Mercurial > hg > octave-nkf
annotate scripts/specfun/expint.m @ 20830:b65888ec820e draft default tip gccjit
dmalcom gcc jit import
| author | Stefan Mahr <dac922@gmx.de> |
|---|---|
| date | Fri, 27 Feb 2015 16:59:36 +0100 |
| parents | 2645f9ef8c88 |
| children |
| rev | line source |
|---|---|
|
17744
d63878346099
maint: Update copyright notices for release.
John W. Eaton <jwe@octave.org>
parents:
17514
diff
changeset
|
1 ## Copyright (C) 2006, 2013 Sylvain Pelissier |
|
16584
2f766ceeb03e
Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff
changeset
|
2 ## |
|
16586
f423873d3275
Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents:
16585
diff
changeset
|
3 ## This file is part of Octave. |
|
f423873d3275
Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents:
16585
diff
changeset
|
4 ## |
|
f423873d3275
Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents:
16585
diff
changeset
|
5 ## Octave is free software; you can redistribute it and/or modify it |
|
f423873d3275
Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents:
16585
diff
changeset
|
6 ## under the terms of the GNU General Public License as published by |
|
f423873d3275
Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents:
16585
diff
changeset
|
7 ## the Free Software Foundation; either version 3 of the License, or (at |
|
f423873d3275
Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents:
16585
diff
changeset
|
8 ## your option) any later version. |
|
16584
2f766ceeb03e
Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff
changeset
|
9 ## |
|
16586
f423873d3275
Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents:
16585
diff
changeset
|
10 ## Octave is distributed in the hope that it will be useful, but |
|
f423873d3275
Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents:
16585
diff
changeset
|
11 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
|
f423873d3275
Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents:
16585
diff
changeset
|
12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
|
f423873d3275
Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents:
16585
diff
changeset
|
13 ## General Public License for more details. |
|
16584
2f766ceeb03e
Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff
changeset
|
14 ## |
|
16586
f423873d3275
Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents:
16585
diff
changeset
|
15 ## You should have received a copy of the GNU General Public License |
|
f423873d3275
Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents:
16585
diff
changeset
|
16 ## along with Octave; see the file COPYING. If not, see |
|
f423873d3275
Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents:
16585
diff
changeset
|
17 ## <http://www.gnu.org/licenses/>. |
|
16584
2f766ceeb03e
Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff
changeset
|
18 |
| 16768 | 19 ## Author: Sylvain Pelissier <sylvain.pelissier@gmail.com> |
| 20 | |
|
16584
2f766ceeb03e
Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff
