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1 /* |
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2 |
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3 Copyright (C) 1997 John W. Eaton |
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4 |
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5 This file is part of Octave. |
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6 |
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7 Octave is free software; you can redistribute it and/or modify it |
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8 under the terms of the GNU General Public License as published by the |
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9 Free Software Foundation; either version 2, or (at your option) any |
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10 later version. |
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11 |
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12 Octave is distributed in the hope that it will be useful, but WITHOUT |
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13 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or |
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14 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
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15 for more details. |
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16 |
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17 You should have received a copy of the GNU General Public License |
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18 along with Octave; see the file COPYING. If not, write to the Free |
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19 Software Foundation, 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. |
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20 |
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21 */ |
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22 |
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23 #ifdef HAVE_CONFIG_H |
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24 #include <config.h> |
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25 #endif |
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26 |
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27 #include "lo-specfun.h" |
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28 |
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29 #include "defun-dld.h" |
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30 #include "error.h" |
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31 #include "gripes.h" |
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32 #include "oct-obj.h" |
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33 #include "utils.h" |
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34 |
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35 enum bessel_type |
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36 { |
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37 BESSEL_J, |
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38 BESSEL_Y, |
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39 BESSEL_I, |
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40 BESSEL_K, |
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41 BESSEL_H1, |
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42 BESSEL_H2 |
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43 }; |
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44 |
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45 #define DO_BESSEL(type, alpha, x, scaled, ierr, result) \ |
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46 do \ |
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47 { \ |
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48 switch (type) \ |
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49 { \ |
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50 case BESSEL_J: \ |
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51 result = besselj (alpha, x, scaled, ierr); \ |
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52 break; \ |
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53 \ |
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54 case BESSEL_Y: \ |
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55 result = bessely (alpha, x, scaled, ierr); \ |
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56 break; \ |
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57 \ |
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58 case BESSEL_I: \ |
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59 result = besseli (alpha, x, scaled, ierr); \ |
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60 break; \ |
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61 \ |
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62 case BESSEL_K: \ |
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63 result = besselk (alpha, x, scaled, ierr); \ |
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64 break; \ |
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65 \ |
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66 case BESSEL_H1: \ |
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67 result = besselh1 (alpha, x, scaled, ierr); \ |
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68 break; \ |
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69 \ |
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70 case BESSEL_H2: \ |
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71 result = besselh2 (alpha, x, scaled, ierr); \ |
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72 break; \ |
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73 \ |
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74 default: \ |
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75 break; \ |
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76 } \ |
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77 } \ |
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78 while (0) |
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79 |
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80 static inline Matrix |
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81 int_array2_to_matrix (const Array2<int>& a) |
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82 { |
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83 int nr = a.rows (); |
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84 int nc = a.cols (); |
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85 |
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86 Matrix retval (nr, nc); |
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87 |
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88 for (int j = 0; j < nc; j++) |
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89 for (int i = 0; i < nr; i++) |
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90 retval(i,j) = (double) (a(i,j)); |
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91 |
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92 return retval; |
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93 } |
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94 |
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95 static void |
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96 gripe_bessel_arg (const char *fn, const char *arg) |
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97 { |
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98 error ("%s: expecting scalar or matrix as %s argument", fn, arg); |
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99 } |
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100 |
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101 octave_value_list |
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102 do_bessel (enum bessel_type type, const char *fn, |
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103 const octave_value_list& args, int nargout) |
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104 { |
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105 octave_value_list retval; |
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106 |
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107 int nargin = args.length (); |
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108 |
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109 if (nargin == 2 || nargin == 3) |
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110 { |
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111 bool scaled = (nargin == 3); |
