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update Octave Project Developers copyright for the new year In files that have the "Octave Project Developers" copyright notice, update for 2021. In all .txi and .texi files except gpl.txi and gpl.texi in the doc/liboctave and doc/interpreter directories, change the copyright to "Octave Project Developers", the same as used for other source files. Update copyright notices for 2022 (not done since 2019). For gpl.txi and gpl.texi, change the copyright notice to be "Free Software Foundation, Inc." and leave the date at 2007 only because this file only contains the text of the GPL, not anything created by the Octave Project Developers. Add Paul Thomas to contributors.in.
author John W. Eaton <jwe@octave.org>
date Tue, 28 Dec 2021 18:22:40 -0500
parents 01de0045b2e3
children 5d3faba0342e
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
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1 ########################################################################
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2 ##
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3 ## Copyright (C) 2017-2022 The Octave Project Developers
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4 ##
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5 ## See the file COPYRIGHT.md in the top-level directory of this
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6 ## distribution or <https://octave.org/copyright/>.
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7 ##
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8 ## This file is part of Octave.
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9 ##
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10 ## Octave is free software: you can redistribute it and/or modify it
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11 ## under the terms of the GNU General Public License as published by
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12 ## the Free Software Foundation, either version 3 of the License, or
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13 ## (at your option) any later version.
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14 ##
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15 ## Octave is distributed in the hope that it will be useful, but
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16 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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17 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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18 ## GNU General Public License for more details.
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19 ##
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20 ## You should have received a copy of the GNU General Public License
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21 ## along with Octave; see the file COPYING. If not, see
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22 ## <https://www.gnu.org/licenses/>.
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23 ##
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24 ########################################################################
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25
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26 ## -*- texinfo -*-
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27 ## @deftypefn {} {} cosint (@var{x})
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28 ## Compute the cosine integral function:
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29 ## @tex
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30 ## $$
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31 ## {\rm Ci} (x) = - \int_x^\infty {{\cos (t)} \over t} dt
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32 ## $$
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33 ## @end tex
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34 ## @ifnottex
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35 ##
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36 ## @example
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37 ## @group
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38 ## +oo
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39 ## /
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40 ## Ci (x) = - | (cos (t)) / t dt
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41 ## /
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42 ## x
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43 ## @end group
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44 ## @end example
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45 ##
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46 ## @end ifnottex
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47 ## An equivalent definition is
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48 ## @tex
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49 ## $$
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50 ## {\rm Ci} (x) = \gamma + \log (x) + \int_0^x {{\cos (t) - 1} \over t} dt
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51 ## $$
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52 ## @end tex
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53 ## @ifnottex
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54 ##
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55 ## @example
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56 ## @group
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57 ## x
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58 ## /
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59 ## | cos (t) - 1
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60 ## Ci (x) = gamma + log (x) + | ------------- dt
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61 ## | t
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62 ## /
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63 ## 0
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64 ## @end group
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65 ## @end example
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66 ##
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67 ## @end ifnottex
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68 ## Reference:
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69 ##
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70 ## @nospell{M. Abramowitz and I.A. Stegun},
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71 ## @cite{Handbook of Mathematical Functions}, 1964.
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72 ##
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73 ## @seealso{sinint, expint, cos}
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74 ##
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75 ## @end deftypefn
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76
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77 function y = cosint (x)
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78
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79 if (nargin < 1)
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80 print_usage ();
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81 endif
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82
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83 if (! isnumeric (x))
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84 error ("cosint: X must be numeric");
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85 endif
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86
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87 ## Convert to floating point if necessary
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88 if (isinteger (x))
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89 x = double (x);
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90 endif
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91
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92 ## Convert to column vector
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93 orig_sz = size (x);
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94 if (iscomplex (x))
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95 ## Work around reshape which narrows to real (bug #52953)
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96 x = complex (real (x)(:), imag (x)(:));
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97 else
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98 x = x(:);
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99 endif
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100
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101 ## Initialize the result
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102 y = zeros (size (x), class (x));
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103 tol = eps (class (x));
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104
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105 todo = true (size (x));
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106
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107 ## Special values
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108 y(x == Inf) = 0;
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109 y((x == -Inf) & ! signbit (imag (x))) = 1i * pi;
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110 y((x == -Inf) & signbit (imag (x))) = -1i * pi;
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111
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112 todo(isinf (x)) = false;
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113
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114 ## For values large in modulus, but not in the range (-oo,0), we use the
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115 ## relation with expint.