changeset
|
21 ## -*- texinfo -*- |
|
16586
f423873d3275
Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents:
16585
diff
changeset
|
22 ## @deftypefn {Function File} {} expint (@var{x}) |
| 17363 | 23 ## Compute the exponential integral: |
|
16587
a3fdd6041e64
Fix ellipj, ellipke, and expint docstrings
Mike Miller <mtmiller@ieee.org>
parents:
16586
diff
changeset
|
24 ## @tex |
|
a3fdd6041e64
Fix ellipj, ellipke, and expint docstrings
Mike Miller <mtmiller@ieee.org>
parents:
16586
diff
changeset
|
25 ## $$ |
| 17363 | 26 ## {\rm E_1} (x) = \int_x^\infty {e^{-t} \over t} dt |
|
16587
a3fdd6041e64
Fix ellipj, ellipke, and expint docstrings
Mike Miller <mtmiller@ieee.org>
parents:
16586
diff
changeset
|
27 ## $$ |
|
a3fdd6041e64
Fix ellipj, ellipke, and expint docstrings
Mike Miller <mtmiller@ieee.org>
parents:
16586
diff
changeset
|
28 ## @end tex |
|
a3fdd6041e64
Fix ellipj, ellipke, and expint docstrings
Mike Miller <mtmiller@ieee.org>
parents:
16586
diff
changeset
|
29 ## @ifnottex |
|
a3fdd6041e64
Fix ellipj, ellipke, and expint docstrings
Mike Miller <mtmiller@ieee.org>
parents:
16586
diff
changeset
|
30 ## |
|
a3fdd6041e64
Fix ellipj, ellipke, and expint docstrings
Mike Miller <mtmiller@ieee.org>
parents:
16586
diff
changeset
|
31 ## @example |
|
a3fdd6041e64
Fix ellipj, ellipke, and expint docstrings
Mike Miller <mtmiller@ieee.org>
parents:
16586
diff
changeset
|
32 ## @group |
| 17363 | 33 ## infinity |
| 34 ## / | |
| 35 ## E_1 (x) = | exp (-t)/t dt | |
| 36 ## / | |
| 37 ## x | |
|
16587
a3fdd6041e64
Fix ellipj, ellipke, and expint docstrings
Mike Miller <mtmiller@ieee.org>
parents:
16586
diff
changeset
|
38 ## @end group |
|
a3fdd6041e64
Fix ellipj, ellipke, and expint docstrings
Mike Miller <mtmiller@ieee.org>
parents:
16586
diff
changeset
|
39 ## @end example |
|
17513
fedcd3717ebc
doc: grammarcheck of documentation before 3.8 release.
Rik <rik@octave.org>
parents:
17363
diff
changeset
|
40 ## |
| 17363 | 41 ## @end ifnottex |
| 42 ## Note: For compatibility, this functions uses the @sc{matlab} definition | |
| 43 ## of the exponential integral. Most other sources refer to this particular | |
|
20372
2645f9ef8c88
doc: Update more docstrings to have one sentence summary as first line.
Rik <rik@octave.org>
parents:
19790
diff
changeset
|
44 ## value as @math{E_1 (x)}, and the exponential integral as |
| 17363 | 45 ## @tex |
| 46 ## $$ | |
| 47 ## {\rm Ei} (x) = - \int_{-x}^\infty {e^{-t} \over t} dt. | |
| 48 ## $$ | |
| 49 ## @end tex | |
| 50 ## @ifnottex | |
| 51 ## | |
| 52 ## @example | |
| 53 ## @group | |
| 54 ## infinity | |
| 55 ## / | |
| 56 ## Ei (x) = - | exp (-t)/t dt | |
| 57 ## / | |
| 58 ## -x | |
| 59 ## @end group | |
| 60 ## @end example | |
|
17513
fedcd3717ebc
doc: grammarcheck of documentation before 3.8 release.
Rik <rik@octave.org>
parents:
17363
diff
changeset
|
61 ## |
| 17363 | 62 ## @end ifnottex |
|
17514
5b916efea542
doc: spellcheck of documentation before 3.8 release.