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112 |
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113 octave_value alpha_arg = args(0); |
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114 octave_value x_arg = args(1); |
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115 |
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116 if (alpha_arg.is_scalar_type ()) |
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117 { |
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118 double alpha = args(0).double_value (); |
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119 |
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120 if (! error_state) |
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121 { |
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122 if (x_arg.is_scalar_type ()) |
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123 { |
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124 Complex x = x_arg.complex_value (); |
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125 |
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126 if (! error_state) |
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127 { |
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128 int ierr; |
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129 octave_value result; |
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130 |
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131 DO_BESSEL (type, alpha, x, scaled, ierr, result); |
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132 |
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133 if (nargout > 1) |
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134 retval(1) = (double) ierr; |
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135 |
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136 retval(0) = result; |
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137 } |
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138 else |
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139 gripe_bessel_arg (fn, "second"); |
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140 } |
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141 else |
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142 { |
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143 ComplexMatrix x = x_arg.complex_matrix_value (); |
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144 |
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145 if (! error_state) |
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146 { |
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147 Array2<int> ierr; |
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148 octave_value result; |
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149 |
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150 DO_BESSEL (type, alpha, x, scaled, ierr, result); |
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151 |
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152 if (nargout > 1) |
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153 retval(1) = int_array2_to_matrix (ierr); |
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154 |
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155 retval(0) = result; |
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156 } |
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157 else |
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158 gripe_bessel_arg (fn, "second"); |
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159 } |
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160 } |
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161 else |
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162 gripe_bessel_arg (fn, "first"); |
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163 } |
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164 else |
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165 { |
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166 Matrix alpha = args(0).matrix_value (); |
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167 |
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168 if (! error_state) |
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169 { |
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170 if (x_arg.is_scalar_type ()) |
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171 { |
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172 Complex x = x_arg.complex_value (); |
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173 |
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174 if (! error_state) |
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175 { |
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176 Array2<int> ierr; |
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177 octave_value result; |
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178 |
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179 DO_BESSEL (type, alpha, x, scaled, ierr, result); |
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180 |
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181 if (nargout > 1) |
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182 retval(1) = int_array2_to_matrix (ierr); |
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183 |
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184 retval(0) = result; |
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185 } |
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186 else |
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187 gripe_bessel_arg (fn, "second"); |
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188 } |
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189 else |
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190 { |
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191 ComplexMatrix x = x_arg.complex_matrix_value (); |
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192 |
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193 if (! error_state) |
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194 { |
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195 if (alpha.rows () == 1 && x.columns () == 1) |
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196 { |
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197 RowVector ralpha = alpha.row (0); |
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198 ComplexColumnVector cx = x.column (0); |
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199 |
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200 Array2<int> ierr; |
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201 octave_value result; |
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202 |
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203 DO_BESSEL (type, ralpha, cx, scaled, ierr, result); |
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204 |
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205 if (nargout > 1) |
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206 retval(1) = int_array2_to_matrix (ierr); |
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207 |
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208 retval(0) = result; |
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209 } |
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210 else |
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211 { |
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212 Array2<int> ierr; |
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213 octave_value result; |
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214 |
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215 DO_BESSEL (type, alpha, x, scaled, ierr, result); |
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216 |
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217 if (nargout > 1) |
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218 retval(1) = int_array2_to_matrix (ierr); |
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219 |
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220 retval(0) = result; |
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221 } |
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222 } |
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223 else |
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224 gripe_bessel_arg (fn, "second"); |
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225 } |
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226 } |
