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annotate src/DLD-FUNCTIONS/gammainc.cc @ 11415:e7ed20f87e82

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Add @tex blocks to gammainc and legendre docstrings.
author Michael Godfrey <godfrey@isl.stanford.edu>
date Sun, 26 Dec 2010 21:28:20 -0800
parents 89f4d7e294cc
children fd0a3ac60b0e
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1 /*
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2
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3 Copyright (C) 1997, 1999, 2000, 2004, 2005, 2006, 2007, 2008,
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4 2009 John W. Eaton
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5
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6 This file is part of Octave.
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7
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8 Octave is free software; you can redistribute it and/or modify it
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9 under the terms of the GNU General Public License as published by the
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10 Free Software Foundation; either version 3 of the License, or (at your
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11 option) any later version.
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12
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13 Octave is distributed in the hope that it will be useful, but WITHOUT
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14 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
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15 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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16 for more details.
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17
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18 You should have received a copy of the GNU General Public License
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19 along with Octave; see the file COPYING. If not, see
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20 <http://www.gnu.org/licenses/>.
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21
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22 */
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23
28d5f556b8cf [project @ 1999-07-15 16:02:57 by jwe]
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24 #ifdef HAVE_CONFIG_H
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25 #include <config.h>
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26 #endif
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27
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28 #include "lo-specfun.h"
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29
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30 #include "defun-dld.h"
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31 #include "error.h"
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32 #include "gripes.h"
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33 #include "oct-obj.h"
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34 #include "utils.h"
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35
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36 DEFUN_DLD (gammainc, args, ,
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37 "-*- texinfo -*-\n\
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38 @deftypefn {Mapping Function} {} gammainc (@var{x}, @var{a})\n\
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39 @deftypefnx {Mapping Function} {} gammainc (@var{x}, @var{a}, \"lower\")\n\
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40 @deftypefnx {Mapping Function} {} gammainc (@var{x}, @var{a}, \"upper\")\n\
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41 Compute the normalized incomplete gamma function,\n\
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42 @tex\n\
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43 $$\n\
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44 \\gamma (x, a) = {1 \\over {\\Gamma (a)}}\\displaystyle{\\int_0^x t^{a-1} e^{-t} dt}\n\
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45 $$\n\
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46 @end tex\n\
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47 @ifnottex\n\
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48 \n\
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49 @example\n\
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50 @group\n\
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51 x\n\
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52 1 /\n\
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53 gammainc (x, a) = --------- | exp (-t) t^(a-1) dt\n\
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54 gamma (a) /\n\
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55 t=0\n\
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56 @end group\n\
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57 @end example\n\
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58 \n\
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59 @end ifnottex\n\
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60 with the limiting value of 1 as @var{x} approaches infinity.\n\
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61 The standard notation is @math{P(a,x)}, e.g., Abramowitz and Stegun (6.5.1).\n\
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62 \n\
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63 If @var{a} is scalar, then @code{gammainc (@var{x}, @var{a})} is returned\n\
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64 for each element of @var{x} and vice versa.\n\
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65 \n\
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66 If neither @var{x} nor @var{a} is scalar, the sizes of @var{x} and\n\
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67 @var{a} must agree, and @code{gammainc} is applied element-by-element.\n\
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68 \n\
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69 By default the incomplete gamma function integrated from 0 to @var{x} is\n\
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70 computed. If \"upper\" is given then the complementary function integrated\n\
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71 from @var{x} to infinity is calculated. It should be noted that\n\
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72 \n\
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73 @example\n\
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74 gammainc (@var{x}, @var{a}) @equiv{} 1 - gammainc (@var{x}, @var{a}, \"upper\")\n\
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75 @end example\n\
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76 @seealso{gamma, lgamma}\n\
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77 @end deftypefn")
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78 {
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79 octave_value retval;
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80 bool lower = true;
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81
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82 int nargin = args.length ();
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83
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84 if (nargin == 3)
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85 {
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86 if (args(2).is_string ())
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87 {
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88 std::string s = args(2).string_value ();
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89 std::transform (s.begin (), s.end (), s.begin (), tolower);
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90 if (s == "upper")
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91 lower = false;
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92 else if (s != "lower")
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93 error ("expecting third argument to be \"lower\" or \"upper\"");
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94 }
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95 else
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96 error ("expecting third argument to be \"lower\" or \"upper\"");
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97
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98 }
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99
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100 if (!error_state && nargin >= 2 && nargin <= 3)
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101 {
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102 octave_value x_arg = args(0);
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103 octave_value a_arg = args(1);
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104
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105 // FIXME Can we make a template version of the duplicated code below
