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annotate src/DLD-FUNCTIONS/besselj.cc @ 8920:eb63fbe60fab

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update copyright notices
author John W. Eaton <jwe@octave.org>
date Sat, 07 Mar 2009 10:41:27 -0500
parents ab0674a8b345
children 7c02ec148a3c
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1 /*
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2
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3 Copyright (C) 1997, 1998, 1999, 2000, 2001, 2002, 2004, 2005, 2006,
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John W. Eaton <jwe@octave.org>
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4 2007, 2008 John W. Eaton
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5
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6 This file is part of Octave.
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7
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8 Octave is free software; you can redistribute it and/or modify it
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9 under the terms of the GNU General Public License as published by the
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10 Free Software Foundation; either version 3 of the License, or (at your
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11 option) any later version.
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12
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13 Octave is distributed in the hope that it will be useful, but WITHOUT
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14 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
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15 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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16 for more details.
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17
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18 You should have received a copy of the GNU General Public License
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19 along with Octave; see the file COPYING. If not, see
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20 <http://www.gnu.org/licenses/>.
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21
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22 */
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23
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24 #ifdef HAVE_CONFIG_H
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25 #include <config.h>
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26 #endif
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27
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28 #include "lo-specfun.h"
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29 #include "quit.h"
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30
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31 #include "defun-dld.h"
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32 #include "error.h"
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33 #include "gripes.h"
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34 #include "oct-obj.h"
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35 #include "utils.h"
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36
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37 enum bessel_type
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38 {
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39 BESSEL_J,
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40 BESSEL_Y,
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41 BESSEL_I,
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42 BESSEL_K,
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43 BESSEL_H1,
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44 BESSEL_H2
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45 };
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46
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47 #define DO_BESSEL(type, alpha, x, scaled, ierr, result) \
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48 do \
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49 { \
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50 switch (type) \
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51 { \
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52 case BESSEL_J: \
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53 result = besselj (alpha, x, scaled, ierr); \
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54 break; \
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55 \
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56 case BESSEL_Y: \
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57 result = bessely (alpha, x, scaled, ierr); \
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58 break; \
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59 \
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60 case BESSEL_I: \
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61 result = besseli (alpha, x, scaled, ierr); \
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62 break; \
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63 \
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64 case BESSEL_K: \
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65 result = besselk (alpha, x, scaled, ierr); \
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66 break; \
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67 \
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68 case BESSEL_H1: \
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69 result = besselh1 (alpha, x, scaled, ierr); \
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70 break; \
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71 \
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72 case BESSEL_H2: \
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73 result = besselh2 (alpha, x, scaled, ierr); \
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74 break; \
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75 \
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76 default: \
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77 break; \
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78 } \
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79 } \
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80 while (0)
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81
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82 static void
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83 gripe_bessel_arg (const char *fn, const char *arg)
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84 {
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85 error ("%s: expecting scalar or matrix as %s argument", fn, arg);
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86 }
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87
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88 octave_value_list
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89 do_bessel (enum bessel_type type, const char *fn,
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90 const octave_value_list& args, int nargout)
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91 {
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92 octave_value_list retval;
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93
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94 int nargin = args.length ();
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95
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96 if (nargin == 2 || nargin == 3)
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97 {
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98 bool scaled = (nargin == 3);
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99
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100 octave_value alpha_arg = args(0);
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101 octave_value x_arg = args(1);
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102
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103 if (alpha_arg.is_single_type () || x_arg.is_single_type ())
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104 {
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105 if (alpha_arg.is_scalar_type ())
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106 {
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107 float alpha = args(0).float_value ();
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108
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109 if (! error_state)
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110 {
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111 if (x_arg.is_scalar_type ())
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112 {
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113 FloatComplex x = x_arg.float_complex_value ();
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114
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115 if (! error_state)
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116 {
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117 octave_idx_type ierr;
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118 octave_value result;
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119
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120 DO_BESSEL (type, alpha, x, scaled, ierr, result);
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121
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122 if (nargout > 1)
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123 retval(1) = static_cast<float> (ierr);
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124
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125 retval(0) = result;
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126 }
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127 else
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128 gripe_bessel_arg (fn, "second");
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129 }
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130 else
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131 {
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132 FloatComplexNDArray x = x_arg.float_complex_array_value ();
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133
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134 if (! error_state)
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135 {
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136 ArrayN<octave_idx_type> ierr;
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137 octave_value result;
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138
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139 DO_BESSEL (type, alpha, x, scaled, ierr, result);
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140
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141 if (nargout > 1)
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142 retval(1) = NDArray (ierr);
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143
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144 retval(0) = result;
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145 }
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146 else
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147 gripe_bessel_arg (fn, "second");
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148 }
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149 }
