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annotate src/DLD-FUNCTIONS/gammainc.cc @ 11586:12df7854fa7c

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author John W. Eaton <jwe@octave.org>
date Thu, 20 Jan 2011 17:24:59 -0500
parents 01f703952eff
children 72c96de7a403
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1 /*
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2
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3 Copyright (C) 1997-2011 John W. Eaton
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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 the
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9 Free Software Foundation; either version 3 of the License, or (at your
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10 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 WITHOUT
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13 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
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14 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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15 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 */
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22
28d5f556b8cf [project @ 1999-07-15 16:02:57 by jwe]
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23 #ifdef HAVE_CONFIG_H
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24 #include <config.h>
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25 #endif
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26
28d5f556b8cf [project @ 1999-07-15 16:02:57 by jwe]
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27 #include "lo-specfun.h"
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28
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29 #include "defun-dld.h"
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30 #include "error.h"
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31 #include "gripes.h"
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32 #include "oct-obj.h"
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33 #include "utils.h"
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34
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35 DEFUN_DLD (gammainc, args, ,
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36 "-*- texinfo -*-\n\
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37 @deftypefn {Mapping Function} {} gammainc (@var{x}, @var{a})\n\
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38 @deftypefnx {Mapping Function} {} gammainc (@var{x}, @var{a}, \"lower\")\n\
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39 @deftypefnx {Mapping Function} {} gammainc (@var{x}, @var{a}, \"upper\")\n\
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40 Compute the normalized incomplete gamma function,\n\
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41 @tex\n\
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42 $$\n\
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43 \\gamma (x, a) = {1 \\over {\\Gamma (a)}}\\displaystyle{\\int_0^x t^{a-1} e^{-t} dt}\n\
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44 $$\n\
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45 @end tex\n\
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46 @ifnottex\n\
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47 \n\
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48 @example\n\
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49 @group\n\
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50 x\n\
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51 1 /\n\
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52 gammainc (x, a) = --------- | exp (-t) t^(a-1) dt\n\
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53 gamma (a) /\n\
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54 t=0\n\
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55 @end group\n\
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56 @end example\n\
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57 \n\
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58 @end ifnottex\n\
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59 with the limiting value of 1 as @var{x} approaches infinity.\n\
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60 The standard notation is @math{P(a,x)}, e.g., Abramowitz and Stegun (6.5.1).\n\
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61 \n\
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62 If @var{a} is scalar, then @code{gammainc (@var{x}, @var{a})} is returned\n\
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63 for each element of @var{x} and vice versa.\n\
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64 \n\
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65 If neither @var{x} nor @var{a} is scalar, the sizes of @var{x} and\n\
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66 @var{a} must agree, and @code{gammainc} is applied element-by-element.\n\
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67 \n\
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68 By default the incomplete gamma function integrated from 0 to @var{x} is\n\
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69 computed. If \"upper\" is given then the complementary function integrated\n\
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70 from @var{x} to infinity is calculated. It should be noted that\n\
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71 \n\
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72 @example\n\
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73 gammainc (@var{x}, @var{a}) @equiv{} 1 - gammainc (@var{x}, @var{a}, \"upper\")\n\
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74 @end example\n\
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75 @seealso{gamma, lgamma}\n\
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76 @end deftypefn")
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77 {
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78 octave_value retval;
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79 bool lower = true;
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80
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81 int nargin = args.length ();
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82
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83 if (nargin == 3)
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84 {
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85 if (args(2).is_string ())
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86 {
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87 std::string s = args(2).string_value ();
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88 std::transform (s.begin (), s.end (), s.begin (), tolower);
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89 if (s == "upper")
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90 lower = false;
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91 else if (s != "lower")
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92 error ("gammainc: third argument must be \"lower\" or \"upper\"");
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93 }
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94 else
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95 error ("gammainc: third argument must be \"lower\" or \"upper\"");
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96
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97 }
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98
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99 if (!error_state && nargin >= 2 && nargin <= 3)
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100 {
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101 octave_value x_arg = args(0);
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102 octave_value a_arg = args(1);
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103
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104 // FIXME Can we make a template version of the duplicated code below
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105 if (x_arg.is_single_type () || a_arg.is_single_type ())
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106 {
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107 if (x_arg.is_scalar_type ())
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108 {
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109 float x = x_arg.float_value ();
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110
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111 if (! error_state)
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112 {
