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maint: merge stable to default.
author Rik <rik@octave.org>
date Fri, 14 May 2021 08:12:42 -0700
parents ce4436d2b206 2a1f57067fbf
children 26bb2cbf6da2
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1 ########################################################################
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2 ##
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3 ## Copyright (C) 2017-2021 The Octave Project Developers
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4 ##
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5 ## See the file COPYRIGHT.md in the top-level directory of this
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6 ## distribution or <https://octave.org/copyright/>.
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7 ##
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8 ## This file is part of Octave.
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9 ##
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10 ## Octave is free software: you can redistribute it and/or modify it
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11 ## under the terms of the GNU General Public License as published by
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12 ## the Free Software Foundation, either version 3 of the License, or
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13 ## (at your option) any later version.
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14 ##
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15 ## Octave is distributed in the hope that it will be useful, but
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16 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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17 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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18 ## GNU General Public License for more details.
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19 ##
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20 ## You should have received a copy of the GNU General Public License
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21 ## along with Octave; see the file COPYING. If not, see
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22 ## <https://www.gnu.org/licenses/>.
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23 ##
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24 ########################################################################
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25
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26 ## -*- texinfo -*-
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27 ## @deftypefn {} {} betaincinv (@var{y}, @var{a}, @var{b})
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28 ## @deftypefnx {} {} betaincinv (@var{y}, @var{a}, @var{b}, "lower")
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29 ## @deftypefnx {} {} betaincinv (@var{y}, @var{a}, @var{b}, "upper")
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30 ## Compute the inverse of the normalized incomplete beta function.
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31 ##
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32 ## The normalized incomplete beta function is defined as
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33 ## @tex
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34 ## $$
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35 ## I_x (a, b) = {1 \over {B(a,b)}} \displaystyle{\int_0^x t^{a-1} (1-t)^{b-1} dt}
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36 ## $$
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37 ## @end tex
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38 ## @ifnottex
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39 ##
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40 ## @example
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41 ## @group
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42 ## x
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43 ## /
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44 ## 1 |
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45 ## I_x (a, b) = ---------- | t^(a-1) (1-t)^(b-1) dt
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46 ## beta (a,b) |
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47 ## /
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48 ## 0
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49 ## @end group
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50 ## @end example
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51 ##
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52 ## @end ifnottex
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53 ##
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54 ## If two inputs are scalar, then @code{betaincinv (@var{y}, @var{a}, @var{b})}
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55 ## is returned for each of the other inputs.
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56 ##
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57 ## If two or more inputs are not scalar, the sizes of them must agree, and
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58 ## @code{betaincinv} is applied element-by-element.
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59 ##
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60 ## The variable @var{y} must be in the interval [0,1], while @var{a} and
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61 ## @var{b} must be real and strictly positive.
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62 ##
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63 ## By default, @var{tail} is @qcode{"lower"} and the inverse of the incomplete
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64 ## beta function integrated from 0 to @var{x} is computed. If @var{tail} is
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65 ## @qcode{"upper"} then the complementary function integrated from @var{x} to 1
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66 ## is inverted.
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67 ##
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68 ## The function is computed by standard Newton's method, by solving
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69 ## @tex
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70 ## $$
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71 ## y - I_x (a, b) = 0
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72 ## $$
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73 ## @end tex
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74 ## @ifnottex
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75 ##
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76 ## @example
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77 ## @var{y} - betainc (@var{x}, @var{a}, @var{b}) = 0
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78 ## @end example
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79 ##
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80 ## @end ifnottex
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81 ##
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82 ## @seealso{betainc, beta, betaln}
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83 ## @end deftypefn
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84
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85 function x = betaincinv (y, a, b, tail = "lower")
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86
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87 if (nargin < 3)
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88 print_usage ();
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89 endif
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90
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91 [err, y, a, b] = common_size (y, a, b);
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92 if (err > 0)
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93 error ("betaincinv: Y, A, and B must be of common size or scalars");
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94 endif
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95
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96 if (! (isfloat (y) && isfloat (a) && isfloat (b)
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97 && isreal (y) && isreal (a) && isreal (b)))
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98 error ("betaincinv: Y, A, and B must be real, floating point values");
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99 endif
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100
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101 ## Remember original shape of data, but convert to column vector for calcs.
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102 orig_sz = size (y);
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103 y = y(:);
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104 a = a(:);
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105 b = b(:);
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106
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107 if (any ((y < 0) | (y > 1)))
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108 error ("betaincinv: Y must be in the range [0, 1]");
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109 endif
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110
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111 if (any (a <= 0))
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112 error ("betaincinv: A must be strictly positive");
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113 endif
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114
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115 if (any (b <= 0))
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116 error ("betaincinv: B must be strictly positive");
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117 endif
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118
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119 ## If any of the arguments is single then the output should be as well.
