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annotate libinterp/corefcn/__betainc__.cc @ 29958:32c3a5805893

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move DEFUN and DEFMETHOD functions inside octave namespace * mk-opts.pl: Surround emitted function definitions with OCTAVE_NAMESPACE_BEGIN and OCTAVE_NAMESPACE_END tags. * mk-builtins.pl: Surround emitted function declarations with OCTAVE_NAMESPACE_BEGIN and OCTAVE_NAMESPACE_END tags. Emit deprecated global inline functions. * __betainc__.cc, __contourc__.cc, __dsearchn__.cc, __eigs__.cc, __expint__.cc, __ftp__.cc, __gammainc__.cc, __ichol__.cc, __ilu__.cc, __lin_interpn__.cc, __magick_read__.cc, __pchip_deriv__.cc, __qp__.cc, amd.cc, balance.cc, besselj.cc, bitfcns.cc, bsxfun.cc, call-stack.cc, ccolamd.cc, cellfun.cc, chol.cc, colamd.cc, colloc.cc, conv2.cc, daspk.cc, dasrt.cc, dassl.cc, data.cc, debug.cc, defaults.cc, defun.cc, det.cc, dirfns.cc, display.cc, dlmread.cc, dmperm.cc, dot.cc, eig.cc, ellipj.cc, environment.cc, error.cc, event-manager.cc, fcn-info.cc, fft.cc, fft2.cc, fftn.cc, file-io.cc, filter.cc, find.cc, gcd.cc, getgrent.cc, getpwent.cc, getrusage.cc, givens.cc, graphics.cc, gsvd.cc, hash.cc, help.cc, hess.cc, hex2num.cc, input.cc, interpreter.cc, inv.cc, jsondecode.cc, jsonencode.cc, kron.cc, load-path.cc, load-save.cc, lookup.cc, ls-oct-text.cc, lsode.cc, lu.cc, mappers.cc, matrix_type.cc, max.cc, mgorth.cc, nproc.cc, oct-hist.cc, ordqz.cc, ordschur.cc, pager.cc, pinv.cc, pr-flt-fmt.cc, pr-output.cc, psi.cc, qr.cc, quad.cc, quadcc.cc, qz.cc, rand.cc, rcond.cc, regexp.cc, schur.cc, settings.cc, sighandlers.cc, sparse.cc, spparms.cc, sqrtm.cc, stream-euler.cc, strfind.cc, strfns.cc, sub2ind.cc, svd.cc, sylvester.cc, symbfact.cc, symrcm.cc, symtab.cc, syscalls.cc, sysdep.cc, time.cc, toplev.cc, tril.cc, tsearch.cc, typecast.cc, urlwrite.cc, utils.cc, variables.cc, __delaunayn__.cc, __fltk_uigetfile__.cc, __glpk__.cc, __init_gnuplot__.cc, __ode15__.cc, __voronoi__.cc, audiodevinfo.cc, audioread.cc, convhulln.cc, fftw.cc, gzip.cc, ov-base.cc, ov-bool-mat.cc, ov-cell.cc, ov-class.cc, ov-classdef.cc, ov-fcn-handle.cc, ov-java.cc, ov-null-mat.cc, ov-oncleanup.cc, ov-struct.cc, ov-typeinfo.cc, ov-usr-fcn.cc, ov.cc, octave.cc, lex.ll, oct-parse.yy, profiler.cc, pt-eval.cc: Surround DEFUN and DEFMETHOD function defnitions with OCTAVE_NAMESPACE_BEGIN and OCTAVE_NAMESPACE_END tags.
author John W. Eaton <jwe@octave.org>
date Fri, 13 Aug 2021 21:53:51 -0400
parents 7854d5752dd2
children 7d6709900da7
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1 ////////////////////////////////////////////////////////////////////////
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2 //
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3 // Copyright (C) 2018-2021 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 #if defined (HAVE_CONFIG_H)
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27 # include "config.h"
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28 #endif
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29
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30 #include "defun.h"
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31 #include "dNDArray.h"
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32 #include "fNDArray.h"
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33
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34 OCTAVE_NAMESPACE_BEGIN
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35
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36 DEFUN (__betainc__, args, ,
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37 doc: /* -*- texinfo -*-
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38 @deftypefn {} {@var{y} =} __betainc__ (@var{x}, @var{a}, @var{b})
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39 Continued fraction for incomplete beta function.