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113 if (a_arg.is_scalar_type ())
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114 {
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115 float a = a_arg.float_value ();
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116
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117 if (! error_state)
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118 retval = lower ? gammainc (x, a)
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119 : static_cast<float>(1) - gammainc (x, a);
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120 }
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121 else
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122 {
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123 FloatNDArray a = a_arg.float_array_value ();
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124
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125 if (! error_state)
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126 retval = lower ? gammainc (x, a)
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127 : static_cast<float>(1) - gammainc (x, a);
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128 }
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129 }
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130 }
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131 else
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132 {
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133 FloatNDArray x = x_arg.float_array_value ();
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134
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135 if (! error_state)
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136 {
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137 if (a_arg.is_scalar_type ())
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138 {
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139 float a = a_arg.float_value ();
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140
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141 if (! error_state)
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142 retval = lower ? gammainc (x, a)
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143 : static_cast<float>(1) - gammainc (x, a);
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144 }
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145 else
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146 {
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147 FloatNDArray a = a_arg.float_array_value ();
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148
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149 if (! error_state)
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150 retval = lower ? gammainc (x, a)
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151 : static_cast<float>(1) - gammainc (x, a);
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152 }
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153 }
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154 }
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155 }
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156 else
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157 {
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158 if (x_arg.is_scalar_type ())
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159 {
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160 double x = x_arg.double_value ();
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161
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162 if (! error_state)
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163 {
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164 if (a_arg.is_scalar_type ())
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165 {
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166 double a = a_arg.double_value ();
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167
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168 if (! error_state)
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169 retval = lower ? gammainc (x, a) : 1. - gammainc (x, a);
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170 }
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171 else
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172 {
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173 NDArray a = a_arg.array_value ();
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174
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175 if (! error_state)
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176 retval = lower ? gammainc (x, a) : 1. - gammainc (x, a);
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177 }
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178 }
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179 }
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180 else
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181 {
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182 NDArray x = x_arg.array_value ();
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183
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184 if (! error_state)
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185 {
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186 if (a_arg.is_scalar_type ())
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187 {
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188 double a = a_arg.double_value ();
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189
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190 if (! error_state)
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191 retval = lower ? gammainc (x, a) : 1. - gammainc (x, a);
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192 }
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193 else
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194 {
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195 NDArray a = a_arg.array_value ();
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196
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197 if (! error_state)
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198 retval = lower ? gammainc (x, a) : 1. - gammainc (x, a);
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199 }
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200 }
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201 }
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202 }
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203 }
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204 else
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205 print_usage ();
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206
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207 return retval;
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208 }
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209
28d5f556b8cf [project @ 1999-07-15 16:02:57 by jwe]
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210 /*
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211
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212 %!test
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213 %! a = [.5 .5 .5 .5 .5];
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214 %! x = [0 1 2 3 4];
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215 %! v1 = sqrt(pi)*erf(x)./gamma(a);
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216 %! v3 = gammainc(x.*x,a);
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217 %! assert(v1, v3, sqrt(eps));
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218
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219 %!assert (gammainc(0:4,0.5,"upper"), 1-gammainc(0:4,0.5),1e-10)
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220
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221 %!test
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222 %! a = single ([.5 .5 .5 .5 .5]);
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223 %! x = single([0 1 2 3 4]);
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224 %! v1 = sqrt(pi('single'))*erf(x)./gamma(a);
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225 %! v3 = gammainc(x.*x,a);
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226 %! assert(v1, v3, sqrt(eps('single')));
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227
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228 %!assert (gammainc(single(0:4),single(0.5),"upper"), single(1)-gammainc(single(0:4),single(0.5)),single(1e-7))
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229
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230 */