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120 if (isa (y, "single") || isa (a, "single") || isa (b, "single"))
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121 y = single (y);
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122 a = single (a);
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123 b = single (b);
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124 endif
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125
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126 ## Initialize output array
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127 x = zeros (size (y), class (y));
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128
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129 ## Parameters for the Newton's method search
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130 maxit = 20;
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131 tol = eps (class (y));
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132
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133 if (strcmpi (tail, "lower"))
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134 p = y;
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diff changeset
135 q = 1 - y;
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diff changeset
136 x(y == 0) = 0;
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diff changeset
137 x(y == 1) = 1;
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diff changeset
138 elseif (strcmpi (tail, "upper"))
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diff changeset
139 p = 1 - y;
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diff changeset
140 q = y;
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diff changeset
141 x(y == 0) = 1;
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142 x(y == 1) = 0;
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143 else
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144 error ("betaincinv: invalid value for TAIL");
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145 endif
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146
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147 ## Special values have been already computed.
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148 todo = (y != 0) & (y != 1);
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149
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150 ## We will invert the lower version for p < 0.5 and the upper otherwise.
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151 i_low = (p < 0.5);
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152 i_upp = (! i_low);
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153
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154 idx = todo & i_low;
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155 if (any (idx))
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156 n = nnz (idx);
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157 ## Function and derivative of the lower version.
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158 F = @(x, a, b, y) y - betainc (x, a, b);
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159 JF = @(x, a, b) -real (exp ((a-1) .* log (x) + (b-1) .* log1p (-x) + ...
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diff changeset
160 gammaln (a+b) - gammaln (a) - gammaln (b)));
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161
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162 ## Compute the initial guess with a bisection method of 10 steps.
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163 x0 = bisection_method (F, zeros (n,1), ones (n,1), ...
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164 a(i_low), b(i_low), p(i_low), 10);
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165
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166 ## Use Newton's method to iteratively find solution.
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167 x(i_low) = newton_method (F, JF, x0, a(i_low), b(i_low), p(i_low), ...
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168 tol, maxit);
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169 endif
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170
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diff changeset
171 idx = todo & i_upp;
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diff changeset
172 if (any (idx))
24927
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173 n = nnz (idx);
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174 ## Function and derivative of the upper version.
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175 F = @(x, a, b, y) y - betainc (x, a, b, "upper");
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176 JF = @(x, a, b) real (exp ((a-1) .* log (x) + (b-1) .* log1p (-x) + ...
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177 gammaln (a+b) - gammaln (a) - gammaln (b)));
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178
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179 ## Compute the initial guess with a bisection method of 10 steps.
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180 x0 = bisection_method (F, zeros (n,1), ones (n,1), ...
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181 a(i_upp), b(i_upp), q(i_upp), 10);
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182
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183 ## Use Newton's method to iteratively find solution.
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184 x(i_upp) = newton_method (F, JF, x0, a(i_upp), b(i_upp), q(i_upp), ...
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185 tol, maxit);
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186 endif
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187
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188 ## Restore original shape
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189 x = reshape (x, orig_sz);
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190
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191 endfunction
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192
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parents:
diff changeset
193
27984
b09432b20a84 maint: Remove special cases of old version control keywords in code base.