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150 else
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151 gripe_bessel_arg (fn, "first");
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152 }
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153 else
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154 {
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155 dim_vector dv0 = args(0).dims ();
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156 dim_vector dv1 = args(1).dims ();
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157
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158 bool args0_is_row_vector = (dv0 (1) == dv0.numel ());
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159 bool args1_is_col_vector = (dv1 (0) == dv1.numel ());
82be108cc558 First attempt at single precision tyeps
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160
82be108cc558 First attempt at single precision tyeps
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parents: 7031
diff changeset
161 if (args0_is_row_vector && args1_is_col_vector)
82be108cc558 First attempt at single precision tyeps
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parents: 7031
diff changeset
162 {
82be108cc558 First attempt at single precision tyeps
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parents: 7031
diff changeset
163 FloatRowVector ralpha = args(0).float_row_vector_value ();
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parents: 7031
diff changeset
164
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parents: 7031
diff changeset
165 if (! error_state)
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parents: 7031
diff changeset
166 {
82be108cc558 First attempt at single precision tyeps
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parents: 7031
diff changeset
167 FloatComplexColumnVector cx =
82be108cc558 First attempt at single precision tyeps
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parents: 7031
diff changeset
168 x_arg.float_complex_column_vector_value ();
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parents: 7031
diff changeset
169
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
170 if (! error_state)
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
171 {
82be108cc558 First attempt at single precision tyeps
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parents: 7031
diff changeset
172 Array2<octave_idx_type> ierr;
82be108cc558 First attempt at single precision tyeps
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parents: 7031
diff changeset
173 octave_value result;
82be108cc558 First attempt at single precision tyeps
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parents: 7031
diff changeset
174
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David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
175 DO_BESSEL (type, ralpha, cx, scaled, ierr, result);
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
176
82be108cc558 First attempt at single precision tyeps
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parents: 7031
diff changeset
177 if (nargout > 1)
7919
9d080df0c843 new NDArray constructor for ArrayN<octave_idx_type>
David Bateman <dbateman@free.fr>
parents: 7789
diff changeset
178 retval(1) = NDArray (ierr);
7789
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diff changeset
179
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diff changeset
180 retval(0) = result;
82be108cc558 First attempt at single precision tyeps
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parents: 7031
diff changeset
181 }
82be108cc558 First attempt at single precision tyeps
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parents: 7031
diff changeset
182 else
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
183 gripe_bessel_arg (fn, "second");
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David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
184 }
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
185 else
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
186 gripe_bessel_arg (fn, "first");
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
187 }
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parents: 7031
diff changeset
188 else
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
189 {
82be108cc558 First attempt at single precision tyeps
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parents: 7031
diff changeset
190 FloatNDArray alpha = args(0).float_array_value ();
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parents: 7031
diff changeset
191
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
192 if (! error_state)
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
193 {
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
194 if (x_arg.is_scalar_type ())
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
195 {
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
196 FloatComplex x = x_arg.float_complex_value ();
82be108cc558 First attempt at single precision tyeps
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parents: 7031
diff changeset
197
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
198 if (! error_state)
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
199 {
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
200 ArrayN<octave_idx_type> ierr;
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
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diff changeset
201 octave_value result;
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
202
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
203 DO_BESSEL (type, alpha, x, scaled, ierr, result);
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
204
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
205 if (nargout > 1)
7919
9d080df0c843 new NDArray constructor for ArrayN<octave_idx_type>
David Bateman <dbateman@free.fr>
parents: 7789
diff changeset
206 retval(1) = NDArray (ierr);
7789
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diff changeset
207
82be108cc558 First attempt at single precision tyeps
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parents: 7031
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208 retval(0) = result;
82be108cc558 First attempt at single precision tyeps
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parents: 7031
diff changeset
209 }
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
210 else
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
211 gripe_bessel_arg (fn, "second");
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
212 }
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
213 else
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
214 {
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
215 FloatComplexNDArray x = x_arg.float_complex_array_value ();
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
216
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
217 if (! error_state)
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
218 {
82be108cc558 First attempt at single precision tyeps
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parents: 7031
diff changeset
219 ArrayN<octave_idx_type> ierr;
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
220 octave_value result;
82be108cc558 First attempt at single precision tyeps
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parents: 7031
diff changeset
221
82be108cc558 First attempt at single precision tyeps
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parents: 7031
diff changeset
222 DO_BESSEL (type, alpha, x, scaled, ierr, result);
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
223
82be108cc558 First attempt at single precision tyeps
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parents: 7031
diff changeset
224 if (nargout > 1)
7919
9d080df0c843 new NDArray constructor for ArrayN<octave_idx_type>
David Bateman <dbateman@free.fr>
parents: 7789
diff changeset
225 retval(1) = NDArray (ierr);
7789
82be108cc558 First attempt at single precision tyeps
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parents: 7031
diff changeset
226
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
227 retval(0) = result;
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
228 }
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
229 else
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
230 gripe_bessel_arg (fn, "second");
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
231 }
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
232 }
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
233 else
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
234 gripe_bessel_arg (fn, "first");
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
235 }
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
236 }
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
237 }
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
238 else
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
239 {
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
240 if (alpha_arg.is_scalar_type ())
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
241 {
82be108cc558 First attempt at single precision tyeps
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parents: 7031
diff changeset
242 double alpha = args(0).double_value ();
3220
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jwe
parents: 3187
diff changeset
243
4844
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jwe
parents: 4153
diff changeset
244 if (! error_state)
9f7ef92b50b0 [project @ 2004-04-02 17:26:53 by jwe]
jwe
parents: 4153
diff changeset
245 {
9f7ef92b50b0 [project @ 2004-04-02 17:26:53 by jwe]
jwe
parents: 4153
diff changeset
246 if (x_arg.is_scalar_type ())
9f7ef92b50b0 [project @ 2004-04-02 17:26:53 by jwe]
jwe
parents: 4153
diff changeset
247 {
9f7ef92b50b0 [project @ 2004-04-02 17:26:53 by jwe]
jwe
parents: 4153
diff changeset
248 Complex x = x_arg.complex_value ();
3155
1016520a9d38 [project @ 1998-02-18 21:51:50 by jwe]
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parents:
diff changeset
249
4844
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jwe
parents: 4153
diff changeset
250 if (! error_state)
3155
1016520a9d38 [project @ 1998-02-18 21:51:50 by jwe]
jwe
parents:
diff changeset
251 {
7789
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
252 octave_idx_type ierr;
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
253 octave_value result;
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
254
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
255 DO_BESSEL (type, alpha, x, scaled, ierr, result);
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
256
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
257 if (nargout > 1)
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
258 retval(1) = static_cast<double> (ierr);
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
259
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
260 retval(0) = result;
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
261 }
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
262 else
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
263 gripe_bessel_arg (fn, "second");
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
264 }
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
265 else
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
266 {
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