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116
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117 flag_large = (abs (x) > 2);
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118 xx = x(flag_large);
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119
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120 ## Abramowitz, relation 5.2.20
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121 ii_sw = (real (xx) <= 0 & imag (xx) < 0);
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122 xx(ii_sw) = conj (xx(ii_sw));
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123 ii_nw = (real (xx) < 0);
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124 xx(ii_nw) *= -1;
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125 yy = -0.5 * (expint (1i * xx) + expint (-1i * xx));
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126 yy(ii_nw) += 1i * pi;
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127 yy(ii_sw) = conj (yy(ii_sw));
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128 y(todo & flag_large) = yy;
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129
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130 todo(flag_large) = false;
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131
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132 ## For values small in modulus, use the series expansion (also near (-oo, 0])
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133 if (iscomplex (x))
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134 ## indexing can lose imag part: if it was -0, we could end up on the
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135 ## wrong right side of the branch cut along the negative real axis.
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136 xx = complex (real (x)(todo), imag (x)(todo));
24913
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Colin Macdonald <cbm@m.fsf.org>
parents: 24911
diff changeset
137 else
24927
c280560d9c96 Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents: 24923
diff changeset
138 xx = x(todo);
28947
b73a54c31152 maint: Use Octave-specific end keywords rather than just 'end'.
Rik <rik@octave.org>
parents: 28923
diff changeset
139 endif
24909
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
140 ssum = - xx .^ 2 / 4; # First term of the series expansion
24927
c280560d9c96 Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents: 24923
diff changeset
141 ## FIXME: This is way more precision than a double value can hold.
24909
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
142 gma = 0.57721566490153286060651209008; # Euler gamma constant
30330
01de0045b2e3 maint: Shorten some long lines to <= 80 characters (bug #57599)
Rik <rik@octave.org>
parents: 30254
diff changeset
143 yy = gma + log (complex (xx)) + ssum; # log (complex (Z)) handles signed zero
24927
c280560d9c96 Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents: 24923
diff changeset
144 flag_sum = true (nnz (todo), 1);
c280560d9c96 Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents: 24923
diff changeset
145 it = 0;
24909
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
146 maxit = 300;
26268
6dd232798997 maint: Remove useless ';' from end of for, if, while, etc. statements.
Rik <rik@octave.org>
parents: 25054
diff changeset
147 while (any (flag_sum) && (++it < maxit))
24909
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
148 ssum .*= - xx .^ 2 * (2 * it) / ((2 * it + 2) ^ 2 * (2 * it + 1));
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
149 yy(flag_sum) += ssum (flag_sum);
24911
8d6f3941a118 Support single precision in sinint/cosint.
Colin Macdonald <cbm@m.fsf.org>
parents: 24910
diff changeset
150 flag_sum = (abs (ssum) >= tol);
24909
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
151 endwhile
24927
c280560d9c96 Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents: 24923
diff changeset
152 y(todo) = yy;
24909
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
153
24927
c280560d9c96 Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents: 24923
diff changeset
154 ## Clean up values which are purely real
c280560d9c96 Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents: 24923
diff changeset
155 flag_neg_zero_imag = (real (x) < 0) & (imag (x) == 0) & signbit (imag (x));
c280560d9c96 Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents: 24923
diff changeset
156 y(flag_neg_zero_imag) = complex (real (y(flag_neg_zero_imag)), -pi);
c280560d9c96 Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents: 24923
diff changeset
157
c280560d9c96 Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents: 24923
diff changeset
158 ## Restore original shape
c280560d9c96 Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents: 24923
diff changeset
159 y = reshape (y, orig_sz);
24909
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
160
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
161 endfunction
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
162
24910
b98755ef7572 Style changes in sinint/cosint.
Colin Macdonald <cbm@m.fsf.org>
parents: 24909
diff changeset
163
28907
11f1207111c5 maint: Don't use semicolon at end of single-line BIST tests.