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parents: 27978
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194 ## subfunctions: Bisection and Newton Methods
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195 function xc = bisection_method (F, xl, xr, a, b, y, maxit)
28945
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diff changeset
196
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197 F_l = F (xl, a, b, y);
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198 F_r = F (xr, a, b, y);
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diff changeset
199 for it = 1:maxit
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200 xc = (xl + xr) / 2;
24927
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diff changeset
201 F_c = F (xc, a, b, y);
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Michele Ginesi <michele.ginesi@gmail.com>
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diff changeset
202 flag_l = ((F_c .* F_r) < 0);
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parents:
diff changeset
203 flag_r = ((F_c .* F_l) < 0);
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Michele Ginesi <michele.ginesi@gmail.com>
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diff changeset
204 flag_c = (F_c == 0);
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Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
205 xl(flag_l) = xc(flag_l);
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Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
206 xr(flag_r) = xc(flag_r);
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Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
207 xl(flag_c) = xr(flag_c) = xc(flag_c);
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Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
208 F_l(flag_l) = F_c(flag_l);
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Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
209 F_r(flag_r) = F_c(flag_r);
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Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
210 F_l(flag_c) = F_r(flag_c) = 0;
24927
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diff changeset
211 endfor
28945
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diff changeset
212
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213 endfunction
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parents:
diff changeset
214
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Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
215 function x = newton_method (F, JF, x0, a, b, y, tol, maxit);
28945
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diff changeset
216
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diff changeset
217 res = -F (x0, a, b, y) ./ JF (x0, a, b);
29656
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Rik <rik@octave.org>
parents: 29616
diff changeset
218 todo = (abs (res) >= tol * abs (x0));
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diff changeset
219 x = x0;
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Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
220 it = 0;
24927
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diff changeset
221 while (any (todo) && (it < maxit))
24907
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Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
222 it++;
24927
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diff changeset
223 x(todo) += res(todo);
29616
69b6b783a8ab betaincinv.m: Correctly handle inputs very close to 1.0 (bug #60528)
Rik <rik@octave.org>
parents: 29614
diff changeset
224 ## Avoid intermediate values outside betainc() range of [0, 1], bug #60528
69b6b783a8ab betaincinv.m: Correctly handle inputs very close to 1.0 (bug #60528)
Rik <rik@octave.org>
parents: 29614
diff changeset
225 x(x(todo) < 0) = eps;
69b6b783a8ab betaincinv.m: Correctly handle inputs very close to 1.0 (bug #60528)
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parents: 29614
diff changeset
226 x(x(todo) > 1) = 1-eps;
24927
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diff changeset
227 res(todo) = -F(x(todo), a(todo), b(todo), y(todo)) ...
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diff changeset
228 ./ JF (x(todo), a(todo), b(todo));
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Rik <rik@octave.org>
parents: 29614
diff changeset
229 todo = (abs (res) >= tol * abs (x));
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diff changeset
230 endwhile
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parents:
diff changeset
231 x += res;
28945
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parents: 28928
diff changeset
232
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diff changeset
233 endfunction
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parents:
diff changeset
234
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
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parents:
diff changeset
235
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
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parents:
diff changeset
236 %!test
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237 %! x = linspace (0.1, 0.9, 11);
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Michele Ginesi <michele.ginesi@gmail.com>
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diff changeset
238 %! a = [2, 3, 4];
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
239 %! [x,a,b] = ndgrid (x,a,a);
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
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diff changeset
240 %! xx = betaincinv (betainc (x, a, b), a, b);
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
241 %! assert (xx, x, 3e-15);
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Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
242
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
243 %!test
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244 %! x = linspace (0.1, 0.9, 11);
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Michele Ginesi <michele.ginesi@gmail.com>
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diff changeset
245 %! a = [2, 3, 4];
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
246 %! [x,a,b] = ndgrid (x,a,a);
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
247 %! xx = betaincinv (betainc (x, a, b, "upper"), a, b, "upper");
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
248 %! assert (xx, x, 3e-15);
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
249
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
250 %!test
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diff changeset
251 %! x = linspace (0.1, 0.9, 11);
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Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
252 %! a = [0.1:0.1:1];
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Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
253 %! [x,a,b] = ndgrid (x,a,a);
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Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
254 %! xx = betaincinv (betainc (x, a, b), a, b);
24996
f80e68529bbf test: relax tolerances on specfun tests to pass on i386 (bug #53437)
Mike Miller <mtmiller@octave.org>
parents: 24927
diff changeset
255 %! assert (xx, x, 5e-15);
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Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
256
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
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parents:
diff changeset
257 %!test
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258 %! x = linspace (0.1, 0.9, 11);
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parents:
diff changeset
259 %! a = [0.1:0.1:1];
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Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
260 %! [x,a,b] = ndgrid (x,a,a);
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
261 %! xx = betaincinv (betainc (x, a, b, "upper"), a, b, "upper");
24996
f80e68529bbf test: relax tolerances on specfun tests to pass on i386 (bug #53437)
Mike Miller <mtmiller@octave.org>
parents: 24927
diff changeset
262 %! assert (xx, x, 5e-15);
24907
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
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263
24927
c280560d9c96 Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents: 24907
diff changeset
264 ## Test the conservation of the input class
24907
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
265 %!assert (class (betaincinv (0.5, 1, 1)), "double")
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
266 %!assert (class (betaincinv (single (0.5), 1, 1)), "single")
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
267 %!assert (class (betaincinv (0.5, single (1), 1)), "single")
29656
7f5bd197fea6 maint: use std::size_t in more instances (bug #60471)
Rik <rik@octave.org>
parents: 29616
diff changeset
268 %!assert (class (betaincinv (0.5, 1, single (1))), "single")
24907
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
269
29616
69b6b783a8ab betaincinv.m: Correctly handle inputs very close to 1.0 (bug #60528)
Rik <rik@octave.org>
parents: 29614
diff changeset
270 %!assert <*60528> (betaincinv (1e-6, 1, 3), 3.3333344444450657e-07, 5*eps)
69b6b783a8ab betaincinv.m: Correctly handle inputs very close to 1.0 (bug #60528)
Rik <rik@octave.org>
parents: 29614
diff changeset
271 %!assert <*60528> (betaincinv (1-1e-6, 3, 1), 0.999999666666556, 5*eps)
29614
26ba91f0eea7 betaincinv.m: Correctly handle small inputs (bug #60528)
Rik <rik@octave.org>
parents: 29358
diff changeset
272
24907
bd89440407aa Incomplete beta function moved to a .m file, fixing accuracy and
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
273 ## Test input validation
28896
90fea9cc9caa test: Add expected error message <Invalid call> to BIST tests for nargin.