267 ComplexNDArray x = x_arg.complex_array_value ();
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
268
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
269 if (! error_state)
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
270 {
5275
23b37da9fd5b [project @ 2005-04-08 16:07:35 by jwe]
jwe
parents: 4844
diff changeset
271 ArrayN<octave_idx_type> ierr;
3220
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
272 octave_value result;
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
273
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
274 DO_BESSEL (type, alpha, x, scaled, ierr, result);
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
275
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
276 if (nargout > 1)
7919
9d080df0c843 new NDArray constructor for ArrayN<octave_idx_type>
David Bateman <dbateman@free.fr>
parents: 7789
diff changeset
277 retval(1) = NDArray (ierr);
3220
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
278
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
279 retval(0) = result;
3155
1016520a9d38 [project @ 1998-02-18 21:51:50 by jwe]
jwe
parents:
diff changeset
280 }
4844
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jwe
parents: 4153
diff changeset
281 else
9f7ef92b50b0 [project @ 2004-04-02 17:26:53 by jwe]
jwe
parents: 4153
diff changeset
282 gripe_bessel_arg (fn, "second");
3155
1016520a9d38 [project @ 1998-02-18 21:51:50 by jwe]
jwe
parents:
diff changeset
283 }
7789
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
284 }
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
285 else
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
286 gripe_bessel_arg (fn, "first");
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
287 }
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
288 else
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
289 {
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
290 dim_vector dv0 = args(0).dims ();
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
291 dim_vector dv1 = args(1).dims ();
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
292
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
293 bool args0_is_row_vector = (dv0 (1) == dv0.numel ());
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
294 bool args1_is_col_vector = (dv1 (0) == dv1.numel ());
82be108cc558 First attempt at single precision tyeps
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parents: 7031
diff changeset
295
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
296 if (args0_is_row_vector && args1_is_col_vector)
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
297 {
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
298 RowVector ralpha = args(0).row_vector_value ();
82be108cc558 First attempt at single precision tyeps
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parents: 7031
diff changeset
299
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
300 if (! error_state)
4844
9f7ef92b50b0 [project @ 2004-04-02 17:26:53 by jwe]
jwe
parents: 4153
diff changeset
301 {
7789
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
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diff changeset
302 ComplexColumnVector cx =
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
303 x_arg.complex_column_vector_value ();
4844
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jwe
parents: 4153
diff changeset
304
9f7ef92b50b0 [project @ 2004-04-02 17:26:53 by jwe]
jwe
parents: 4153
diff changeset
305 if (! error_state)
9f7ef92b50b0 [project @ 2004-04-02 17:26:53 by jwe]
jwe
parents: 4153
diff changeset
306 {
7789
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
307 Array2<octave_idx_type> ierr;
4844
9f7ef92b50b0 [project @ 2004-04-02 17:26:53 by jwe]
jwe
parents: 4153
diff changeset
308 octave_value result;
7789
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David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
309
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
310 DO_BESSEL (type, ralpha, cx, scaled, ierr, result);
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
311
4844
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jwe
parents: 4153
diff changeset
312 if (nargout > 1)
7919
9d080df0c843 new NDArray constructor for ArrayN<octave_idx_type>
David Bateman <dbateman@free.fr>
parents: 7789
diff changeset
313 retval(1) = NDArray (ierr);
7789
82be108cc558 First attempt at single precision tyeps
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diff changeset
314
4844
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jwe
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diff changeset
315 retval(0) = result;
9f7ef92b50b0 [project @ 2004-04-02 17:26:53 by jwe]
jwe
parents: 4153
diff changeset
316 }
9f7ef92b50b0 [project @ 2004-04-02 17:26:53 by jwe]
jwe
parents: 4153
diff changeset
317 else
9f7ef92b50b0 [project @ 2004-04-02 17:26:53 by jwe]
jwe
parents: 4153
diff changeset
318 gripe_bessel_arg (fn, "second");
9f7ef92b50b0 [project @ 2004-04-02 17:26:53 by jwe]
jwe
parents: 4153
diff changeset
319 }
7789
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
320 else
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
321 gripe_bessel_arg (fn, "first");
3155
1016520a9d38 [project @ 1998-02-18 21:51:50 by jwe]
jwe
parents:
diff changeset
322 }
4844
9f7ef92b50b0 [project @ 2004-04-02 17:26:53 by jwe]
jwe
parents: 4153
diff changeset
323 else
7789
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
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324 {
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325 NDArray alpha = args(0).array_value ();
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326
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327 if (! error_state)
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328 {
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329 if (x_arg.is_scalar_type ())
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330 {
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331 Complex x = x_arg.complex_value ();
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332
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333 if (! error_state)
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334 {
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335 ArrayN<octave_idx_type> ierr;
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336 octave_value result;
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337
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338 DO_BESSEL (type, alpha, x, scaled, ierr, result);
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339
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340 if (nargout > 1)
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341 retval(1) = NDArray (ierr);
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342
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343 retval(0) = result;
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344 }
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345 else
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346 gripe_bessel_arg (fn, "second");
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347 }
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348 else
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349 {
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350 ComplexNDArray x = x_arg.complex_array_value ();
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351
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352 if (! error_state)
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353 {
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354 ArrayN<octave_idx_type> ierr;
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355 octave_value result;
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356
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357 DO_BESSEL (type, alpha, x, scaled, ierr, result);
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358
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359 if (nargout > 1)
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360 retval(1) = NDArray (ierr);
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361
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362 retval(0) = result;
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363 }
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364 else
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365 gripe_bessel_arg (fn, "second");
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366 }
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367 }
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368 else
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369 gripe_bessel_arg (fn, "first");
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370 }
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371 }
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372 }
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373 }
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374 else
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375 print_usage ();
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376
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377 return retval;
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378 }
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379
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380 DEFUN_DLD (besselj, args, nargout,
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381 "-*- texinfo -*-\n\
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382 @deftypefn {Loadable Function} {[@var{j}, @var{ierr}] =} besselj (@var{alpha}, @var{x}, @var{opt})\n\
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383 @deftypefnx {Loadable Function} {[@var{y}, @var{ierr}] =} bessely (@var{alpha}, @var{x}, @var{opt})\n\
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384 @deftypefnx {Loadable Function} {[@var{i}, @var{ierr}] =} besseli (@var{alpha}, @var{x}, @var{opt})\n\
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385 @deftypefnx {Loadable Function} {[@var{k}, @var{ierr}] =} besselk (@var{alpha}, @var{x}, @var{opt})\n\
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386 @deftypefnx {Loadable Function} {[@var{h}, @var{ierr}] =} besselh (@var{alpha}, @var{k}, @var{x}, @var{opt})\n\
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387 Compute Bessel or Hankel functions of various kinds:\n\
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388 \n\
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389 @table @code\n\
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390 @item besselj\n\
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391 Bessel functions of the first kind. If the argument @var{opt} is supplied, \n\
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392 the result is multiplied by @code{exp(-abs(imag(x)))}.\n\
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393 @item bessely\n\
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394 Bessel functions of the second kind. If the argument @var{opt} is supplied,\n\
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395 the result is multiplied by @code{exp(-abs(imag(x)))}.\n\
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396 @item besseli\n\
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397 Modified Bessel functions of the first kind. If the argument @var{opt} is supplied,\n\