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227 else |
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228 gripe_bessel_arg (fn, "first"); |
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229 } |
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230 } |
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231 else |
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232 print_usage (fn); |
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233 |
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234 return retval; |
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235 } |
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236 |
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237 DEFUN_DLD (besselj, args, nargout, |
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238 "[J, IERR] = BESSELJ (ALPHA, X [, 1])\n\ |
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239 \n\ |
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240 Compute Bessel functions of the first kind.\n\ |
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241 \n\ |
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242 If a third argument is supplied, scale the result by exp(-I*Z) for\n\ |
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243 K = 1 or exp(I*Z) for K = 2.\n\ |
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244 \n\ |
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245 If ALPHA is a scalar, the result is the same size as X. If X is a\n\ |
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246 scalar, the result is the same size as ALPHA. If ALPHA is a row\n\ |
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247 vector and X is a column vector, the result is a matrix with\n\ |
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248 length(X) rows and length(ALPHA) columns. Otherwise, ALPHA and X must\n\ |
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249 conform and the result will be the same size.\n\ |
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250 \n\ |
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251 ALPHA must be real. X may be complex.\n\ |
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252 \n\ |
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253 If requested, IERR contains the following status information and is\n\ |
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254 the same size as the result.\n\ |
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255 \n |
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256 0 normal return\n\ |
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257 1 input error, return NaN\n\ |
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258 2 overflow, return Inf\n\ |
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259 3 loss of significance by argument reduction results in less than\n\ |
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260 half of machine accuracy\n\ |
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261 4 complete loss of significance by argument reduction, return NaN\n\ |
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262 5 error -- no computation, algorithm termination condition not met,\n\ |
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263 return NaN") |
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264 { |
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265 return do_bessel (BESSEL_J, "besselj", args, nargout); |
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266 } |
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267 |
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268 DEFUN_DLD (bessely, args, nargout, |
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269 "[Y, IERR] = BESSELY (ALPHA, X [, 1])\n\ |
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270 \n\ |
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271 Compute Bessel functions of the second kind.\n\ |
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272 \n\ |
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273 If a third argument is supplied, scale the result by exp(-I*Z) for\n\ |
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274 K = 1 or exp(I*Z) for K = 2.\n\ |
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275 \n\ |
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276 If ALPHA is a scalar, the result is the same size as X. If X is a\n\ |
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277 scalar, the result is the same size as ALPHA. If ALPHA is a row\n\ |
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278 vector and X is a column vector, the result is a matrix with\n\ |
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279 length(X) rows and length(ALPHA) columns. Otherwise, ALPHA and X must\n\ |
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280 conform and the result will be the same size.\n\ |
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281 \n\ |
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282 ALPHA must be real. X may be complex.\n\ |
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283 \n\ |
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284 If requested, IERR contains the following status information and is\n\ |
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285 the same size as the result.\n\ |
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286 \n |
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287 0 normal return\n\ |
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288 1 input error, return NaN\n\ |
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289 2 overflow, return Inf\n\ |
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290 3 loss of significance by argument reduction results in less than\n\ |
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291 half of machine accuracy\n\ |
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292 4 complete loss of significance by argument reduction, return NaN\n\ |
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293 5 error -- no computation, algorithm termination condition not met,\n\ |
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294 return NaN") |
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295 { |
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296 return do_bessel (BESSEL_Y, "bessely", args, nargout); |
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297 } |
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298 |
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299 DEFUN_DLD (besseli, args, nargout, |
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300 "[I, IERR] = BESSELI (ALPHA, X [, 1])\n\ |
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301 \n\ |
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302 Compute modified Bessel functions of the first kind.\n\ |
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303 \n\ |
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304 If a third argument is supplied, scale the result by exp(-I*Z) for\n\ |
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305 K = 1 or exp(I*Z) for K = 2.\n\ |
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306 \n\ |
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307 If ALPHA is a scalar, the result is the same size as X. If X is a\n\ |
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308 scalar, the result is the same size as ALPHA. If ALPHA is a row\n\ |
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309 vector and X is a column vector, the result is a matrix with\n\ |
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310 length(X) rows and length(ALPHA) columns. Otherwise, ALPHA and X must\n\ |
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311 conform and the result will be the same size.\n\ |
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312 \n\ |
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313 ALPHA must be real. X may be complex.\n\ |
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314 \n\ |
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315 If requested, IERR contains the following status information and is\n\ |
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316 the same size as the result.\n\ |
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317 \n |
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318 0 normal return\n\ |
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319 1 input error, return NaN\n\ |
