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nbininv.m: Increase speed (85X) and accuracy of function (bug #34363). * nbininv.m: Call new function scalar_nbininv to calculate nbininv for scalar. If there are still uncalculated values then call bin_search_nbininv. Call bin_search_nbininv directly for vectors. Add more BIST tests. * nbininv.m (scalar_binoinv): New subfunction to calculate nbininv for scalar x. Stops when x > 1000. * nbininv.m (bin_search_nbininv): New subfunction to do binary search for nbininv.
author Lachlan Andrew <lachlanbis@gmail.com>
date Sun, 11 Oct 2015 20:33:37 -0700
parents d9341b422488
children
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1 ## Copyright (C) 2013-2015 Julien Bect
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2 ## Copyright (C) 2012 Rik Wehbring
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3 ## Copyright (C) 1995-2015 Kurt Hornik
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4 ##
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5 ## This file is part of Octave.
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6 ##
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7 ## Octave is free software; you can redistribute it and/or modify it
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8 ## under the terms of the GNU General Public License as published by
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9 ## the Free Software Foundation; either version 3 of the License, or (at
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10 ## your option) any later version.
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11 ##
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12 ## Octave is distributed in the hope that it will be useful, but
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13 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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14 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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15 ## General Public License for more details.
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16 ##
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17 ## You should have received a copy of the GNU General Public License
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18 ## along with Octave; see the file COPYING. If not, see
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19 ## <http://www.gnu.org/licenses/>.
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20
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21 ## -*- texinfo -*-
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22 ## @deftypefn {Function File} {} tcdf (@var{x}, @var{n})
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23 ## For each element of @var{x}, compute the cumulative distribution function
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24 ## (CDF) at @var{x} of the t (Student) distribution with
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25 ## @var{n} degrees of freedom.
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26 ## @end deftypefn
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27
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28 ## Author: KH <Kurt.Hornik@wu-wien.ac.at>
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29 ## Description: CDF of the t distribution
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30
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31 function cdf = tcdf (x, n)
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32
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33 if (nargin != 2)
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34 print_usage ();
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35 endif
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36
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37 if (! isscalar (n))
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38 [retval, x, n] = common_size (x, n);
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39 if (retval > 0)
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40 error ("tcdf: X and N must be of common size or scalars");
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41 endif
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42 endif
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43
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44 if (iscomplex (x) || iscomplex (n))
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45 error ("tcdf: X and N must not be complex");
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46 endif
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47
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48 if (isa (x, "single") || isa (n, "single"))
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49 cdf = zeros (size (x), "single");
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50 else
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51 cdf = zeros (size (x));
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52 endif
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53
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54 k = ! isinf (x) & (n > 0);
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55
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56 xx = x .^ 2;
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57 x_big_abs = (xx > n);
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58
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59 ## deal with the case "abs(x) big"
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60 kk = k & x_big_abs;
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61 if (isscalar (n))
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62 cdf(kk) = betainc (n ./ (n + xx(kk)), n/2, 1/2) / 2;
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63 else
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64 cdf(kk) = betainc (n(kk) ./ (n(kk) + xx(kk)), n(kk)/2, 1/2) / 2;
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65 endif
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66
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67 ## deal with the case "abs(x) small"
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68 kk = k & !x_big_abs;
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69 if (isscalar (n))
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70 cdf(kk) = 0.5 * (1 - betainc (xx(kk) ./ (n + xx(kk)), 1/2, n/2));
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71 else
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72 cdf(kk) = 0.5 * (1 - betainc (xx(kk) ./ (n(kk) + xx(kk)), 1/2, n(kk)/2));
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73 endif
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74
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75 k &= (x > 0);
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76 if (any (k(:)))
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77 cdf(k) = 1 - cdf(k);
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78 endif