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40 @end deftypefn */)
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41 {
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42 if (args.length () != 3)
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43 print_usage ();
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44
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45 bool is_single = (args(0).is_single_type () || args(1).is_single_type ()
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46 || args(2).is_single_type ());
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47
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48 // Total number of scenarios: get maximum of length of all vectors
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49 int numel_x = args(0).numel ();
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50 int numel_a = args(1).numel ();
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51 int numel_b = args(2).numel ();
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52 int len = std::max (std::max (numel_x, numel_a), numel_b);
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53
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54 octave_value_list retval;
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55 // Initialize output dimension vector
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56 dim_vector output_dv (len, 1);
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57
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58 // Lentz's algorithm in two cases: single and double precision
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59 if (is_single)
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60 {
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61 // Initialize output and inputs
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62 FloatColumnVector output (output_dv);
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63 FloatNDArray x, a, b;
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64
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65 if (numel_x == 1)
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66 x = FloatNDArray (output_dv, args(0).float_scalar_value ());
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67 else
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68 x = args(0).float_array_value ();
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69
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70
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71 if (numel_a == 1)
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72 a = FloatNDArray (output_dv, args(1).float_scalar_value ());
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73 else
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74 a = args(1).float_array_value ();
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75
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76 if (numel_b == 1)
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77 b = FloatNDArray (output_dv, args(2).float_scalar_value ());
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78 else
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79 b = args(2).float_array_value ();
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80
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81 // Initialize variables used in algorithm
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82 static const float tiny = octave::math::exp2 (-50.0f);
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83 static const float eps = std::numeric_limits<float>::epsilon ();
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84 float xj, x2, y, Cj, Dj, aj, bj, Deltaj, alpha_j, beta_j;
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85 int j, maxit;
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86 maxit = 200;
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87
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88 // Loop over all elements
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89 for (octave_idx_type i = 0; i < len; ++i)
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90 {
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91 // Catch Ctrl+C
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92 OCTAVE_QUIT;
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93
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94 // Variable initialization for the current element
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95 xj = x(i);
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96 y = tiny;
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97 Cj = y;
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98 Dj = 0;
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99 aj = a(i);
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100 bj = b(i);
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101 Deltaj = 0;
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102 alpha_j = 1;
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103 beta_j = aj - (aj * (aj + bj)) / (aj + 1) * xj;
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104 x2 = xj * xj;
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105 j = 1;
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106
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107 // Lentz's algorithm
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108 while ((std::abs ((Deltaj - 1)) > eps) && (j < maxit))
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109 {
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110 Dj = beta_j + alpha_j * Dj;
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111 if (Dj == 0)
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112 Dj = tiny;
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113 Cj = beta_j + alpha_j / Cj;
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114 if (Cj == 0)
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115 Cj = tiny;
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116 Dj = 1 / Dj;
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117 Deltaj = Cj * Dj;
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118 y *= Deltaj;
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119 alpha_j = ((aj + j - 1) * (aj + bj + j -1) * (bj - j) * j)
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120 / ((aj + 2 * j - 1) * (aj + 2 * j - 1)) * x2;
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121 beta_j = aj + 2 * j + ((j * (bj - j)) / (aj + 2 * j - 1)
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122 - ((aj + j) * (aj + bj + j)) / (aj + 2 * j + 1)) * xj;
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123 j++;
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124 }
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125
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126 output(i) = y;
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127 }
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128
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129 retval(0) = output;
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130 }
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131 else
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132 {
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133 // Initialize output and inputs
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134 ColumnVector output (output_dv);
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135 NDArray x, a, b;
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136
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137 if (numel_x == 1)
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138 x = NDArray (output_dv, args(0).scalar_value ());
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139 else
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140 x = args(0).array_value ();
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141
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142 if (numel_a == 1)
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143 a = NDArray (output_dv, args(1).scalar_value ());
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144 else
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145 a = args(1).array_value ();
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146
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147 if (numel_b == 1)
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148 b = NDArray (output_dv, args(2).scalar_value ());
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149 else
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150 b = args(2).array_value ();
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151
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152 // Initialize variables used in algorithm
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153 static const double tiny = octave::math::exp2 (-100.0);
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154 static const double eps = std::numeric_limits<double>::epsilon ();
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155 double xj, x2, y, Cj, Dj, aj, bj, Deltaj, alpha_j, beta_j;
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156 int j, maxit;
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157 maxit = 200;
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158
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159 // Loop over all elements
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160 for (octave_idx_type i = 0; i < len; ++i)
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161 {
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162 // Catch Ctrl+C
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163 OCTAVE_QUIT;
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164
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165 // Variable initialization for the current element
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166 xj = x(i);
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167 y = tiny;
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168 Cj = y;
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169 Dj = 0;
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170 aj = a(i);
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171 bj = b(i);
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172 Deltaj = 0;
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173 alpha_j = 1;
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174 beta_j = aj - (aj * (aj + bj)) / (aj + 1) * xj;
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175 x2 = xj * xj;
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176 j = 1;
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177
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178 // Lentz's algorithm
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179 while ((std::abs ((Deltaj - 1)) > eps) && (j < maxit))
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180 {
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181 Dj = beta_j + alpha_j * Dj;
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182 if (Dj == 0)
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183 Dj = tiny;
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184 Cj = beta_j + alpha_j / Cj;
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185 if (Cj == 0)
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186 Cj = tiny;
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187 Dj = 1 / Dj;
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188 Deltaj = Cj * Dj;
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189 y *= Deltaj;
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190 alpha_j = ((aj + j - 1) * (aj + bj + j - 1) * (bj - j) * j)
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191 / ((aj + 2 * j - 1) * (aj + 2 * j - 1)) * x2;
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192 beta_j = aj + 2 * j + ((j * (bj - j)) / (aj + 2 * j - 1)
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193 - ((aj + j) * (aj + bj + j)) / (aj + 2 * j + 1)) * xj;
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194 j++;
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195 }
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196
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197 output(i) = y;
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198 }
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199
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200 retval(0) = output;
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201 }
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202
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203 return retval;
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204 }
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205
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206 OCTAVE_NAMESPACE_END