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320 2 overflow, return Inf\n\ |
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321 3 loss of significance by argument reduction results in less than\n\ |
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322 half of machine accuracy\n\ |
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323 4 complete loss of significance by argument reduction, return NaN\n\ |
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324 5 error -- no computation, algorithm termination condition not met,\n\ |
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325 return NaN") |
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326 { |
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327 return do_bessel (BESSEL_I, "besseli", args, nargout); |
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328 } |
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329 |
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330 DEFUN_DLD (besselk, args, nargout, |
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331 "[K, IERR] = BESSELK (ALPHA, X [, 1])\n\ |
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332 \n\ |
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333 Compute modified Bessel functions of the second kind.\n\ |
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334 \n\ |
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335 If a third argument is supplied, scale the result by exp(-I*Z) for\n\ |
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336 K = 1 or exp(I*Z) for K = 2.\n\ |
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337 \n\ |
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338 If ALPHA is a scalar, the result is the same size as X. If X is a\n\ |
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339 scalar, the result is the same size as ALPHA. If ALPHA is a row\n\ |
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340 vector and X is a column vector, the result is a matrix with\n\ |
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341 length(X) rows and length(ALPHA) columns. Otherwise, ALPHA and X must\n\ |
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342 conform and the result will be the same size.\n\ |
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343 \n\ |
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344 ALPHA must be real. X may be complex.\n\ |
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345 \n\ |
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346 If requested, IERR contains the following status information and is\n\ |
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347 the same size as the result.\n\ |
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348 \n |
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349 0 normal return\n\ |
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350 1 input error, return NaN\n\ |
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351 2 overflow, return Inf\n\ |
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352 3 loss of significance by argument reduction results in less than\n\ |
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353 half of machine accuracy\n\ |
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354 4 complete loss of significance by argument reduction, return NaN\n\ |
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355 5 error -- no computation, algorithm termination condition not met,\n\ |
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356 return NaN") |
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357 { |
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358 return do_bessel (BESSEL_K, "besselk", args, nargout); |
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359 } |
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360 |
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361 DEFUN_DLD (besselh, args, nargout, |
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362 "[H, IERR] = besselh (ALPHA, K, X [, 1])\n\ |
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363 \n\ |
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364 Compute Hankel functions of the first (K = 1) or second (K = 2) kind.\n\ |
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365 \n\ |
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366 If a fourth argument is supplied, scale the result by exp(-I*Z) for\n\ |
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367 K = 1 or exp(I*Z) for K = 2.\n\ |
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368 \n\ |
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369 If ALPHA is a scalar, the result is the same size as X. If X is a\n\ |
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370 scalar, the result is the same size as ALPHA. If ALPHA is a row\n\ |
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371 vector and X is a column vector, the result is a matrix with\n\ |
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372 length(X) rows and length(ALPHA) columns. Otherwise, ALPHA and X must\n\ |
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373 conform and the result will be the same size.\n\ |
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374 \n\ |
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375 ALPHA must be real. X may be complex.\n\ |
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376 \n\ |
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377 If requested, IERR contains the following status information and is\n\ |
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378 the same size as the result.\n\ |
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379 \n |
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380 0 normal return\n\ |
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381 1 input error, return NaN\n\ |
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382 2 overflow, return Inf\n\ |
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383 3 loss of significance by argument reduction results in less than\n\ |
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384 half of machine accuracy\n\ |
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385 4 complete loss of significance by argument reduction, return NaN\n\ |
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386 5 error -- no computation, algorithm termination condition not met,\n\ |
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387 return NaN") |
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388 { |
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389 octave_value_list retval; |
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390 |
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391 int nargin = args.length (); |
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392 |
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393 int kind = 1; |
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394 |
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395 if (nargin == 2) |
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396 { |
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397 retval = do_bessel (BESSEL_H1, "besselh", args, nargout); |
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398 } |
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399 else if (nargin == 3 || nargin == 4) |
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400 { |
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401 double d_kind = args(1).double_value (); |
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402 |
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403 if (! error_state && D_NINT (d_kind) == d_kind) |
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404 { |
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405 octave_value_list tmp_args; |
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406 |
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407 if (nargin == 4) |
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408 tmp_args(2) = args(3); |
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409 |
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410 tmp_args(1) = args(2); |
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411 tmp_args(0) = args(0); |
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412 |
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413 if (kind == 1) |
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414 retval = do_bessel (BESSEL_H1, "besselh", tmp_args, nargout); |