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398 the result is multiplied by @code{exp(-abs(real(x)))}.\n\
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399 @item besselk\n\
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diff changeset
400 Modified Bessel functions of the second kind. If the argument @var{opt} is supplied,\n\
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
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diff changeset
401 the result is multiplied by @code{exp(x)}.\n\
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402 @item besselh\n\
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403 Compute Hankel functions of the first (@var{k} = 1) or second (@var{k}\n\
8278
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diff changeset
404 = 2) kind. If the argument @var{opt} is supplied, the result is multiplied by\n\
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
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parents: 7919
diff changeset
405 @code{exp (-I*@var{x})} for @var{k} = 1 or @code{exp (I*@var{x})} for\n\
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
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diff changeset
406 @var{k} = 2.\n\
3459
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diff changeset
407 @end table\n\
3220
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diff changeset
408 \n\
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diff changeset
409 If @var{alpha} is a scalar, the result is the same size as @var{x}.\n\
8e36c45e3a61 [project @ 2000-01-19 10:26:18 by jwe]
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diff changeset
410 If @var{x} is a scalar, the result is the same size as @var{alpha}.\n\
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diff changeset
411 If @var{alpha} is a row vector and @var{x} is a column vector, the\n\
8e36c45e3a61 [project @ 2000-01-19 10:26:18 by jwe]
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diff changeset
412 result is a matrix with @code{length (@var{x})} rows and\n\
8e36c45e3a61 [project @ 2000-01-19 10:26:18 by jwe]
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diff changeset
413 @code{length (@var{alpha})} columns. Otherwise, @var{alpha} and\n\
8e36c45e3a61 [project @ 2000-01-19 10:26:18 by jwe]
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diff changeset
414 @var{x} must conform and the result will be the same size.\n\
3155
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415 \n\
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diff changeset
416 The value of @var{alpha} must be real. The value of @var{x} may be\n\
8e36c45e3a61 [project @ 2000-01-19 10:26:18 by jwe]
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diff changeset
417 complex.\n\
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diff changeset
418 \n\
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diff changeset
419 If requested, @var{ierr} contains the following status information\n\
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diff changeset
420 and is the same size as the result.\n\
3548
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diff changeset
421 \n\
3459
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diff changeset
422 @enumerate 0\n\
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diff changeset
423 @item\n\
8e36c45e3a61 [project @ 2000-01-19 10:26:18 by jwe]
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diff changeset
424 Normal return.\n\
8e36c45e3a61 [project @ 2000-01-19 10:26:18 by jwe]
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diff changeset
425 @item\n\
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diff changeset
426 Input error, return @code{NaN}.\n\
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diff changeset
427 @item\n\
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diff changeset
428 Overflow, return @code{Inf}.\n\
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diff changeset
429 @item\n\
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diff changeset
430 Loss of significance by argument reduction results in less than\n\
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diff changeset
431 half of machine accuracy.\n\
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diff changeset
432 @item\n\
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diff changeset
433 Complete loss of significance by argument reduction, return @code{NaN}.\n\
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diff changeset
434 @item\n\
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diff changeset
435 Error---no computation, algorithm termination condition not met,\n\
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diff changeset
436 return @code{NaN}.\n\
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diff changeset
437 @end enumerate\n\
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diff changeset
438 @end deftypefn")
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diff changeset
439 {
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diff changeset
440 return do_bessel (BESSEL_J, "besselj", args, nargout);
3155
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diff changeset
441 }
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diff changeset
442
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diff changeset
443 DEFUN_DLD (bessely, args, nargout,
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diff changeset
444 "-*- texinfo -*-\n\
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diff changeset
445 @deftypefn {Loadable Function} {[@var{y}, @var{ierr}] =} bessely (@var{alpha}, @var{x}, @var{opt})\n\
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diff changeset
446 See besselj.\n\
8e36c45e3a61 [project @ 2000-01-19 10:26:18 by jwe]
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diff changeset
447 @end deftypefn")
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diff changeset
448 {
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diff changeset
449 return do_bessel (BESSEL_Y, "bessely", args, nargout);
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diff changeset
450 }
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diff changeset
451
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diff changeset
452 DEFUN_DLD (besseli, args, nargout,
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diff changeset
453 "-*- texinfo -*-\n\
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diff changeset
454 @deftypefn {Loadable Function} {[@var{i}, @var{ierr}] =} besseli (@var{alpha}, @var{x}, @var{opt})\n\
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diff changeset
455 See besselj.\n\
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diff changeset
456 @end deftypefn")
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diff changeset
457 {
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diff changeset
458 return do_bessel (BESSEL_I, "besseli", args, nargout);
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diff changeset
459 }
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diff changeset
460
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diff changeset
461 DEFUN_DLD (besselk, args, nargout,
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diff changeset
462 "-*- texinfo -*-\n\
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diff changeset
463 @deftypefn {Loadable Function} {[@var{k}, @var{ierr}] =} besselk (@var{alpha}, @var{x}, @var{opt})\n\
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diff changeset
464 See besselj.\n\
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diff changeset
465 @end deftypefn")
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diff changeset
466 {
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
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diff changeset
467 return do_bessel (BESSEL_K, "besselk", args, nargout);
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diff changeset
468 }
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diff changeset
469
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
470 DEFUN_DLD (besselh, args, nargout,
3459
8e36c45e3a61 [project @ 2000-01-19 10:26:18 by jwe]
jwe
parents: 3325
diff changeset
471 "-*- texinfo -*-\n\
8e36c45e3a61 [project @ 2000-01-19 10:26:18 by jwe]
jwe
parents: 3325
diff changeset
472 @deftypefn {Loadable Function} {[@var{h}, @var{ierr}] =} besselh (@var{alpha}, @var{k}, @var{x}, @var{opt})\n\
8e36c45e3a61 [project @ 2000-01-19 10:26:18 by jwe]
jwe
parents: 3325
diff changeset
473 See besselj.\n\
8e36c45e3a61 [project @ 2000-01-19 10:26:18 by jwe]
jwe
parents: 3325
diff changeset
474 @end deftypefn")
3220
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
475 {
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
476 octave_value_list retval;
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
477
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
478 int nargin = args.length ();
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
479
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
480 if (nargin == 2)
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
481 {
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
482 retval = do_bessel (BESSEL_H1, "besselh", args, nargout);
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
483 }
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
484 else if (nargin == 3 || nargin == 4)
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
485 {
5275
23b37da9fd5b [project @ 2005-04-08 16:07:35 by jwe]
jwe
parents: 4844
diff changeset
486 octave_idx_type kind = args(1).int_value ();
3220
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
487
3810
f19f00339363 [project @ 2001-03-29 21:03:01 by jwe]
jwe
parents: 3568
diff changeset
488 if (! error_state)
3220
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
489 {
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
490 octave_value_list tmp_args;
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
491
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
492 if (nargin == 4)
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
493 tmp_args(2) = args(3);
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
494
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
495 tmp_args(1) = args(2);
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
496 tmp_args(0) = args(0);
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
497
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
498 if (kind == 1)
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
499 retval = do_bessel (BESSEL_H1, "besselh", tmp_args, nargout);
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
500 else if (kind == 2)
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
501 retval = do_bessel (BESSEL_H2, "besselh", tmp_args, nargout);
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
502 else
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
503 error ("besselh: expecting K = 1 or 2");
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
504 }
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
505 else
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
506 error ("besselh: invalid value of K");
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
507 }
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
508 else
5823
080c08b192d8 [project @ 2006-05-19 05:32:17 by jwe]
jwe
parents: 5760
diff changeset
509 print_usage ();
3220