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106 if (x_arg.is_single_type () || a_arg.is_single_type ())
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107 {
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108 if (x_arg.is_scalar_type ())
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109 {
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110 float x = x_arg.float_value ();
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111
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112 if (! error_state)
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113 {
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114 if (a_arg.is_scalar_type ())
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115 {
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116 float a = a_arg.float_value ();
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117
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118 if (! error_state)
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119 retval = lower ? gammainc (x, a)
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120 : static_cast<float>(1) - gammainc (x, a);
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121 }
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122 else
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123 {
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124 FloatNDArray a = a_arg.float_array_value ();
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125
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126 if (! error_state)
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127 retval = lower ? gammainc (x, a)
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128 : static_cast<float>(1) - gammainc (x, a);
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129 }
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130 }
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131 }
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132 else
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133 {
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134 FloatNDArray x = x_arg.float_array_value ();
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135
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136 if (! error_state)
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137 {
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138 if (a_arg.is_scalar_type ())
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139 {
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140 float a = a_arg.float_value ();
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141
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142 if (! error_state)
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143 retval = lower ? gammainc (x, a)
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144 : static_cast<float>(1) - gammainc (x, a);
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145 }
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146 else
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147 {
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148 FloatNDArray a = a_arg.float_array_value ();
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149
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150 if (! error_state)
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151 retval = lower ? gammainc (x, a)
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152 : static_cast<float>(1) - gammainc (x, a);
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153 }
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154 }
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155 }
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156 }
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157 else
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158 {
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159 if (x_arg.is_scalar_type ())
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160 {
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161 double x = x_arg.double_value ();
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162
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163 if (! error_state)
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164 {
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165 if (a_arg.is_scalar_type ())
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166 {
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167 double a = a_arg.double_value ();
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168
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169 if (! error_state)
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170 retval = lower ? gammainc (x, a) : 1. - gammainc (x, a);
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171 }
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172 else
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173 {
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174 NDArray a = a_arg.array_value ();
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175
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176 if (! error_state)
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177 retval = lower ? gammainc (x, a) : 1. - gammainc (x, a);
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178 }
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179 }
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180 }
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181 else
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182 {
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183 NDArray x = x_arg.array_value ();
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184
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185 if (! error_state)
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186 {
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187 if (a_arg.is_scalar_type ())
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188 {
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189 double a = a_arg.double_value ();
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190
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191 if (! error_state)
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192 retval = lower ? gammainc (x, a) : 1. - gammainc (x, a);
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193 }
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194 else
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195 {
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196 NDArray a = a_arg.array_value ();
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197
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198 if (! error_state)
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199 retval = lower ? gammainc (x, a) : 1. - gammainc (x, a);
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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 }
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205 else
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206 print_usage ();
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207
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208 return retval;
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209 }
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210
28d5f556b8cf [project @ 1999-07-15 16:02:57 by jwe]
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211 /*
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212
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213 %!test
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214 %! a = [.5 .5 .5 .5 .5];
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215 %! x = [0 1 2 3 4];
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216 %! v1 = sqrt(pi)*erf(x)./gamma(a);
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217 %! v3 = gammainc(x.*x,a);
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218 %! assert(v1, v3, sqrt(eps));
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219
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220 %!assert (gammainc(0:4,0.5,"upper"), 1-gammainc(0:4,0.5),1e-10)
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221
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222 %!test
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223 %! a = single ([.5 .5 .5 .5 .5]);
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224 %! x = single([0 1 2 3 4]);
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225 %! v1 = sqrt(pi('single'))*erf(x)./gamma(a);
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226 %! v3 = gammainc(x.*x,a);
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227 %! assert(v1, v3, sqrt(eps('single')));
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228
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229 %!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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230
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231 */