Rik <rik@octave.org>
parents: 28891
diff changeset
164 %!assert (cosint (1.1), 0.38487337742465081550, 2 * eps)
24909
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
165
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
166 %!test
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
167 %! x = [2, 3, pi; exp(1), 5, 6];
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
168 %! A = cosint (x);
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
169 %! B = [0.422980828774864996, 0.119629786008000328, 0.0736679120464254860; ...
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
170 %! 0.213958001340379779, -0.190029749656643879, -0.0680572438932471262];
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
171 %! assert (A, B, -5e-15);
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
172
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
173 %!assert (cosint (0), - Inf)
24913
9da779d2f029 cosint improve signed zero imag input near branch cut
Colin Macdonald <cbm@m.fsf.org>
parents: 24911
diff changeset
174 %!assert (cosint (-0), -inf + 1i*pi)
9da779d2f029 cosint improve signed zero imag input near branch cut
Colin Macdonald <cbm@m.fsf.org>
parents: 24911
diff changeset
175 %!assert (cosint (complex (-0, 0)), -inf + 1i*pi)
9da779d2f029 cosint improve signed zero imag input near branch cut
Colin Macdonald <cbm@m.fsf.org>
parents: 24911
diff changeset
176 %!assert (cosint (complex (-0, -0)), -inf - 1i*pi)
24909
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
177 %!assert (cosint (inf), 0)
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
178 %!assert (cosint (-inf), 1i * pi)
24913
9da779d2f029 cosint improve signed zero imag input near branch cut
Colin Macdonald <cbm@m.fsf.org>
parents: 24911
diff changeset
179 %!assert (cosint (complex (-inf, -0)), -1i * pi)
24911
8d6f3941a118 Support single precision in sinint/cosint.
Colin Macdonald <cbm@m.fsf.org>
parents: 24910
diff changeset
180 %!assert (isnan (cosint (nan)))
8d6f3941a118 Support single precision in sinint/cosint.
Colin Macdonald <cbm@m.fsf.org>
parents: 24910
diff changeset
181
8d6f3941a118 Support single precision in sinint/cosint.
Colin Macdonald <cbm@m.fsf.org>
parents: 24910
diff changeset
182 %!assert (class (cosint (single (1))), "single")
24909
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
183
24927
c280560d9c96 Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents: 24923
diff changeset
184 ## tests against maple
24909
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
185 %!assert (cosint (1), 0.337403922900968135, -2*eps)
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
186 %!assert (cosint (-1), 0.337403922900968135 + 3.14159265358979324*I, -2*eps)
30254
0fc950301a50 cosint.m: Increase tolerance in BIST (bug #61358).
Markus Mützel <markus.muetzel@gmx.de>
parents: 29793
diff changeset
187 %!assert (cosint (pi), 0.0736679120464254860, -4e-15)
24909
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
188 %!assert (cosint (-pi), 0.0736679120464254860 + 3.14159265358979324*I, -2*eps)
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
189 %!assert (cosint (300), -0.00333219991859211178, -2*eps)
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
190 %!assert (cosint (1e4), -0.0000305519167244852127, -2*eps)
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
191 %!assert (cosint (20i), 1.28078263320282944e7 + 1.57079632679489662*I, -2*eps)
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
192
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
193 %!test
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
194 %! x = (0:4).';
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
195 %! y_ex = [-Inf
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
196 %! 0.337403922900968135
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
197 %! 0.422980828774864996
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
198 %! 0.119629786008000328
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
199 %! -0.140981697886930412];
24927
c280560d9c96 Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents: 24923
diff changeset
200 %! assert (cosint (x), y_ex, -3e-15);
24909
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
201
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
202 %!test
24913
9da779d2f029 cosint improve signed zero imag input near branch cut
Colin Macdonald <cbm@m.fsf.org>