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415 else if (kind == 2) |
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416 retval = do_bessel (BESSEL_H2, "besselh", tmp_args, nargout); |
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417 else |
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418 error ("besselh: expecting K = 1 or 2"); |
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419 } |
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420 else |
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421 error ("besselh: invalid value of K"); |
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422 } |
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423 else |
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424 print_usage ("besselh"); |
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425 |
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426 return retval; |
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427 } |
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428 |
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429 DEFUN_DLD (airy, args, nargout, |
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430 "[A, IERR] = airy (K, Z, [, 1])\n\ |
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431 \n\ |
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432 Compute Airy functions of the first and second kind, and their\n\ |
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433 derivatives.\n\ |
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434 \n\ |
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435 K Function Scale factor (if a third argument is supplied)\n\ |
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436 --- -------- ----------------------------------------------\n\ |
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437 0 Ai (Z) exp ((2/3) * Z * sqrt (Z))\n\ |
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438 1 dAi(Z)/dZ exp ((2/3) * Z * sqrt (Z))\n\ |
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439 2 Bi (Z) exp (-abs (real ((2/3) * Z *sqrt (Z))))\n\ |
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440 3 dBi(Z)/dZ exp (-abs (real ((2/3) * Z *sqrt (Z))))\n\ |
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441 \n\ |
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442 The function call airy (Z) is equivalent to airy (0, Z).\n\ |
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3155
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443 \n\ |
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3220
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444 The result is the same size as Z. |
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445 \n\ |
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446 If requested, IERR contains the following status information and is\n\ |
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447 the same size as the result.\n\ |
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448 \n |
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449 0 normal return\n\ |
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450 1 input error, return NaN\n\ |
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451 2 overflow, return Inf\n\ |
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452 3 loss of significance by argument reduction results in less than\n\ |
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453 half of machine accuracy\n\ |
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454 4 complete loss of significance by argument reduction, return NaN\n\ |
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455 5 error -- no computation, algorithm termination condition not met,\n\ |
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456 return NaN") |
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3155
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457 { |
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3220
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458 octave_value_list retval; |
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459 |
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460 int nargin = args.length (); |
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461 |
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462 if (nargin > 0 && nargin < 4) |
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463 { |
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464 bool scale = (nargin == 3); |
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465 |
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466 int kind = 0; |
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467 |
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468 ComplexMatrix z; |
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469 |
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470 if (nargin > 1) |
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471 { |
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472 double d_kind = args(0).double_value (); |
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473 |
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474 if (! error_state) |
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475 { |
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476 kind = (int) d_kind; |
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477 |
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478 if (kind < 0 || kind > 3) |
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479 error ("airy: expecting K = 0, 1, 2, or 3"); |
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480 } |
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481 else |
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482 error ("airy: expecting integer value for K"); |
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483 } |
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484 |
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485 if (! error_state) |
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486 { |
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487 z = args(nargin == 1 ? 0 : 1).complex_matrix_value (); |
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488 |
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489 if (! error_state) |
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490 { |
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491 Array2<int> ierr; |
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492 octave_value result; |
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493 |
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494 if (kind > 1) |
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495 result = biry (z, kind == 3, scale, ierr); |
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496 else |
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497 result = airy (z, kind == 1, scale, ierr); |
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498 |
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499 if (nargout > 1) |
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500 retval(1) = int_array2_to_matrix (ierr); |
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501 |
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502 retval(0) = result; |
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503 } |
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504 else |
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505 error ("airy: expecting complex matrix for Z"); |
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506 } |
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507 } |
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508 else |
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509 print_usage ("airy"); |
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510 |
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511 return retval; |
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3155
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512 } |
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513 |
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514 /* |
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515 ;;; Local Variables: *** |
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516 ;;; mode: C++ *** |
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517 ;;; End: *** |
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518 */ |