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
510
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
511 return retval;
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
512 }
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
513
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
514 DEFUN_DLD (airy, args, nargout,
3459
8e36c45e3a61 [project @ 2000-01-19 10:26:18 by jwe]
jwe
parents: 3325
diff changeset
515 "-*- texinfo -*-\n\
8e36c45e3a61 [project @ 2000-01-19 10:26:18 by jwe]
jwe
parents: 3325
diff changeset
516 @deftypefn {Loadable Function} {[@var{a}, @var{ierr}] =} airy (@var{k}, @var{z}, @var{opt})\n\
3220
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
517 Compute Airy functions of the first and second kind, and their\n\
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
518 derivatives.\n\
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
519 \n\
3459
8e36c45e3a61 [project @ 2000-01-19 10:26:18 by jwe]
jwe
parents: 3325
diff changeset
520 @example\n\
7031
120f3135952f [project @ 2007-10-15 15:30:03 by jwe]
jwe
parents: 7017
diff changeset
521 K Function Scale factor (if 'opt' is supplied)\n\
120f3135952f [project @ 2007-10-15 15:30:03 by jwe]
jwe
parents: 7017
diff changeset
522 --- -------- ---------------------------------------\n\
120f3135952f [project @ 2007-10-15 15:30:03 by jwe]
jwe
parents: 7017
diff changeset
523 0 Ai (Z) exp ((2/3) * Z * sqrt (Z))\n\
120f3135952f [project @ 2007-10-15 15:30:03 by jwe]
jwe
parents: 7017
diff changeset
524 1 dAi(Z)/dZ exp ((2/3) * Z * sqrt (Z))\n\
120f3135952f [project @ 2007-10-15 15:30:03 by jwe]
jwe
parents: 7017
diff changeset
525 2 Bi (Z) exp (-abs (real ((2/3) * Z *sqrt (Z))))\n\
120f3135952f [project @ 2007-10-15 15:30:03 by jwe]
jwe
parents: 7017
diff changeset
526 3 dBi(Z)/dZ exp (-abs (real ((2/3) * Z *sqrt (Z))))\n\
3459
8e36c45e3a61 [project @ 2000-01-19 10:26:18 by jwe]
jwe
parents: 3325
diff changeset
527 @end example\n\
3220
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
528 \n\
3549
03025e79d8b9 [project @ 2000-02-03 01:28:24 by jwe]
jwe
parents: 3548
diff changeset
529 The function call @code{airy (@var{z})} is equivalent to\n\
3459
8e36c45e3a61 [project @ 2000-01-19 10:26:18 by jwe]
jwe
parents: 3325
diff changeset
530 @code{airy (0, @var{z})}.\n\
3155
1016520a9d38 [project @ 1998-02-18 21:51:50 by jwe]
jwe
parents:
diff changeset
531 \n\
3549
03025e79d8b9 [project @ 2000-02-03 01:28:24 by jwe]
jwe
parents: 3548
diff changeset
532 The result is the same size as @var{z}.\n\
3220
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
533 \n\
3459
8e36c45e3a61 [project @ 2000-01-19 10:26:18 by jwe]
jwe
parents: 3325
diff changeset
534 If requested, @var{ierr} contains the following status information and\n\
8e36c45e3a61 [project @ 2000-01-19 10:26:18 by jwe]
jwe
parents: 3325
diff changeset
535 is the same size as the result.\n\
3548
ab7fa5a8f23f [project @ 2000-02-03 01:17:15 by jwe]
jwe
parents: 3499
diff changeset
536 \n\
3459
8e36c45e3a61 [project @ 2000-01-19 10:26:18 by jwe]
jwe
parents: 3325
diff changeset
537 @enumerate 0\n\
8e36c45e3a61 [project @ 2000-01-19 10:26:18 by jwe]
jwe
parents: 3325
diff changeset
538 @item\n\
8e36c45e3a61 [project @ 2000-01-19 10:26:18 by jwe]
jwe
parents: 3325
diff changeset
539 Normal return.\n\
8e36c45e3a61 [project @ 2000-01-19 10:26:18 by jwe]
jwe
parents: 3325
diff changeset
540 @item\n\
8e36c45e3a61 [project @ 2000-01-19 10:26:18 by jwe]
jwe
parents: 3325
diff changeset
541 Input error, return @code{NaN}.\n\
8e36c45e3a61 [project @ 2000-01-19 10:26:18 by jwe]
jwe
parents: 3325
diff changeset
542 @item\n\
8e36c45e3a61 [project @ 2000-01-19 10:26:18 by jwe]
jwe
parents: 3325
diff changeset
543 Overflow, return @code{Inf}.\n\
8e36c45e3a61 [project @ 2000-01-19 10:26:18 by jwe]
jwe
parents: 3325
diff changeset
544 @item\n\
8e36c45e3a61 [project @ 2000-01-19 10:26:18 by jwe]
jwe
parents: 3325
diff changeset
545 Loss of significance by argument reduction results in less than half\n\
8e36c45e3a61 [project @ 2000-01-19 10:26:18 by jwe]
jwe
parents: 3325
diff changeset
546 of machine accuracy.\n\
8e36c45e3a61 [project @ 2000-01-19 10:26:18 by jwe]
jwe
parents: 3325
diff changeset
547 @item\n\
8e36c45e3a61 [project @ 2000-01-19 10:26:18 by jwe]
jwe
parents: 3325
diff changeset
548 Complete loss of significance by argument reduction, return @code{NaN}.\n\
8e36c45e3a61 [project @ 2000-01-19 10:26:18 by jwe]
jwe
parents: 3325
diff changeset
549 @item\n\
8e36c45e3a61 [project @ 2000-01-19 10:26:18 by jwe]
jwe
parents: 3325
diff changeset
550 Error---no computation, algorithm termination condition not met,\n\
5448
ebe5d7d15522 [project @ 2005-09-14 18:55:04 by jwe]
jwe
parents: 5307
diff changeset
551 return @code{NaN}.\n\
3459
8e36c45e3a61 [project @ 2000-01-19 10:26:18 by jwe]
jwe
parents: 3325
diff changeset
552 @end enumerate\n\
8e36c45e3a61 [project @ 2000-01-19 10:26:18 by jwe]
jwe
parents: 3325
diff changeset
553 @end deftypefn")
3155
1016520a9d38 [project @ 1998-02-18 21:51:50 by jwe]
jwe
parents:
diff changeset
554 {
3220
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
555 octave_value_list retval;
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
556
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
557 int nargin = args.length ();
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
558
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
559 if (nargin > 0 && nargin < 4)
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
560 {
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
561 bool scale = (nargin == 3);
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
562
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
563 int kind = 0;
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
564
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
565 if (nargin > 1)
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
566 {
5760
8d7162924bd3 [project @ 2006-04-14 04:01:37 by jwe]
jwe
parents: 5448
diff changeset
567 kind = args(0).int_value ();
3220
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
568
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
569 if (! error_state)
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
570 {
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
571 if (kind < 0 || kind > 3)
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
572 error ("airy: expecting K = 0, 1, 2, or 3");
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
573 }
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
574 else
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
575 error ("airy: expecting integer value for K");
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
576 }
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
577
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
578 if (! error_state)
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
579 {
7789
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
580 int idx = nargin == 1 ? 0 : 1;
3220
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
581
7789
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
582 if (args (idx).is_single_type ())
3220
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
583 {
7789
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
584 FloatComplexNDArray z = args(idx).float_complex_array_value ();
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
585
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
586 if (! error_state)
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
587 {
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
588 ArrayN<octave_idx_type> ierr;
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
589 octave_value result;
3220
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
590
7789
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
591 if (kind > 1)
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
592 result = biry (z, kind == 3, scale, ierr);
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
593 else
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
594 result = airy (z, kind == 1, scale, ierr);
3220
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
595
7789
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
596 if (nargout > 1)
7919
9d080df0c843 new NDArray constructor for ArrayN<octave_idx_type>
David Bateman <dbateman@free.fr>
parents: 7789
diff changeset
597 retval(1) = NDArray (ierr);
3220
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
598
7789
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
599 retval(0) = result;
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
600 }
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
601 else
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
602 error ("airy: expecting complex matrix for Z");
3220
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
603 }
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
604 else
7789
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
605 {
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
606 ComplexNDArray z = args(idx).complex_array_value ();
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
607
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
608 if (! error_state)
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
609 {
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
610 ArrayN<octave_idx_type> ierr;
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
611 octave_value result;
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
612
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
613 if (kind > 1)
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
614 result = biry (z, kind == 3, scale, ierr);
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
615 else
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
616 result = airy (z, kind == 1, scale, ierr);
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
617
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
618 if (nargout > 1)
7919
9d080df0c843 new NDArray constructor for ArrayN<octave_idx_type>
David Bateman <dbateman@free.fr>
parents: 7789
diff changeset
619 retval(1) = NDArray (ierr);
7789
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
620
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
621 retval(0) = result;
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
622 }
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
623 else
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
624 error ("airy: expecting complex matrix for Z");
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7031
diff changeset
625 }
3220
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
626 }
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
627 }
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
628 else
5823
080c08b192d8 [project @ 2006-05-19 05:32:17 by jwe]
jwe
parents: 5760
diff changeset
629 print_usage ();
3220
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
630
3deb1105fbc1 [project @ 1998-11-19 00:06:30 by jwe]
jwe
parents: 3187
diff changeset
631 return retval;
3155
1016520a9d38 [project @ 1998-02-18 21:51:50 by jwe]
jwe
parents:
diff changeset
632 }
1016520a9d38 [project @ 1998-02-18 21:51:50 by jwe]
jwe
parents:
diff changeset
633
1016520a9d38 [project @ 1998-02-18 21:51:50 by jwe]
jwe
parents:
diff changeset
634 /*
8278
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
635 %! # Test values computed with GP/PARI version 2.3.3
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
636 %!
