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Fix ellipj, ellipke, and expint docstrings * ellipj.cc, ellipke.m, expint.m: Fix docstring signatures and wording.
author Mike Miller <mtmiller@ieee.org>
date Sun, 28 Apr 2013 19:25:50 -0400
parents f423873d3275
children e2de3c8882be
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1 ## Copyright (C) 2006 Sylvain Pelissier <sylvain.pelissier@gmail.com>
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2 ##
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3 ## This file is part of Octave.
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4 ##
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5 ## Octave is free software; you can redistribute it and/or modify it
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6 ## under the terms of the GNU General Public License as published by
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7 ## the Free Software Foundation; either version 3 of the License, or (at
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8 ## your option) any later version.
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9 ##
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10 ## Octave is distributed in the hope that it will be useful, but
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11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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13 ## General Public License for more details.
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14 ##
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15 ## You should have received a copy of the GNU General Public License
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16 ## along with Octave; see the file COPYING. If not, see
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17 ## <http://www.gnu.org/licenses/>.
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18
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19 ## -*- texinfo -*-
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20 ## @deftypefn {Function File} {} expint (@var{x})
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21 ## Compute the exponential integral,
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22 ## @tex
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23 ## $$
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24 ## E_1 (x) = \int_x^\infty {e^{-t} \over t} dt.
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25 ## $$
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26 ## @end tex
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27 ## @ifnottex
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28 ##
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29 ## @example
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30 ## @group
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31 ## infinity
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32 ## /
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33 ## expint (x) = | exp (-t)/t dt
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34 ## /
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35 ## x
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36 ## @end group
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37 ## @end example
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38 ##
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39 ## @end ifnottex
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40 ## @end deftypefn
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41
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42 function y = expint (x)
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43
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44 if (nargin != 1)
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45 print_usage ();
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46 endif
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47
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48 y = expint_E1 (x);
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49
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50 endfunction
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51
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52 ## -*- texinfo -*-
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53 ## @deftypefn {Function File} {@var{y} =} expint_E1 (@var{x})
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54 ## Compute the exponential integral,
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55 ## @verbatim
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56 ## infinity
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57 ## /
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58 ## expint(x) = | exp(-t)/t dt
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59 ## /
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60 ## x
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61 ## @end verbatim
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62 ## @end deftypefn
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63
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64 function y = expint_E1 (x)
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65
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66 if (nargin != 1)
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67 print_usage ();
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68 endif
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69
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70 y = x;
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71
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72 idx = (imag (x) > 0 & imag (x) != 0);
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73 y(idx) = -expint_Ei (-y(idx)) - i.*pi;
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74
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75 idx = (imag (x) < 0 & imag (x) != 0);
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76 y(idx) = -expint_Ei (-y(idx)) + i.*pi;
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77
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78 idx = (real (x) >= 0 & imag (x) == 0);
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79 y(idx) = -expint_Ei (-y(idx));
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80
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81 idx = (real (x) < 0 & imag (x) == 0);
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82 y(idx) = -expint_Ei (-y(idx)) - i.*pi;
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83
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84 endfunction
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85
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86 ## -*- texinfo -*-
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87 ## @deftypefn {Function File} {@var{y} =} expint_Ei (@var{x})
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88 ## Compute the exponential integral,
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89 ## @verbatim
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90 ## infinity
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91 ## /
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92 ## expint_Ei(x) = - | exp(t)/t dt
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93 ## /
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94 ## -x
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95 ## @end verbatim
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96 ## @end deftypefn
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97
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98 function y = expint_Ei (x)
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99
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100 if (nargin != 1)
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101 print_usage ();
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102 endif
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103
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104 y = zeros (size (x));
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105 F = @(x) exp (-x)./x;
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106 s = prod (size (x));
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107
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108 for t = 1:s;
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109 if (x(t) < 0 && imag (x(t)) == 0)
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110 y(t) = -quad (F, -x(t), Inf);
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111 else
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112 if (abs (x(t)) > 2 && imag (x(t)) == 0)
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113 y(t) = expint_Ei (2) - quad (F, -x(t), -2);
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114 else
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115 if (abs (x(t)) >= 10)
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116 if (imag (x(t)) <= 0)
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117 a1 = 4.03640;
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118 a2 = 1.15198;
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119 b1 = 5.03637;
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120 b2 = 4.19160;
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121 y(t) = -(x(t).^2 - a1.*x(t) + a2) ...