Rik <rik@octave.org>
parents:
17513
diff
changeset
|
63 ## The two definitions are related, for positive real values of @var{x}, by |
| 17363 | 64 ## @tex |
| 65 ## $ | |
| 66 ## E_1 (-x) = -{\rm Ei} (x) - i\pi. | |
| 67 ## $ | |
| 68 ## @end tex | |
| 69 ## @ifnottex | |
| 70 ## @w{@code{E_1 (-x) = -Ei (x) - i*pi}}. | |
|
16587
a3fdd6041e64
Fix ellipj, ellipke, and expint docstrings
Mike Miller <mtmiller@ieee.org>
parents:
16586
diff
changeset
|
71 ## @end ifnottex |
|
16584
2f766ceeb03e
Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff
changeset
|
72 ## @end deftypefn |
|
2f766ceeb03e
Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff
changeset
|
73 |
|
16586
f423873d3275
Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents:
16585
diff
changeset
|
74 function y = expint (x) |
|
f423873d3275
Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents:
16585
diff
changeset
|
75 |
|
16584
2f766ceeb03e
Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff
changeset
|
76 if (nargin != 1) |
|
16586
f423873d3275
Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents:
16585
diff
changeset
|
77 print_usage (); |
|
16584
2f766ceeb03e
Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff
changeset
|
78 endif |
|
16586
f423873d3275
Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents:
16585
diff
changeset
|
79 |
| 17363 | 80 y = x; # Copy over all values, including NaNs |
|
16584
2f766ceeb03e
Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff
changeset
|
81 |
| 17363 | 82 if (isreal (x)) |
| 83 idx = (x >= 0); | |
| 84 y(idx) = -expint_Ei (-x(idx)); | |
|
16586
f423873d3275
Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents:
16585
diff
changeset
|
85 |
| 17363 | 86 idx = (x < 0); |
| 87 y(idx) = -expint_Ei (-x(idx)) - i*pi; | |
| 88 else | |
| 89 idx = (imag (x) > 0); | |
| 90 y(idx) = -expint_Ei (-x(idx)) - i*pi; | |
|
16586
f423873d3275
Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents:
16585
diff
changeset
|
91 |
| 17363 | 92 idx = (imag (x) < 0); |
| 93 y(idx) = -expint_Ei (-x(idx)) + i*pi; | |
|
16586
f423873d3275
Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents:
16585
diff
changeset
|
94 |
| 17363 | 95 isreal_idx = (imag (x) == 0); |
| 96 idx = (isreal_idx & real (x) >= 0); | |
| 97 y(idx) = -expint_Ei (-x(idx)); | |
|
16586
f423873d3275
Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents:
16585
diff
changeset
|
98 |
| 17363 | 99 idx = (isreal_idx & real (x) < 0); |
| 100 y(idx) = -expint_Ei (-x(idx)) - i*pi; | |
| 101 endif | |
|
16586
f423873d3275
Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents:
16585
diff
changeset
|
102 |
|
16584
2f766ceeb03e
Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff
changeset
|
103 endfunction |
|
2f766ceeb03e
Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff
changeset
|
104 |
|
2f766ceeb03e
Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff
changeset
|
105 ## -*- texinfo -*- |
|
2f766ceeb03e
Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff
changeset
|
106 ## @deftypefn {Function File} {@var{y} =} expint_Ei (@var{x}) |
| 17363 | 107 ## Compute the exponential integral: |
|
16584
2f766ceeb03e
Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff
changeset
|
108 ## @verbatim |
| 17363 | 109 ## infinity |
| 110 ## / | |
| 111 ## expint_Ei (x) = - | exp(-t)/t dt | |
| 112 ## / | |
| 113 ## -x | |
|
16584
2f766ceeb03e
Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff
changeset
|
114 ## @end verbatim |
|
2f766ceeb03e
Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff
changeset
|
115 ## @end deftypefn |
|
2f766ceeb03e
Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff
changeset
|
116 |
|
16586
f423873d3275
Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents:
16585
diff
changeset
|
117 function y = expint_Ei (x) |
|
f423873d3275
Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents:
