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Add and fix tests for ellipj, ellipke, and expint * ellipj.cc: Fix demo, add validation tests. * ellipke.m: Fix assert arguments, add tests. * expint.m: Add tests.
author Mike Miller <mtmiller@ieee.org>
date Sun, 28 Apr 2013 17:08:11 -0400
parents 2f766ceeb03e
children f423873d3275
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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 program is free software; you can redistribute it and/or modify it under
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4 ## the terms of the GNU General Public License as published by the Free Software
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5 ## Foundation; either version 3 of the License, or (at your option) any later
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6 ## version.
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7 ##
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8 ## This program is distributed in the hope that it will be useful, but WITHOUT
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9 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
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10 ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
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11 ## details.
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12 ##
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13 ## You should have received a copy of the GNU General Public License along with
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14 ## this program; if not, see <http://www.gnu.org/licenses/>.
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15
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16 ## -*- texinfo -*-
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17 ## @deftypefn {Function File} {@var{y} =} expint (@var{x})
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18 ## Compute the exponential integral,
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19 ## @verbatim
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20 ## infinity
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21 ## /
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22 ## expint(x) = | exp(t)/t dt
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23 ## /
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24 ## x
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25 ## @end verbatim
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26 ## @seealso{expint_E1, expint_Ei}
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27 ## @end deftypefn
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28
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29 function y = expint(x)
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30 if (nargin != 1)
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31 print_usage;
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32 endif
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33 y = expint_E1(x);
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34 endfunction
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35
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36 ## -*- texinfo -*-
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37 ## @deftypefn {Function File} {@var{y} =} expint_E1 (@var{x})
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38 ## Compute the exponential integral,
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39 ## @verbatim
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40 ## infinity
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41 ## /
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42 ## expint(x) = | exp(t)/t dt
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43 ## /
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44 ## x
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45 ## @end verbatim
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46 ## @seealso{expint, expint_Ei}
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47 ## @end deftypefn
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48
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49 function y = expint_E1(x)
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50 if (nargin != 1)
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51 print_usage;
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52 endif
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53 y = x;
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54 y(imag(x) > 0 & imag(x) != 0) = -expint_Ei(-y(imag(x) > 0 & imag(x) != 0)) -i.*pi;
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55 y(imag(x) < 0 & imag(x) != 0) = -expint_Ei(-y(imag(x) < 0 & imag(x) != 0)) +i.*pi;
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56 y(real(x) >= 0 & imag(x)==0) = -expint_Ei(-y(real(x) >= 0 & imag(x)==0));
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57 y(real(x) < 0 & imag(x)==0) = -expint_Ei(-y(real(x) < 0 & imag(x)==0)) -i.*pi;
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58 endfunction
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59
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60 ## -*- texinfo -*-
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61 ## @deftypefn {Function File} {@var{y} =} expint_Ei (@var{x})
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62 ## Compute the exponential integral,
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63 ## @verbatim
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64 ## infinity
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65 ## /
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66 ## expint_Ei(x) = - | exp(t)/t dt
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67 ## /
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68 ## -x
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69 ## @end verbatim
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70 ## @seealso{expint, expint_E1}
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71 ## @end deftypefn
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72
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73 function y = expint_Ei(x)
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74 if (nargin != 1)
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75 print_usage;
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76 endif
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77 y = zeros(size(x));
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78 F = @(x) exp(-x)./x;
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79 s = prod(size(x));
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80 for t = 1:s;
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81 if(x(t)<0 && imag(x(t)) == 0)
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82 y(t) = -quad(F,-x(t),Inf);
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83 else
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84 if(abs(x(t)) > 2 && imag(x(t)) == 0)
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85 y(t) = expint_Ei(2) - quad(F,-x(t),-2);
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86 else
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87 if(abs(x(t)) >= 10)
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88 if(imag(x(t)) <= 0)
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89 a1 = 4.03640;
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90 a2 = 1.15198;
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91 b1 = 5.03637;
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92 b2 = 4.19160;
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93 y(t) = -(x(t).^2 - a1.*x(t) + a2)./((x(t).^2-b1.*x(t)+b2).*(-x(t)).*exp(-x(t)))-i.*pi;
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94 else
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95 y(t) = conj(expint_Ei(conj(x(t))));
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96 endif;
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97 ## Serie Expansion
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98 else
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99 for k = 1:100;
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100 y(t) = y(t) + x(t).^k./(k.*factorial(k));
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101 endfor
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102 y(t) = 0.577215664901532860606512090082402431 + log(x(t)) + y(t);
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103 endif
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104 endif
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105 endif
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106 endfor
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107 endfunction
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108
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109 %% Test against A&S Table 5.1
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110 %!test
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111 %! x = [5:5:50]'/100;
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112 %! gamma = 0.5772156649;
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113 %! y_exp = [0.9876375971;
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114 %! 0.9755453033;
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115 %! 0.9637156702;
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116 %! 0.9521414833;
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117 %! 0.9408157528;
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118 %! 0.9297317075;
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119 %! 0.9188827858;
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120 %! 0.9082626297;
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121 %! 0.8978650778;
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122 %! 0.8876841584 ];
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123 %! y = (expint (x) + log(x) + gamma) ./ x;
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124 %! assert (y, y_exp, 1e-9);
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125 %!test
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126 %! x = [50:5:95]'/100;
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127 %! y_exp = [0.559773595;
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128 %! 0.503364081;
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129 %! 0.454379503;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
130 %! 0.411516976;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
131 %! 0.373768843;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
132 %! 0.340340813;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
133 %! 0.310596579;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
134 %! 0.284019269;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
135 %! 0.260183939;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
136 %! 0.238737524 ];
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
137 %! y = expint (x);
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
138 %! assert (y, y_exp, 1e-9);
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
139 %!test
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
140 %! x = [100:5:145]'/100;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
141 %! y_exp = [0.219383934;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
142 %! 0.201872813;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
143 %! 0.185990905;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
144 %! 0.171555354;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
145 %! 0.158408437;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
146 %! 0.146413373;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
147 %! 0.135450958;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
148 %! 0.125416844;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
149 %! 0.116219313;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
150 %! 0.107777440 ];
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
151 %! y = expint (x);
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
152 %! assert (y, y_exp, 1e-9);
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
153 %!test
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
154 %! x = [150:5:200]'/100;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
155 %! y_exp = [0.100019582;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
156 %! 0.092882108;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
157 %! 0.086308334;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
158 %! 0.080247627;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
159 %! 0.074654644;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
160 %! 0.069488685;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
161 %! 0.064713129;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
162 %! 0.060294967;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
163 %! 0.056204378;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
164 %! 0.052414380;
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
165 %! 0.048900511 ];
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
166 %! y = expint (x);
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
167 %! assert (y, y_exp, 1e-9);
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
168
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
169 %% Test input validation
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
170 %!error expint ()
1a3bfb14b5da Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents: 16584
diff changeset
171 %!error expint (1,2)