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122 ./ ((x(t).^2 - b1.*x(t) + b2) .* (-x(t)) .* exp (-x(t))) ...
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123 - i.*pi;
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124 else
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125 y(t) = conj (expint_Ei (conj (x(t))));
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126 endif;
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127 ## Serie Expansion
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128 else
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129 for k = 1:100;
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130 y(t) = y(t) + x(t).^k ./ (k.*factorial (k));
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131 endfor
16586
f423873d3275 Style fixes for ellipj.cc, ellipke.m, and expint.m
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132 y(t) = 0.577215664901532860606512090082402431 + log (x(t)) + y(t);
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133 endif
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134 endif
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135 endif
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136 endfor
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137 endfunction
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138
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139 %% Test against A&S Table 5.1
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140 %!test
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141 %! x = [5:5:50]'/100;
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142 %! gamma = 0.5772156649;
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143 %! y_exp = [0.9876375971;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
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parents: 16584
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144 %! 0.9755453033;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
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parents: 16584
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145 %! 0.9637156702;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
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146 %! 0.9521414833;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
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147 %! 0.9408157528;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
148 %! 0.9297317075;
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Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
149 %! 0.9188827858;
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parents: 16584
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150 %! 0.9082626297;
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parents: 16584
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151 %! 0.8978650778;
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parents: 16584
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152 %! 0.8876841584 ];
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153 %! y = (expint (x) + log(x) + gamma) ./ x;
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154 %! assert (y, y_exp, 1e-9);
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155 %!test
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156 %! x = [50:5:95]'/100;
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157 %! y_exp = [0.559773595;
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parents: 16584
diff changeset
158 %! 0.503364081;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
159 %! 0.454379503;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
160 %! 0.411516976;
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Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
161 %! 0.373768843;
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Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
162 %! 0.340340813;
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Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
163 %! 0.310596579;
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Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
164 %! 0.284019269;
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Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
165 %! 0.260183939;
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Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
166 %! 0.238737524 ];
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parents: 16584
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167 %! y = expint (x);
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168 %! assert (y, y_exp, 1e-9);
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169 %!test
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170 %! x = [100:5:145]'/100;
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171 %! y_exp = [0.219383934;
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parents: 16584
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172 %! 0.201872813;
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Mike Miller <mtmiller@ieee.org>
parents: 16584
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173 %! 0.185990905;
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Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
174 %! 0.171555354;
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Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
175 %! 0.158408437;
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Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
176 %! 0.146413373;
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Mike Miller <mtmiller@ieee.org>
parents: 16584
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177 %! 0.135450958;
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Mike Miller <mtmiller@ieee.org>
parents: 16584
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178 %! 0.125416844;
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parents: 16584
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179 %! 0.116219313;
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Mike Miller <mtmiller@ieee.org>
parents: 16584
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180 %! 0.107777440 ];
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181 %! y = expint (x);
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182 %! assert (y, y_exp, 1e-9);
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183 %!test
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184 %! x = [150:5:200]'/100;
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185 %! y_exp = [0.100019582;
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186 %! 0.092882108;
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Mike Miller <mtmiller@ieee.org>
parents: 16584
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187 %! 0.086308334;
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Mike Miller <mtmiller@ieee.org>
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188 %! 0.080247627;
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Mike Miller <mtmiller@ieee.org>
parents: 16584
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189 %! 0.074654644;
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Mike Miller <mtmiller@ieee.org>
parents: 16584
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190 %! 0.069488685;
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Mike Miller <mtmiller@ieee.org>
parents: 16584
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191 %! 0.064713129;
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Mike Miller <mtmiller@ieee.org>
parents: 16584
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192 %! 0.060294967;
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Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
193 %! 0.056204378;
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Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
194 %! 0.052414380;
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Mike Miller <mtmiller@ieee.org>
parents: 16584
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195 %! 0.048900511 ];
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196 %! y = expint (x);
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197 %! assert (y, y_exp, 1e-9);
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198
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199 %% Test input validation
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200 %!error expint ()
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201 %!error expint (1,2)