16585
diff
changeset
|
118 |
|
f423873d3275
Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents:
16585
diff
changeset
|
119 y = zeros (size (x)); |
|
f423873d3275
Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents:
16585
diff
changeset
|
120 F = @(x) exp (-x)./x; |
|
f423873d3275
Style fixes for ellipj.cc, ellipke.m, and expint.m
Mike Miller <mtmiller@ieee.org>
parents:
16585
diff
changeset
|
121 |
| 17363 | 122 for t = 1:numel (x) |
| 123 xt = x(t); | |
| 124 if (xt < 0 && imag (xt) == 0) | |
| 125 ## Direct integration for most real inputs | |
| 126 y(t) = -quad (F, -xt, Inf, [0, 1e-10]); | |
| 127 elseif (xt > 2 && imag (xt) == 0) | |
| 128 persistent Ei_2 = 4.954234356001890; | |
| 129 y(t) = Ei_2 - quad (F, -xt, -2); | |
| 130 elseif (abs (xt) < 10) | |
| 131 ## Series Expansion for real (range [0,2]) or complex inputs (r < 10) | |
| 132 k = 1; | |
| 133 do | |
| 134 term = xt^k / (k*factorial (k)); | |
| 135 y(t) += term; | |
| 136 until (abs (term) < eps (abs (y(t))) / 2 || k++ >= 100) | |
| 137 y(t) = 0.57721566490153286 + log (xt) + y(t); | |
|
16584
2f766ceeb03e
Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff
changeset
|
138 else |
| 17363 | 139 ## FIXME: This expansion is accurate to only 1e-13 at the beginning |
| 140 ## near 10+i, although it becomes more accurate as the magnitude | |
| 141 ## of xt grows. | |
| 142 if (imag (xt) <= 0) | |
| 143 persistent a1 = 4.03640; | |
| 144 persistent a2 = 1.15198; | |
| 145 persistent b1 = 5.03637; | |
| 146 persistent b2 = 4.19160; | |
| 147 y(t) = -(xt^2 - a1*xt + a2) ... | |
| 148 / ((xt^2 - b1*xt + b2) * (-xt) * exp (-xt)) ... | |
| 149 - i*pi; | |
|
16584
2f766ceeb03e
Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff
changeset
|
150 else |
| 17363 | 151 y(t) = conj (expint_Ei (conj (xt))); |
| 152 endif; | |
|
16584
2f766ceeb03e
Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff
changeset
|
153 endif |
|
2f766ceeb03e
Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff
changeset
|
154 endfor |
|
2f766ceeb03e
Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents:
diff
changeset
|
155 endfunction |
|
16585
1a3bfb14b5da
Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents:
16584
diff
changeset
|
156 |
| 17363 | 157 |
| 158 ## Test against A&S Table 5.1 | |
|
16585
1a3bfb14b5da
Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents:
16584
diff
changeset
|
159 %!test |
|
1a3bfb14b5da
Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents:
16584
diff
changeset
|
160 %! x = [5:5:50]'/100; |
|
1a3bfb14b5da
Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents:
16584
diff
changeset
|
161 %! gamma = 0.5772156649; |
|
1a3bfb14b5da
Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents:
16584
diff
changeset
|
162 %! y_exp = [0.9876375971; |
|
1a3bfb14b5da
Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents:
16584
diff
changeset
|
163 %! 0.9755453033; |
|
1a3bfb14b5da
Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents:
16584
diff
changeset
|
164 %! 0.9637156702; |
|
1a3bfb14b5da
Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents:
16584
diff
changeset
|
165 %! 0.9521414833; |
|
1a3bfb14b5da
Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents:
16584
diff
changeset
|
166 %! 0.9408157528; |
|
1a3bfb14b5da
Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents:
16584
diff
changeset
|
167 %! 0.9297317075; |
|
1a3bfb14b5da
Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents:
16584
diff
changeset
|
168 %! 0.9188827858; |
|
1a3bfb14b5da
Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents:
16584
diff
changeset
|
169 %! 0.9082626297; |
|
1a3bfb14b5da
Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents:
16584
diff
changeset
|
170 %! 0.8978650778; |
|
1a3bfb14b5da
Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents:
16584
diff
changeset
|
171 %! 0.8876841584 ]; |
|
1a3bfb14b5da
Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents:
16584
diff
changeset
|
172 %! y = (expint (x) + log(x) + gamma) ./ x; |
|
1a3bfb14b5da
Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents:
16584
diff
changeset
|
173 %! 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
|
174 %!test |
|
1a3bfb14b5da
Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents:
16584
diff
changeset
|
175 %! x = [50:5:95]'/100; |
|
1a3bfb14b5da
Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents:
16584
diff
changeset
|
176 %! y_exp = [0.559773595; |
|
1a3bfb14b5da
Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents:
16584
diff
changeset
|
177 %! 0.503364081; |
|
1a3bfb14b5da
Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents:
16584
diff
changeset
|
178 %! 0.454379503; |
|
1a3bfb14b5da
Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents:
16584
diff
changeset
|
179 %! 0.411516976; |
|
1a3bfb14b5da
Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents:
16584
diff
changeset
|
180 %! 0.373768843; |
|
1a3bfb14b5da
Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents:
16584
diff
changeset
|
181 %! 0.340340813; |
|
1a3bfb14b5da
Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents:
16584
diff
changeset
|
182 %! 0.310596579; |
|
1a3bfb14b5da
Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents:
16584
diff
changeset
|
183 %! 0.284019269; |
|
1a3bfb14b5da
Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents:
16584
diff
changeset
|
184 %! 0.260183939; |
|
1a3bfb14b5da
Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents:
16584
diff
changeset
|
185 %! 0.238737524 ]; |
|
1a3bfb14b5da
Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents:
16584
diff
changeset
|
186 %! y = expint (x); |
|
1a3bfb14b5da
Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents:
16584
diff
changeset
|
187 %! 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
|
188 %!test |
|
1a3bfb14b5da
Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents:
16584
diff
changeset
|
189 %! x = [100:5:145]'/100; |
|
1a3bfb14b5da
Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents:
16584
diff
changeset
|
190 %! y_exp = [0.219383934; |
|
1a3bfb14b5da
Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents:
16584
diff
changeset
|
191 %! 0.201872813; |
|
1a3bfb14b5da
Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents:
16584
diff
changeset
|
192 %! 0.185990905; |
|
1a3bfb14b5da
Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents:
16584
diff
changeset
|
193 %! 0.171555354; |
|
1a3bfb14b5da
Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents:
16584
diff
changeset
|
194 %! 0.158408437; |
|
1a3bfb14b5da
Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents:
16584
diff
changeset
|
195 %! 0.146413373; |
|
1a3bfb14b5da
Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents:
16584
diff
changeset
|
196 %! 0.135450958; |
|
1a3bfb14b5da
Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents:
16584
diff
changeset
|
197 %! 0.125416844; |
|
1a3bfb14b5da
Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents:
16584
diff
changeset
|
198 %! 0.116219313; |
|
1a3bfb14b5da
Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents:
16584
diff
changeset
|
199 %! 0.107777440 ]; |
|
1a3bfb14b5da
Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents:
16584
diff
changeset
|
200 %! y = expint (x); |
|
1a3bfb14b5da
Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents:
16584
diff
changeset
|
201 %! 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
|
202 %!test |
|
1a3bfb14b5da
Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents:
16584
diff
changeset
|
203 %! x = [150:5:200]'/100; |
|
1a3bfb14b5da
Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents:
16584
diff
changeset
|
204 %! y_exp = [0.100019582; |
|
1a3bfb14b5da
Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents:
16584
