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annotate scripts/specfun/sinint.m @ 31230:6646f2b5a3d1

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lcm.m: Emit warnings when results not exact (Bug #32924)
author Arun Giridhar <arungiridhar@gmail.com>
date Sat, 17 Sep 2022 04:22:38 -0400
parents 5d3faba0342e
children 597f3ee61a48
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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 {} {@var{y} =} sinint (@var{x})
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28 ## Compute the sine integral function:
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29 ## @tex
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30 ## $$
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31 ## {\rm Si} (x) = \int_0^x {\sin (t) \over t} dt
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32 ## $$
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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 ## x
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39 ## /
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40 ## Si (x) = | sin (t) / t dt
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41 ## /
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42 ## 0
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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 ##
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48 ## Reference:
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49 ## @nospell{M. Abramowitz and I.A. Stegun},
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50 ## @cite{Handbook of Mathematical Functions}, 1964.
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51 ##
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52 ## @seealso{cosint, expint, sin}
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53 ## @end deftypefn
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54
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55 function y = sinint (x)
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56
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57 if (nargin < 1)
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58 print_usage ();
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59 endif
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60
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61 if (! isnumeric (x))
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62 error ("sinint: X must be numeric");
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63 endif
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64
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65 ## Convert to floating point if necessary
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66 if (isinteger (x))
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67 x = double (x);
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68 endif
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69
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70 ## Convert to column vector
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71 orig_sz = size (x);
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72 x = x(:);
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73 if (iscomplex (x))
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74 ## Work around reshape which narrows to real (bug #52953)
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75 x = complex (real (x)(:), imag (x)(:));
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76 else
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77 x = x(:);
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78 endif
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79
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80 ## Initialize the result
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81 y = zeros (size (x), class (x));
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82 tol = eps (class (x));
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83
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84 todo = true (size (x));
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85
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86 ## Special values
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87 y(x == 0) = x(x == 0); # correctly signed zero
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88 y(x == Inf) = pi / 2;
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89 y(x == - Inf) = - pi / 2;
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90
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91 todo = ((todo) & (x != 0) & (x != Inf) & (x != - Inf));
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92
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93 ## For values large in modulus we use the relation with expint
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94
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95 flag_large = abs (x) > 2;
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96 xx = x(flag_large & todo);
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97 ii_neg = (real (xx) < 0);
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98 xx(ii_neg) *= -1;
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99 ii_conj = (real (xx) == 0) & (imag (xx) < 0);
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100 xx(ii_conj) = conj (xx(ii_conj));
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101 yy = -0.5i * (expint (1i * xx) - expint (-1i * xx)) + pi / 2;
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102 yy(ii_neg) *= -1;
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103 yy(ii_conj) = conj (yy(ii_conj));
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104 y(todo & flag_large) = yy;
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105
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106 ## For values small in modulus we use the series expansion
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107
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108 todo = (todo) & (! flag_large);
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109 xx = x(todo);
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110 ssum = xx; # First term of the series expansion
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111 yy = ssum;
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112 flag_sum = true (nnz (todo), 1);
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113 it = 0;
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114 maxit = 300;
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115 while (any (flag_sum) && (it < maxit))
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116 ssum .*= - xx .^ 2 * (2 * it + 1) / ((2 * it + 3) ^ 2 * (2 * it + 2));
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117 yy(flag_sum) += ssum (flag_sum);
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118 flag_sum = (abs (ssum) >= tol);
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119 it++;
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120 endwhile
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121
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122 y(todo) = yy;
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123
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124 y = reshape (y, orig_sz);
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125
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126 endfunction
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127
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128
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129 %!assert (sinint (1.1), 1.02868521867373, -5e-15)
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130
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131 %!test
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132 %! x = [2, 3, pi; exp(1), 5, 6];
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133 %! A = sinint (x);
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134 %! B = [1.60541297680269, 1.84865252799947, 1.85193705198247e+00; ...
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135 %! 1.82104026914757, 1.54993124494467, 1.42468755128051e+00];
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136 %! assert (A, B, -5e-15);
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137
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138 ## Test exceptional values
24909
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139 %!assert (sinint (0), 0)
24912
08c871c4147b sinint(0) returns correctly signed zero output.
Colin Macdonald <cbm@m.fsf.org>
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140 %!assert (signbit (sinint (-0)))
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141 %!assert (sinint (Inf), pi/2)
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142 %!assert (sinint (-Inf), -pi/2)
c280560d9c96 Overhaul special functions modified by GSOC2018 project.
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143 %!assert (isnan (sinint (NaN)))
24911
8d6f3941a118 Support single precision in sinint/cosint.
Colin Macdonald <cbm@m.fsf.org>
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144
24927
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145 ## Check single data type is preserved
24911
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Colin Macdonald <cbm@m.fsf.org>
parents: 24910
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146 %!assert (class (sinint (single (1))), "single")
24909
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Michele Ginesi <michele.ginesi@gmail.com>
parents:
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147
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148 ## Tests against Maple
c280560d9c96 Overhaul special functions modified by GSOC2018 project.
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149 %!assert (sinint (1) , 0.9460830703671830149414, -2*eps)
c280560d9c96 Overhaul special functions modified by GSOC2018 project.