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
637 %!shared alpha, x, jx, yx, ix, kx, nix
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
638 %!
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
639 %! # Bessel functions, even order, positive and negative x
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
640 %! alpha = 2; x = 1.25;
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
641 %! jx = 0.1710911312405234823613091417;
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
642 %! yx = -1.193199310178553861283790424;
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
643 %! ix = 0.2220184483766341752692212604;
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
644 %! kx = 0.9410016167388185767085460540;
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
645 %!
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
646 %!assert(besselj(alpha,x), jx, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
647 %!assert(bessely(alpha,x), yx, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
648 %!assert(besseli(alpha,x), ix, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
649 %!assert(besselk(alpha,x), kx, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
650 %!assert(besselh(alpha,1,x), jx + I*yx, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
651 %!assert(besselh(alpha,2,x), jx - I*yx, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
652 %!
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
653 %!assert(besselj(alpha,x,1), jx*exp(-abs(imag(x))), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
654 %!assert(bessely(alpha,x,1), yx*exp(-abs(imag(x))), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
655 %!assert(besseli(alpha,x,1), ix*exp(-abs(real(x))), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
656 %!assert(besselk(alpha,x,1), kx*exp(x), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
657 %!assert(besselh(alpha,1,x,1), (jx + I*yx)*exp(-I*x), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
658 %!assert(besselh(alpha,2,x,1), (jx - I*yx)*exp(I*x), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
659 %!
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
660 %!assert(besselj(-alpha,x), jx, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
661 %!assert(bessely(-alpha,x), yx, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
662 %!assert(besseli(-alpha,x), ix, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
663 %!assert(besselk(-alpha,x), kx, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
664 %!assert(besselh(-alpha,1,x), jx + I*yx, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
665 %!assert(besselh(-alpha,2,x), jx - I*yx, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
666 %!
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
667 %!assert(besselj(-alpha,x,1), jx*exp(-abs(imag(x))), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
668 %!assert(bessely(-alpha,x,1), yx*exp(-abs(imag(x))), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
669 %!assert(besseli(-alpha,x,1), ix*exp(-abs(real(x))), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
670 %!assert(besselk(-alpha,x,1), kx*exp(x), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
671 %!assert(besselh(-alpha,1,x,1), (jx + I*yx)*exp(-I*x), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
672 %!assert(besselh(-alpha,2,x,1), (jx - I*yx)*exp(I*x), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
673 %!
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
674 %! x *= -1;
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
675 %! yx = -1.193199310178553861283790424 + 0.3421822624810469647226182835*I;
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
676 %! kx = 0.9410016167388185767085460540 - 0.6974915263814386815610060884*I;
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
677 %!
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
678 %!assert(besselj(alpha,x), jx, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
679 %!assert(bessely(alpha,x), yx, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
680 %!assert(besseli(alpha,x), ix, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
681 %!assert(besselk(alpha,x), kx, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
682 %!assert(besselh(alpha,1,x), jx + I*yx, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
683 %!assert(besselh(alpha,2,x), jx - I*yx, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
684 %!
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
685 %!assert(besselj(alpha,x,1), jx*exp(-abs(imag(x))), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
686 %!assert(bessely(alpha,x,1), yx*exp(-abs(imag(x))), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
687 %!assert(besseli(alpha,x,1), ix*exp(-abs(real(x))), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
688 %!assert(besselk(alpha,x,1), kx*exp(x), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
689 %!assert(besselh(alpha,1,x,1), (jx + I*yx)*exp(-I*x), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
690 %!assert(besselh(alpha,2,x,1), (jx - I*yx)*exp(I*x), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
691 %!
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
692 %! # Bessel functions, odd order, positive and negative x
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
693 %! alpha = 3; x = 2.5;
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
694 %! jx = 0.2166003910391135247666890035;
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
695 %! yx = -0.7560554967536709968379029772;
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
696 %! ix = 0.4743704087780355895548240179;
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
697 %! kx = 0.2682271463934492027663765197;
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
698 %!
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
699 %!assert(besselj(alpha,x), jx, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
700 %!assert(bessely(alpha,x), yx, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
701 %!assert(besseli(alpha,x), ix, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
702 %!assert(besselk(alpha,x), kx, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
703 %!assert(besselh(alpha,1,x), jx + I*yx, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
704 %!assert(besselh(alpha,2,x), jx - I*yx, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
705 %!
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
706 %!assert(besselj(alpha,x,1), jx*exp(-abs(imag(x))), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
707 %!assert(bessely(alpha,x,1), yx*exp(-abs(imag(x))), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
708 %!assert(besseli(alpha,x,1), ix*exp(-abs(real(x))), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
709 %!assert(besselk(alpha,x,1), kx*exp(x), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
710 %!assert(besselh(alpha,1,x,1), (jx + I*yx)*exp(-I*x), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
711 %!assert(besselh(alpha,2,x,1), (jx - I*yx)*exp(I*x), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
712 %!
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
713 %!assert(besselj(-alpha,x), -jx, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
714 %!assert(bessely(-alpha,x), -yx, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
715 %!assert(besseli(-alpha,x), ix, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
716 %!assert(besselk(-alpha,x), kx, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
717 %!assert(besselh(-alpha,1,x), -(jx + I*yx), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
718 %!assert(besselh(-alpha,2,x), -(jx - I*yx), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
719 %!