diff
changeset
|
205 %! 0.092882108; |
|
1a3bfb14b5da
Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents:
16584
diff
changeset
|
206 %! 0.086308334; |
|
1a3bfb14b5da
Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents:
16584
diff
changeset
|
207 %! 0.080247627; |
|
1a3bfb14b5da
Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents:
16584
diff
changeset
|
208 %! 0.074654644; |
|
1a3bfb14b5da
Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents:
16584
diff
changeset
|
209 %! 0.069488685; |
|
1a3bfb14b5da
Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents:
16584
diff
changeset
|
210 %! 0.064713129; |
|
1a3bfb14b5da
Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents:
16584
diff
changeset
|
211 %! 0.060294967; |
|
1a3bfb14b5da
Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents:
16584
diff
changeset
|
212 %! 0.056204378; |
|
1a3bfb14b5da
Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents:
16584
diff
changeset
|
213 %! 0.052414380; |
|
1a3bfb14b5da
Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents:
16584
diff
changeset
|
214 %! 0.048900511 ]; |
|
1a3bfb14b5da
Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents:
16584
diff
changeset
|
215 %! y = expint (x); |
|
1a3bfb14b5da
Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents:
16584
diff
changeset
|
216 %! 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
|
217 |
| 17363 | 218 ## Series expansion (-2 < x < 0) |
| 219 ## Expected values from Mathematica | |
|
19790
446c46af4b42
strip trailing whitespace from most source files
John W. Eaton <jwe@octave.org>
parents:
17744
diff
changeset
|
220 %!test |
| 17363 | 221 %! x = [-0.1; -0.5; -1; -1.5; -2]; |
| 222 %! y_exp = [ 1.6228128139692767 - i*pi; | |
| 223 %! -0.45421990486317358 - i*pi; | |
| 224 %! -1.8951178163559368 - i*pi; | |
| 225 %! -3.3012854491297978 - i*pi; | |
| 226 %! -4.9542343560018902 - i*pi]; | |
| 227 %! y = expint (x); | |
| 228 %! assert (y, y_exp, eps (real (y_exp))); | |
| 229 | |
| 230 ## (x < -2, x real) | |
|
19790
446c46af4b42
strip trailing whitespace from most source files
John W. Eaton <jwe@octave.org>
parents:
17744
diff
changeset
|
231 %!test |
| 17363 | 232 %! x = [-2.5; -3; -10;-15; -25]; |
| 233 %! y_exp = [-7.0737658945786007 - i*pi; | |
| 234 %! -9.9338325706254165 - i*pi; | |
| 235 %! -2492.2289762418777 - i*pi; | |
| 236 %! -234955.85249076830 - i*pi; | |
| 237 %! -3.0059509065255486e9 - i*pi]; | |
| 238 %! y = expint (x); | |
| 239 %! assert (y, y_exp, 8*eps (real (y_exp))); | |
| 240 | |
| 241 ## Complex values | |
| 242 %!test | |
| 243 %! x = [i; -1-i; 10-i; 10+i]; | |
| 244 %! y_exp = [-0.33740392290096813 - i*0.62471325642771360; | |
| 245 %! -1.7646259855638540 + i*0.75382280207927082; | |
| 246 %! 1.90746381979783120e-6 + i*3.67354374003294739e-6; | |
| 247 %! 1.90746381979783120e-6 - i*3.67354374003294739e-6]; | |
| 248 %! y = expint (x); | |
| 249 %! assert (y, y_exp, 1e-12); | |
| 250 | |
| 251 ## Exceptional values (-Inf, Inf, NaN, 0, 0.37250741078) | |
|
19790
446c46af4b42
strip trailing whitespace from most source files
John W. Eaton <jwe@octave.org>
parents:
17744
diff
changeset
|
252 %!test |
| 17363 | 253 %! x = [-Inf; Inf; NaN; 0; -0.3725074107813668]; |
| 254 %! y_exp = [-Inf - i*pi; | |
| 255 %! -Inf; # should be 0; | |
| 256 %! NaN; | |
| 257 %! Inf; | |
| 258 %! 0 - i*pi]; | |
| 259 %! y = expint (x); | |
| 260 %! assert (y, y_exp, 5*eps); | |
| 261 | |
| 262 ## Test input validation | |
|
16585
1a3bfb14b5da
Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents:
16584
diff
changeset
|
263 %!error expint () |
|
1a3bfb14b5da
Add and fix tests for ellipj, ellipke, and expint
Mike Miller <mtmiller@ieee.org>
parents:
16584
diff
changeset
|
264 %!error expint (1,2) |
|
17338
1c89599167a6
maint: End m-files with 1 blank line.
Rik <rik@octave.org>
parents:
16768
diff
changeset
|
265 |
| 17363 | 266 |