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150 %!assert (sinint (-1) , -0.9460830703671830149414, -2*eps)
24996
f80e68529bbf test: relax tolerances on specfun tests to pass on i386 (bug #53437)
Mike Miller <mtmiller@octave.org>
parents: 24927
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151 %!assert (sinint (pi) , 1.851937051982466170361, -3*eps)
f80e68529bbf test: relax tolerances on specfun tests to pass on i386 (bug #53437)
Mike Miller <mtmiller@octave.org>
parents: 24927
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152 %!assert (sinint (-pi), -1.851937051982466170361, -3*eps)
24927
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153 %!assert (sinint (300), 1.5708810882137495193, -2*eps)
c280560d9c96 Overhaul special functions modified by GSOC2018 project.
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154 %!assert (sinint (1e4), 1.5708915453859619157, -2*eps)
c280560d9c96 Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
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155 %!assert (sinint (20i), 1.2807826332028294459e7*1i, -2*eps)
24909
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Michele Ginesi <michele.ginesi@gmail.com>
parents:
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156
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
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157 %!test
24910
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Colin Macdonald <cbm@m.fsf.org>
parents: 24909
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158 %! x = (0:4)';
24909
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Michele Ginesi <michele.ginesi@gmail.com>
parents:
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159 %! y_ex = [0
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
160 %! 0.946083070367183015
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
161 %! 1.60541297680269485
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
162 %! 1.84865252799946826
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
163 %! 1.75820313894905306];
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
164 %! assert (sinint (x), y_ex, -4*eps);
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
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165
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
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166 %!test
24910
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Colin Macdonald <cbm@m.fsf.org>
parents: 24909
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167 %! x = -(0:4)';
24909
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Michele Ginesi <michele.ginesi@gmail.com>
parents:
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168 %! y_ex = - [0
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
169 %! 0.946083070367183015
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
170 %! 1.60541297680269485
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
171 %! 1.84865252799946826
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
172 %! 1.75820313894905306];
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
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173 %! assert (sinint (x), y_ex, -4*eps);
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
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174
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
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175 %!test
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Michele Ginesi <michele.ginesi@gmail.com>
parents:
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176 %! x = 1i * (0:4).';
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
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177 %! y_ex = [0
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Michele Ginesi <michele.ginesi@gmail.com>
parents:
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178 %! 1.05725087537572851*I
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
179 %! 2.50156743335497564*I
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
180 %! 4.97344047585980680*I
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
181 %! 9.81732691123303446*I];
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
182 %! assert (sinint (x), y_ex, -4*eps);
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
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183
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
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184 %!test
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
185 %! x = - 1i * (0:4).';
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
186 %! y_ex = - [0
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Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
187 %! 1.05725087537572851*I
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
188 %! 2.50156743335497564*I
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
189 %! 4.97344047585980680*I
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
190 %! 9.81732691123303446*I];
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
191 %! assert (sinint (x), y_ex, -4*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:
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193 %!test
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
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194 %! % maple:
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
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195 %! % > A := [1+2*I, -2 + 5*I, 100, 10*I, -1e-4 + 1e-6*I, -20 + I];
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Michele Ginesi <michele.ginesi@gmail.com>
parents:
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196 %! % > for a in A do evalf(Si(a)) end do;
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
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197 %! x = [1+2i; -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:
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198 %! A = [ 1.6782404878293681180 + 2.0396845546022061045*1i
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
199 %! -18.154174221650281533 + 1.6146414539230479060*1i
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
200 %! 1.5622254668890562934
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
201 %! 1246.1144901994233444*1i
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
202 %! -0.000099999999944461111128 + 0.99999999833338888972e-6*1i
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
203 %! -1.5386156269726011209 - 0.053969388020443786229*1i ];
4a341330ee15 Added sine integral and cosine integral functions.
Michele Ginesi <michele.ginesi@gmail.com>
parents:
diff changeset
204 %! B = sinint (x);
28929
9e43deb9bfc3 maint: Use semicolon after assert statement inside %!test blocks.
Rik <rik@octave.org>
parents: 28891
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205 %! assert (A, B, -3*eps);
24911
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Colin Macdonald <cbm@m.fsf.org>
parents: 24910
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206 %! B = sinint (single (x));
28929
9e43deb9bfc3 maint: Use semicolon after assert statement inside %!test blocks.
Rik <rik@octave.org>
parents: 28891
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207 %! assert (A, B, -3*eps ("single"));
24927
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208
c280560d9c96 Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents: 24923
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209 ## FIXME: Need a test for bug #52953
c280560d9c96 Overhaul special functions modified by GSOC2018 project.
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diff changeset
210 %#!test <*52953>
c280560d9c96 Overhaul special functions modified by GSOC2018 project.
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diff changeset
211
c280560d9c96 Overhaul special functions modified by GSOC2018 project.
Rik <rik@octave.org>
parents: 24923
diff changeset
212 ## Test input validation
28886
d8318c12d903 test: remove unnecessary BIST tests in m-files checking for excessive number of inputs.
Rik <rik@octave.org>
parents: 27923
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213 %!error <Invalid call> sinint ()
24927
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parents: 24923
diff changeset
214 %!error <X must be numeric> sinint ("1")