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
720 %!assert(besselj(-alpha,x,1), -jx*exp(-abs(imag(x))), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
721 %!assert(bessely(-alpha,x,1), -yx*exp(-abs(imag(x))), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
722 %!assert(besseli(-alpha,x,1), ix*exp(-abs(real(x))), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
723 %!assert(besselk(-alpha,x,1), kx*exp(x), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
724 %!assert(besselh(-alpha,1,x,1), -(jx + I*yx)*exp(-I*x), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
725 %!assert(besselh(-alpha,2,x,1), -(jx - I*yx)*exp(I*x), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
726 %!
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
727 %! x *= -1;
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
728 %! jx = -jx;
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
729 %! yx = 0.7560554967536709968379029772 - 0.4332007820782270495333780070*I;
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
730 %! ix = -ix;
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
731 %! kx = -0.2682271463934492027663765197 - 1.490278591297463775542004240*I;
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
732 %!
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
733 %!assert(besselj(alpha,x), jx, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
734 %!assert(bessely(alpha,x), yx, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
735 %!assert(besseli(alpha,x), ix, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
736 %!assert(besselk(alpha,x), kx, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
737 %!assert(besselh(alpha,1,x), jx + I*yx, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
738 %!assert(besselh(alpha,2,x), jx - I*yx, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
739 %!
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
740 %!assert(besselj(alpha,x,1), jx*exp(-abs(imag(x))), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
741 %!assert(bessely(alpha,x,1), yx*exp(-abs(imag(x))), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
742 %!assert(besseli(alpha,x,1), ix*exp(-abs(real(x))), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
743 %!assert(besselk(alpha,x,1), kx*exp(x), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
744 %!assert(besselh(alpha,1,x,1), (jx + I*yx)*exp(-I*x), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
745 %!assert(besselh(alpha,2,x,1), (jx - I*yx)*exp(I*x), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
746 %!
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
747 %! # Bessel functions, fractional order, positive and negative x
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
748 %!
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
749 %! alpha = 3.5; x = 2.75;
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
750 %! jx = 0.1691636439842384154644784389;
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
751 %! yx = -0.8301381935499356070267953387;
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
752 %! ix = 0.3930540878794826310979363668;
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
753 %! kx = 0.2844099013460621170288192503;
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
754 %!
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
755 %!assert(besselj(alpha,x), jx, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
756 %!assert(bessely(alpha,x), yx, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
757 %!assert(besseli(alpha,x), ix, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
758 %!assert(besselk(alpha,x), kx, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
759 %!assert(besselh(alpha,1,x), jx + I*yx, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
760 %!assert(besselh(alpha,2,x), jx - I*yx, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
761 %!
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
762 %!assert(besselj(alpha,x,1), jx*exp(-abs(imag(x))), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
763 %!assert(bessely(alpha,x,1), yx*exp(-abs(imag(x))), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
764 %!assert(besseli(alpha,x,1), ix*exp(-abs(real(x))), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
765 %!assert(besselk(alpha,x,1), kx*exp(x), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
766 %!assert(besselh(alpha,1,x,1), (jx + I*yx)*exp(-I*x), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
767 %!assert(besselh(alpha,2,x,1), (jx - I*yx)*exp(I*x), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
768 %!
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
769 %! nix = 0.2119931212254662995364461998;
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
770 %!
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
771 %!assert(besselj(-alpha,x), yx, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
772 %!assert(bessely(-alpha,x), -jx, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
773 %!assert(besseli(-alpha,x), nix, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
774 %!assert(besselk(-alpha,x), kx, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
775 %!assert(besselh(-alpha,1,x), -I*(jx + I*yx), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
776 %!assert(besselh(-alpha,2,x), I*(jx - I*yx), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
777 %!
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
778 %!assert(besselj(-alpha,x,1), yx*exp(-abs(imag(x))), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
779 %!assert(bessely(-alpha,x,1), -jx*exp(-abs(imag(x))), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
780 %!assert(besseli(-alpha,x,1), nix*exp(-abs(real(x))), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
781 %!assert(besselk(-alpha,x,1), kx*exp(x), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
782 %!assert(besselh(-alpha,1,x,1), -I*(jx + I*yx)*exp(-I*x), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
783 %!assert(besselh(-alpha,2,x,1), I*(jx - I*yx)*exp(I*x), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
784 %!
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
785 %! x *= -1;
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
786 %! jx *= -I;
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
787 %! yx = -0.8301381935499356070267953387*I;
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
788 %! ix *= -I;
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
789 %! kx = -0.9504059335995575096509874508*I;
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
790 %!
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
791 %!assert(besselj(alpha,x), jx, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
792 %!assert(bessely(alpha,x), yx, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
793 %!assert(besseli(alpha,x), ix, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
794 %!assert(besselk(alpha,x), kx, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
795 %!assert(besselh(alpha,1,x), jx + I*yx, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
796 %!assert(besselh(alpha,2,x), jx - I*yx, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
797 %!
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
798 %!assert(besselj(alpha,x,1), jx*exp(-abs(imag(x))), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
799 %!assert(bessely(alpha,x,1), yx*exp(-abs(imag(x))), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
800 %!assert(besseli(alpha,x,1), ix*exp(-abs(real(x))), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
801 %!assert(besselk(alpha,x,1), kx*exp(x), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
802 %!assert(besselh(alpha,1,x,1), (jx + I*yx)*exp(-I*x), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
803 %!assert(besselh(alpha,2,x,1), (jx - I*yx)*exp(I*x), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
804 %!
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
805 %! # Bessel functions, even order, complex x
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
806 %!
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
807 %! alpha = 2; x = 1.25 + 3.625 * I;
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
808 %! jx = -1.299533366810794494030065917 + 4.370833116012278943267479589*I;
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
809 %! yx = -4.370357232383223896393056727 - 1.283083391453582032688834041*I;
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
810 %! ix = -0.6717801680341515541002273932 - 0.2314623443930774099910228553*I;
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
811 %! kx = -0.01108009888623253515463783379 + 0.2245218229358191588208084197*I;
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
812 %!
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
813 %!assert(besselj(alpha,x), jx, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
814 %!assert(bessely(alpha,x), yx, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
815 %!assert(besseli(alpha,x), ix, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
816 %!assert(besselk(alpha,x), kx, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
817 %!assert(besselh(alpha,1,x), jx + I*yx, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
818 %!assert(besselh(alpha,2,x), jx - I*yx, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
819 %!
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
820 %!assert(besselj(alpha,x,1), jx*exp(-abs(imag(x))), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
821 %!assert(bessely(alpha,x,1), yx*exp(-abs(imag(x))), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
822 %!assert(besseli(alpha,x,1), ix*exp(-abs(real(x))), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
823 %!assert(besselk(alpha,x,1), kx*exp(x), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
824 %!assert(besselh(alpha,1,x,1), (jx + I*yx)*exp(-I*x), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
825 %!assert(besselh(alpha,2,x,1), (jx - I*yx)*exp(I*x), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
826 %!