parents: 24911
diff changeset
203 %! x = -(1:4).';
9da779d2f029 cosint improve signed zero imag input near branch cut
Colin Macdonald <cbm@m.fsf.org>
parents: 24911
diff changeset
204 %! y_ex = [0.337403922900968135 + pi*1i
9da779d2f029 cosint improve signed zero imag input near branch cut
Colin Macdonald <cbm@m.fsf.org>
parents: 24911
diff changeset
205 %! 0.422980828774864996 + pi*1i
9da779d2f029 cosint improve signed zero imag input near branch cut
Colin Macdonald <cbm@m.fsf.org>
parents: 24911
diff changeset
206 %! 0.119629786008000328 + pi*1i
9da779d2f029 cosint improve signed zero imag input near branch cut
Colin Macdonald <cbm@m.fsf.org>
parents: 24911
diff changeset
207 %! -0.140981697886930412 + pi*1i];
9da779d2f029 cosint improve signed zero imag input near branch cut
Colin Macdonald <cbm@m.fsf.org>
parents: 24911
diff changeset
208 %! assert (cosint (x), y_ex, -4*eps);
9da779d2f029 cosint improve signed zero imag input near branch cut
Colin Macdonald <cbm@m.fsf.org>
parents: 24911
diff changeset
209
24916
bddd9ecfa420 Cosint: solved problem with -0i
Michele Ginesi <michele.ginesi@gmail.com>
parents: 24915
diff changeset
210 %!test
24927
c280560d9c96 Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents: 24923
diff changeset
211 %! x = complex (-(1:4).', 0);
24916
bddd9ecfa420 Cosint: solved problem with -0i
Michele Ginesi <michele.ginesi@gmail.com>
parents: 24915
diff changeset
212 %! y_ex = [0.337403922900968135 + pi*1i
bddd9ecfa420 Cosint: solved problem with -0i
Michele Ginesi <michele.ginesi@gmail.com>
parents: 24915
diff changeset
213 %! 0.422980828774864996 + pi*1i
bddd9ecfa420 Cosint: solved problem with -0i
Michele Ginesi <michele.ginesi@gmail.com>
parents: 24915
diff changeset
214 %! 0.119629786008000328 + pi*1i
bddd9ecfa420 Cosint: solved problem with -0i
Michele Ginesi <michele.ginesi@gmail.com>
parents: 24915
diff changeset
215 %! -0.140981697886930412 + pi*1i];
bddd9ecfa420 Cosint: solved problem with -0i
Michele Ginesi <michele.ginesi@gmail.com>
parents: 24915
diff changeset
216 %! assert (cosint (x), y_ex, -4*eps);
bddd9ecfa420 Cosint: solved problem with -0i
Michele Ginesi <michele.ginesi@gmail.com>
parents: 24915
diff changeset
217
bddd9ecfa420 Cosint: solved problem with -0i
Michele Ginesi <michele.ginesi@gmail.com>
parents: 24915
diff changeset
218 %!test
24913
9da779d2f029 cosint improve signed zero imag input near branch cut
Colin Macdonald <cbm@m.fsf.org>
parents: 24911
diff changeset
219 %! x = complex (-(1:4).', -0);
9da779d2f029 cosint improve signed zero imag input near branch cut
Colin Macdonald <cbm@m.fsf.org>
parents: 24911
diff changeset
220 %! y_ex = [0.337403922900968135 - pi*1i
9da779d2f029 cosint improve signed zero imag input near branch cut
Colin Macdonald <cbm@m.fsf.org>
parents: 24911
diff changeset
221 %! 0.422980828774864996 - pi*1i
9da779d2f029 cosint improve signed zero imag input near branch cut
Colin Macdonald <cbm@m.fsf.org>
parents: 24911
diff changeset
222 %! 0.119629786008000328 - pi*1i
9da779d2f029 cosint improve signed zero imag input near branch cut
Colin Macdonald <cbm@m.fsf.org>
parents: 24911
diff changeset
223 %! -0.140981697886930412 - pi*1i];
24909
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
224 %! assert (cosint (x), y_ex, -4*eps);
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
225
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
226 %!test
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
227 %! x = 1i * (0:4).';
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
228 %! y_ex = [-Inf
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
229 %! 0.837866940980208241 + 1.57079632679489662*I
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
230 %! 2.45266692264691452 + 1.57079632679489662*I
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
231 %! 4.96039209476560976 + 1.57079632679489662*I
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
232 %! 9.81354755882318556 + 1.57079632679489662*I];
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
233 %! assert (cosint (x), y_ex, -4*eps);
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
234
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
235 %!test
24913
9da779d2f029 cosint improve signed zero imag input near branch cut
Colin Macdonald <cbm@m.fsf.org>
parents: 24911
diff changeset
236 %! x = -1i * (1:4).';
