4, sqrt (eps ("single"))); |
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187 |
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188 ## Mixed double/single precision |
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189 %!test |
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190 %! a = single ([1, 1.5, 2, 3]); |
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191 %! b = [4, 3, 2, 1]; |
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192 %! v1 = betainc (1,a,b); |
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193 %! v2 = single ([1,1,1,1]); |
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194 %! x = [.2, .4, .6, .8]; |
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195 %! v3 = betainc (x, a, b); |
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196 %! v4 = 1-betainc (1.-x, b, a); |
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197 %! assert (v1, v2, sqrt (eps ("single"))); |
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198 %! assert (v3, v4, sqrt (eps ("single"))); |
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199 |
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200 %!test <*51157> |
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201 %! y = betainc ([0.00780;0.00782;0.00784],250.005,49750.995); |
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202 %! y_ex = [0.999999999999989; 0.999999999999992; 0.999999999999995]; |
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203 %! assert (y, y_ex, -1e-14); |
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204 |
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205 %!assert (betainc (0.001, 20, 30), 2.750687665855991e-47, -3e-14); |
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206 %!assert (betainc (0.0001, 20, 30), 2.819953178893307e-67, -7e-14); |
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207 %!assert <*54383> (betainc (0.99, 20, 30, "upper"), 1.5671643161872703e-47, -7e-14); |
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208 %!assert (betainc (0.999, 20, 30, "upper"), 1.850806276141535e-77, -7e-14); |
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209 %!assert (betainc (0.5, 200, 300), 0.9999964565197356, -1e-15); |
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210 %!assert (betainc (0.5, 200, 300, "upper"), 3.54348026439253e-06, -3e-13); |
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211 |
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212 ## Test trivial values |
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213 %!test |
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214 %! [a,b] = ndgrid (linspace (1e-4, 100, 20), linspace (1e-4, 100, 20)); |
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215 %! assert (betainc (0, a, b), zeros (20)); |
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216 %! assert (betainc (1, a, b), ones (20)); |
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Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
217 |
26946
04e5cb5e2cb3
update bug status in tests
John W. Eaton <jwe@octave.org>
parents:
26514
diff
changeset
|
218 %!test <*34405> |
25015
baa7e37453b1
Added more tests for betainc and expint.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
24996
diff
changeset
|
219 %! assert (betainc (NaN, 1, 2), NaN); |
baa7e37453b1
Added more tests for betainc and expint.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
24996
diff
changeset
|
220 %! assert (betainc (0.5, 1, Inf), NaN); |
baa7e37453b1
Added more tests for betainc and expint.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
24996
diff
changeset
|
221 |
24907
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 %!error betainc () |
bd89440407aa
Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
224 %!error betainc (1) |
bd89440407aa
Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
225 %!error betainc (1,2) |
bd89440407aa
Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff
changeset
|
226 %!error betainc (1,2,3,4,5) |
24927
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24923
diff
changeset
|
227 %!error <must be of common size or scalars> betainc (ones (2,2), ones (1,2), 1) |
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24923
diff
changeset
|
228 %!error <all inputs must be real> betainc (0.5i, 1, 2) |
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24923
diff
changeset
|
229 %!error <all inputs must be real> betainc (0, 1i, 1) |
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24923
diff
changeset
|
230 %!error <all inputs must be real> betainc (0, 1, 1i) |
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24923
diff
changeset
|
231 %!error <X must be in the range \[0, 1\]> betainc (-0.1,1,1) |
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24923
diff
changeset
|
232 %!error <X must be in the range \[0, 1\]> betainc (1.1,1,1) |
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24923
diff
changeset
|
233 %!error <X must be in the range \[0, 1\]> |
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24923
diff
changeset
|
234 %! x = ones (1, 1, 2); |
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24923
diff
changeset
|
235 %! x(1,1,2) = -1; |
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24923
diff
changeset
|
236 %! betainc (x,1,1); |
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24923
diff
changeset
|
237 %!error <A must be strictly positive> betainc (0.5,0,1) |
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24923
diff
changeset
|
238 %!error <A must be strictly positive> |
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24923
diff
changeset
|
239 %! a = ones (1, 1, 2); |
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24923
diff
changeset
|
240 %! a(1,1,2) = 0; |
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24923
diff
changeset
|
241 %! betainc (1,a,1); |
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24923
diff
changeset
|
242 %!error <B must be strictly positive> betainc (0.5,1,0) |
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24923
diff
changeset
|
243 %!error <B must be strictly positive> |
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24923
diff
changeset
|
244 %! b = ones (1, 1, 2); |
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24923
diff
changeset
|
245 %! b(1,1,2) = 0; |
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24923
diff
changeset
|
246 %! betainc (1,1,b); |
c280560d9c96
Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents:
24923
diff
changeset
|
247 %!error <invalid value for TAIL> betainc (1,2,3, "foobar") |