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
827 %!assert(besselj(-alpha,x), jx, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
828 %!assert(bessely(-alpha,x), yx, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
829 %!assert(besseli(-alpha,x), ix, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
830 %!assert(besselk(-alpha,x), kx, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
831 %!assert(besselh(-alpha,1,x), jx + I*yx, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
832 %!assert(besselh(-alpha,2,x), jx - I*yx, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
833 %!
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
834 %!assert(besselj(-alpha,x,1), jx*exp(-abs(imag(x))), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
835 %!assert(bessely(-alpha,x,1), yx*exp(-abs(imag(x))), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
836 %!assert(besseli(-alpha,x,1), ix*exp(-abs(real(x))), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
837 %!assert(besselk(-alpha,x,1), kx*exp(x), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
838 %!assert(besselh(-alpha,1,x,1), (jx + I*yx)*exp(-I*x), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
839 %!assert(besselh(-alpha,2,x,1), (jx - I*yx)*exp(I*x), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
840 %!
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
841 %! # Bessel functions, odd order, complex x
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
842 %!
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
843 %! alpha = 3; x = 2.5 + 1.875 * I;
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
844 %! jx = 0.1330721523048277493333458596 + 0.5386295217249660078754395597*I;
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
845 %! yx = -0.6485072392105829901122401551 + 0.2608129289785456797046996987*I;
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
846 %! ix = -0.6182064685486998097516365709 + 0.4677561094683470065767989920*I;
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
847 %! kx = -0.1568585587733540007867882337 - 0.05185853709490846050505141321*I;
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
848 %!
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
849 %!assert(besselj(alpha,x), jx, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
850 %!assert(bessely(alpha,x), yx, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
851 %!assert(besseli(alpha,x), ix, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
852 %!assert(besselk(alpha,x), kx, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
853 %!assert(besselh(alpha,1,x), jx + I*yx, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
854 %!assert(besselh(alpha,2,x), jx - I*yx, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
855 %!
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
856 %!assert(besselj(alpha,x,1), jx*exp(-abs(imag(x))), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
857 %!assert(bessely(alpha,x,1), yx*exp(-abs(imag(x))), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
858 %!assert(besseli(alpha,x,1), ix*exp(-abs(real(x))), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
859 %!assert(besselk(alpha,x,1), kx*exp(x), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
860 %!assert(besselh(alpha,1,x,1), (jx + I*yx)*exp(-I*x), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
861 %!assert(besselh(alpha,2,x,1), (jx - I*yx)*exp(I*x), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
862 %!
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
863 %!assert(besselj(-alpha,x), -jx, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
864 %!assert(bessely(-alpha,x), -yx, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
865 %!assert(besseli(-alpha,x), ix, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
866 %!assert(besselk(-alpha,x), kx, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
867 %!assert(besselh(-alpha,1,x), -(jx + I*yx), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
868 %!assert(besselh(-alpha,2,x), -(jx - I*yx), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
869 %!
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
870 %!assert(besselj(-alpha,x,1), -jx*exp(-abs(imag(x))), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
871 %!assert(bessely(-alpha,x,1), -yx*exp(-abs(imag(x))), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
872 %!assert(besseli(-alpha,x,1), ix*exp(-abs(real(x))), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
873 %!assert(besselk(-alpha,x,1), kx*exp(x), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
874 %!assert(besselh(-alpha,1,x,1), -(jx + I*yx)*exp(-I*x), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
875 %!assert(besselh(-alpha,2,x,1), -(jx - I*yx)*exp(I*x), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
876 %!
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
877 %! # Bessel functions, fractional order, complex x
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
878 %!
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
879 %! alpha = 3.5; x = 1.75 + 4.125 * I;
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
880 %! jx = -3.018566131370455929707009100 - 0.7585648436793900607704057611*I;
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
881 %! yx = 0.7772278839106298215614791107 - 3.018518722313849782683792010*I;
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
882 %! ix = 0.2100873577220057189038160913 - 0.6551765604618246531254970926*I;
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
883 %! kx = 0.1757147290513239935341488069 + 0.08772348296883849205562558311*I;
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
884 %!
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
885 %!assert(besselj(alpha,x), jx, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
886 %!assert(bessely(alpha,x), yx, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
887 %!assert(besseli(alpha,x), ix, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
888 %!assert(besselk(alpha,x), kx, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
889 %!assert(besselh(alpha,1,x), jx + I*yx, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
890 %!assert(besselh(alpha,2,x), jx - I*yx, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
891 %!
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
892 %!assert(besselj(alpha,x,1), jx*exp(-abs(imag(x))), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
893 %!assert(bessely(alpha,x,1), yx*exp(-abs(imag(x))), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
894 %!assert(besseli(alpha,x,1), ix*exp(-abs(real(x))), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
895 %!assert(besselk(alpha,x,1), kx*exp(x), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
896 %!assert(besselh(alpha,1,x,1), (jx + I*yx)*exp(-I*x), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
897 %!assert(besselh(alpha,2,x,1), (jx - I*yx)*exp(I*x), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
898 %!
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
899 %! nix = 0.09822388691172060573913739253 - 0.7110230642207380127317227407*I;
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
900 %!
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
901 %!assert(besselj(-alpha,x), yx, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
902 %!assert(bessely(-alpha,x), -jx, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
903 %!assert(besseli(-alpha,x), nix, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
904 %!assert(besselk(-alpha,x), kx, 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
905 %!assert(besselh(-alpha,1,x), -I*(jx + I*yx), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
906 %!assert(besselh(-alpha,2,x), I*(jx - I*yx), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
907 %!
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
908 %!assert(besselj(-alpha,x,1), yx*exp(-abs(imag(x))), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
909 %!assert(bessely(-alpha,x,1), -jx*exp(-abs(imag(x))), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
910 %!assert(besseli(-alpha,x,1), nix*exp(-abs(real(x))), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
911 %!assert(besselk(-alpha,x,1), kx*exp(x), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
912 %!assert(besselh(-alpha,1,x,1), -I*(jx + I*yx)*exp(-I*x), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
913 %!assert(besselh(-alpha,2,x,1), I*(jx - I*yx)*exp(I*x), 100*eps)
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
914 */
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
915
ab0674a8b345 fix scaling factor for negative alpha in zbesi,cbesi
Brian Gough <bjg@gnu.org>
parents: 7919
diff changeset
916 /*
3155
1016520a9d38 [project @ 1998-02-18 21:51:50 by jwe]
jwe
parents:
diff changeset
917 ;;; Local Variables: ***
1016520a9d38 [project @ 1998-02-18 21:51:50 by jwe]
jwe
parents:
diff changeset
918 ;;; mode: C++ ***
1016520a9d38 [project @ 1998-02-18 21:51:50 by jwe]
jwe
parents:
diff changeset
919 ;;; End: ***
1016520a9d38 [project @ 1998-02-18 21:51:50 by jwe]
jwe
parents:
diff changeset
920 */