9da779d2f029 cosint improve signed zero imag input near branch cut
Colin Macdonald <cbm@m.fsf.org>
parents: 24911
diff changeset
237 %! y_ex = [0.837866940980208241 - 1.57079632679489662*I
24909
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
238 %! 2.45266692264691452 - 1.57079632679489662*I
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
239 %! 4.96039209476560976 - 1.57079632679489662*I
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
240 %! 9.81354755882318556 - 1.57079632679489662*I];
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
241 %! assert (cosint (x), y_ex, -4*eps);
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
242
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
243 %!test
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
244 %! x = [1+2i; -2+5i; 2-5i; 100; 10i; -1e-4 + 1e-6*1i; -20-1i];
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
245 %! A = [ 2.03029639329172164 - 0.151907155175856884*I
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
246 %! 1.61538963829107749 + 19.7257540553382650*I
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
247 %! 1.61538963829107749 + 16.5841614017484717*I
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
248 %! -0.00514882514261049214
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
249 %! 1246.11448604245441 + 1.57079632679489662*I
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
250 %! -8.63307471207423322 + 3.13159298695312800*I
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
251 %! 0.0698222284673061493 - 3.11847446254772946*I ];
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
252 %! B = cosint (x);
24927
c280560d9c96 Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents: 24923
diff changeset
253 %! assert (A, B, -3*eps);
24911
8d6f3941a118 Support single precision in sinint/cosint.
Colin Macdonald <cbm@m.fsf.org>
parents: 24910
diff changeset
254 %! B = cosint (single (x));
24927
c280560d9c96 Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents: 24923
diff changeset
255 %! assert (A, B, -3*eps ("single"));
24914
d7293106945c cosint fails for large x along negative real axis.
Colin Macdonald <cbm@m.fsf.org>
parents: 24913
diff changeset
256
24927
c280560d9c96 Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents: 24923
diff changeset
257 ## Fails along negative real axis
24915
c6cdacb1794e cosint: solved problem with big negative real values.
Michele Ginesi <michele.ginesi@gmail.com>
parents: 24914
diff changeset
258 %!test
c6cdacb1794e cosint: solved problem with big negative real values.
Michele Ginesi <michele.ginesi@gmail.com>
parents: 24914
diff changeset
259 %! x = [-25; -100; -1000];
24914
d7293106945c cosint fails for large x along negative real axis.
Colin Macdonald <cbm@m.fsf.org>
parents: 24913
diff changeset
260 %! yex = [-0.0068485971797025909189 + pi*1i
d7293106945c cosint fails for large x along negative real axis.
Colin Macdonald <cbm@m.fsf.org>
parents: 24913
diff changeset
261 %! -0.0051488251426104921444 + pi*1i
d7293106945c cosint fails for large x along negative real axis.
Colin Macdonald <cbm@m.fsf.org>
parents: 24913
diff changeset
262 %! 0.000826315511090682282 + pi*1i];
d7293106945c cosint fails for large x along negative real axis.
Colin Macdonald <cbm@m.fsf.org>
parents: 24913
diff changeset
263 %! y = cosint (x);
24927
c280560d9c96 Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents: 24923
diff changeset
264 %! assert (y, yex, -5*eps);
c280560d9c96 Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents: 24923
diff changeset
265
c280560d9c96 Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents: 24923
diff changeset
266 ## FIXME: Need a test for bug #52953
c280560d9c96 Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents: 24923
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267 %#!test <*52953>
c280560d9c96 Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents: 24923
diff changeset
268
c280560d9c96 Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents: 24923
diff changeset
269 ## Test input validation
28886
d8318c12d903 test: remove unnecessary BIST tests in m-files checking for excessive number of inputs.
Rik <rik@octave.org>
parents: 27978
diff changeset
270 %!error <Invalid call> cosint ()
24927
c280560d9c96 Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents: 24923
diff changeset
271 %!error <X must be numeric> cosint ("1")