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79
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80 k = isnan (x) | !(n > 0);
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81 cdf(k) = NaN;
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82
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83 k = (x == Inf) & (n > 0);
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84 cdf(k) = 1;
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85
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86 endfunction
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87
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88
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89 %!shared x,y
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90 %! x = [-Inf 0 1 Inf];
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91 %! y = [0 1/2 3/4 1];
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92 %!assert (tcdf (x, ones (1,4)), y, eps)
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93 %!assert (tcdf (x, 1), y, eps)
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94 %!assert (tcdf (x, [0 1 NaN 1]), [NaN 1/2 NaN 1], eps)
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95 %!assert (tcdf ([x(1:2) NaN x(4)], 1), [y(1:2) NaN y(4)], eps)
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96
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97 ## Test class of input preserved
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98 %!assert (tcdf ([x, NaN], 1), [y, NaN], eps)
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99 %!assert (tcdf (single ([x, NaN]), 1), single ([y, NaN]), eps ("single"))
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100 %!assert (tcdf ([x, NaN], single (1)), single ([y, NaN]), eps ("single"))
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101
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102 ## Test input validation
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103 %!error tcdf ()
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104 %!error tcdf (1)
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105 %!error tcdf (1,2,3)
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106 %!error tcdf (ones (3), ones (2))
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107 %!error tcdf (ones (2), ones (3))
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108 %!error tcdf (i, 2)
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109 %!error tcdf (2, i)
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110
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111 ## Check some reference values
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112
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113 %!shared tol_rel
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114 %! tol_rel = 10 * eps;
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115
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116 ## check accuracy for small positive values
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117 %!assert (tcdf (10^(-10), 2.5), 0.50000000003618087, -tol_rel)
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118 %!assert (tcdf (10^(-11), 2.5), 0.50000000000361809, -tol_rel)
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119 %!assert (tcdf (10^(-12), 2.5), 0.50000000000036181, -tol_rel)
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120 %!assert (tcdf (10^(-13), 2.5), 0.50000000000003618, -tol_rel)
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121 %!assert (tcdf (10^(-14), 2.5), 0.50000000000000362, -tol_rel)
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122 %!assert (tcdf (10^(-15), 2.5), 0.50000000000000036, -tol_rel)
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123 %!assert (tcdf (10^(-16), 2.5), 0.50000000000000004, -tol_rel)
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124
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125 ## check accuracy for large negative values
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126 %!assert (tcdf (-10^1, 2.5), 2.2207478836537124e-03, -tol_rel)
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127 %!assert (tcdf (-10^2, 2.5), 7.1916492116661878e-06, -tol_rel)
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128 %!assert (tcdf (-10^3, 2.5), 2.2747463948307452e-08, -tol_rel)
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129 %!assert (tcdf (-10^4, 2.5), 7.1933970159922115e-11, -tol_rel)
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130 %!assert (tcdf (-10^5, 2.5), 2.2747519231756221e-13, -tol_rel)
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131
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Julien Bect <julien.bect@supelec.fr>
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132 ## # Reference values obtained using Python 2.7.4 and mpmath 0.17
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133 ##
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134 ## from mpmath import *
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135 ##
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136 ## mp.dps = 100
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137 ##
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138 ## def F(x_in, nu_in):
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139 ## x = mpf(x_in);
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140 ## nu = mpf(nu_in);
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141 ## t = nu / (nu + x*x)
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142 ## a = nu / 2
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143 ## b = mpf(0.5)
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144 ## F = betainc(a, b, 0, t, regularized=True) / 2
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145 ## if (x > 0):
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146 ## F = 1 - F
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147 ## return F
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148 ##
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149 ## nu = 2.5
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150 ##
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151 ## for i in range(1, 6):
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152 ## x = - power(mpf(10), mpf(i))
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153 ## print "%%!assert (tcdf (-10^%d, 2.5), %s, -eps)" \
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154 ## % (i, nstr(F(x, nu), 17))
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155 ##
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156 ## for i in range(10, 17):
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157 ## x = power(mpf(10), -mpf(i))
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158 ## print "%%!assert (tcdf (10^(-%d), 2.5), %s, -eps)" \
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159 ## % (i, nstr(F(x, nu), 17))
17338
1c89599167a6 maint: End m-files with 1 blank line.
Rik <rik@octave.org>
parents: 17218
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160