Rik <rik@octave.org>
parents: 28789
diff changeset
274 %!error <Invalid call> betaincinv ()
90fea9cc9caa test: Add expected error message <Invalid call> to BIST tests for nargin.
Rik <rik@octave.org>
parents: 28789
diff changeset
275 %!error <Invalid call> betaincinv (1)
90fea9cc9caa test: Add expected error message <Invalid call> to BIST tests for nargin.
Rik <rik@octave.org>
parents: 28789
diff changeset
276 %!error <Invalid call> betaincinv (1,2)
24927
c280560d9c96 Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents: 24907
diff changeset
277 %!error <must be of common size or scalars>
c280560d9c96 Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents: 24907
diff changeset
278 %! betaincinv (ones (2,2), ones (1,2), 1);
29656
7f5bd197fea6 maint: use std::size_t in more instances (bug #60471)
Rik <rik@octave.org>
parents: 29616
diff changeset
279 %!error <must be .* floating point> betaincinv ('a', 1, 2)
7f5bd197fea6 maint: use std::size_t in more instances (bug #60471)
Rik <rik@octave.org>
parents: 29616
diff changeset
280 %!error <must be .* floating point> betaincinv (0, int8 (1), 1)
7f5bd197fea6 maint: use std::size_t in more instances (bug #60471)
Rik <rik@octave.org>
parents: 29616
diff changeset
281 %!error <must be .* floating point> betaincinv (0, 1, true)
7f5bd197fea6 maint: use std::size_t in more instances (bug #60471)
Rik <rik@octave.org>
parents: 29616
diff changeset
282 %!error <must be real> betaincinv (0.5i, 1, 2)
7f5bd197fea6 maint: use std::size_t in more instances (bug #60471)
Rik <rik@octave.org>
parents: 29616
diff changeset
283 %!error <must be real> betaincinv (0, 1i, 1)
7f5bd197fea6 maint: use std::size_t in more instances (bug #60471)
Rik <rik@octave.org>
parents: 29616
diff changeset
284 %!error <must be real> betaincinv (0, 1, 1i)
24927
c280560d9c96 Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents: 24907
diff changeset
285 %!error <Y must be in the range \[0, 1\]> betaincinv (-0.1,1,1)
c280560d9c96 Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents: 24907
diff changeset
286 %!error <Y must be in the range \[0, 1\]> betaincinv (1.1,1,1)
c280560d9c96 Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents: 24907
diff changeset
287 %!error <Y must be in the range \[0, 1\]>
c280560d9c96 Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents: 24907
diff changeset
288 %! y = ones (1, 1, 2);
c280560d9c96 Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents: 24907
diff changeset
289 %! y(1,1,2) = -1;
c280560d9c96 Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents: 24907
diff changeset
290 %! betaincinv (y,1,1);
c280560d9c96 Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents: 24907
diff changeset
291 %!error <A must be strictly positive> betaincinv (0.5,0,1)
c280560d9c96 Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents: 24907
diff changeset
292 %!error <A must be strictly positive>
c280560d9c96 Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents: 24907
diff changeset
293 %! a = ones (1, 1, 2);
c280560d9c96 Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents: 24907
diff changeset
294 %! a(1,1,2) = 0;
c280560d9c96 Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents: 24907
diff changeset
295 %! betaincinv (1,a,1);
c280560d9c96 Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents: 24907
diff changeset
296 %!error <B must be strictly positive> betaincinv (0.5,1,0)
c280560d9c96 Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents: 24907
diff changeset
297 %!error <B must be strictly positive>
c280560d9c96 Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents: 24907
diff changeset
298 %! b = ones (1, 1, 2);
c280560d9c96 Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents: 24907
diff changeset
299 %! b(1,1,2) = 0;
c280560d9c96 Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents: 24907
diff changeset
300 %! betaincinv (1,1,b);
c280560d9c96 Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents: 24907
diff changeset
301 %!error <invalid value for TAIL> betaincinv (1,2,3, "foobar")