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1 /* |
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2 |
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3 Copyright (C) 1996 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 "Range.h" |
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28 #include "CColVector.h" |
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29 #include "CMatrix.h" |
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30 #include "dRowVector.h" |
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31 #include "dMatrix.h" |
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32 #include "f77-fcn.h" |
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33 #include "lo-error.h" |
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34 #include "lo-ieee.h" |
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35 #include "lo-specfun.h" |
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36 #include "mx-inlines.cc" |
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37 |
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38 #ifndef M_PI |
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39 #define M_PI 3.14159265358979323846 |
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40 #endif |
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41 |
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42 extern "C" |
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43 { |
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44 F77_RET_T |
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45 F77_FUNC (zbesj, ZBESJ) (const double&, const double&, const double&, |
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46 const int&, const int&, double*, double*, |
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47 int&, int&); |
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48 |
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49 F77_RET_T |
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50 F77_FUNC (zbesy, ZBESY) (const double&, const double&, const double&, |
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51 const int&, const int&, double*, double*, |
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52 int&, double*, double*, int&); |
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53 |
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54 F77_RET_T |
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55 F77_FUNC (zbesi, ZBESI) (const double&, const double&, const double&, |
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56 const int&, const int&, double*, double*, |
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57 int&, int&); |
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58 |
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59 F77_RET_T |
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60 F77_FUNC (zbesk, ZBESK) (const double&, const double&, const double&, |
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61 const int&, const int&, double*, double*, |
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62 int&, int&); |
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63 |
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64 F77_RET_T |
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65 F77_FUNC (zbesh, ZBESH) (const double&, const double&, const double&, |
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66 const int&, const int&, const int&, double*, |
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67 double*, int&, int&); |
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68 |
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69 F77_RET_T |
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70 F77_FUNC (zairy, ZAIRY) (const double&, const double&, const int&, |
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71 const int&, double&, double&, int&, int&); |
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72 |
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73 F77_RET_T |
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74 F77_FUNC (zbiry, ZBIRY) (const double&, const double&, const int&, |
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75 const int&, double&, double&, int&); |
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76 |
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77 F77_RET_T |
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78 F77_FUNC (xdacosh, XDACOSH) (const double&, double&); |
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79 |
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80 F77_RET_T |
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81 F77_FUNC (xdasinh, XDASINH) (const double&, double&); |
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82 |
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83 F77_RET_T |
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84 F77_FUNC (xdatanh, XDATANH) (const double&, double&); |
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85 |
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86 F77_RET_T |
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87 F77_FUNC (xderf, XDERF) (const double&, double&); |
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88 |
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89 F77_RET_T |
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90 F77_FUNC (xderfc, XDERFC) (const double&, double&); |
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91 |
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92 F77_RET_T |
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93 F77_FUNC (xdbetai, XDBETAI) (const double&, const double&, |
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94 const double&, double&); |
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95 |
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96 F77_RET_T |
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97 F77_FUNC (xdgamma, XDGAMMA) (const double&, double&); |
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98 |
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99 F77_RET_T |
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100 F77_FUNC (xgammainc, XGAMMAINC) (const double&, const double&, double&); |
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101 |
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102 F77_RET_T |
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103 F77_FUNC (dlgams, DLGAMS) (const double&, double&, double&); |
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104 } |
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105 |
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106 #if !defined (HAVE_ACOSH) |
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107 double |
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108 acosh (double x) |
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109 { |
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110 double retval; |
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111 F77_FUNC (xdacosh, XDACOSH) (x, retval); |
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112 return retval; |
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113 } |
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114 #endif |
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115 |
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116 #if !defined (HAVE_ASINH) |
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117 double |
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118 asinh (double x) |
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119 { |
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120 double retval; |
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121 F77_FUNC (xdasinh, XDASINH) (x, retval); |
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122 return retval; |
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123 } |
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124 #endif |
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125 |
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126 #if !defined (HAVE_ATANH) |
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127 double |
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128 atanh (double x) |
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129 { |
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130 double retval; |
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131 F77_FUNC (xdatanh, XDATANH) (x, retval); |
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132 return retval; |
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133 } |
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134 #endif |
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135 |
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136 #if !defined (HAVE_ERF) |
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137 double |
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138 erf (double x) |
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139 { |
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140 double retval; |
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141 F77_FUNC (xderf, XDERF) (x, retval); |
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142 return retval; |
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143 } |
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144 #endif |
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145 |
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146 #if !defined (HAVE_ERFC) |
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147 double |
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148 erfc (double x) |
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149 { |
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150 double retval; |
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151 F77_FUNC (xderfc, XDERFC) (x, retval); |
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152 return retval; |
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153 } |
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154 #endif |
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155 |
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156 double |
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157 xgamma (double x) |
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158 { |
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159 double result; |
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160 F77_FUNC (xdgamma, XDGAMMA) (x, result); |
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161 return result; |
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162 } |
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163 |
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164 double |
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165 xlgamma (double x) |
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166 { |
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167 double result; |
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168 double sgngam; |
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169 |
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170 if (x < 0) |
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171 (*current_liboctave_error_handler) |
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172 ("xlgamma: argument must be nonnegative"); |
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173 |
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174 F77_FUNC (dlgams, DLGAMS) (x, result, sgngam); |
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175 |
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176 return result; |
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177 } |
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178 |
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179 static inline Complex |
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180 zbesj (const Complex& z, double alpha, int kode, int& ierr); |
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181 |
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182 static inline Complex |
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183 zbesy (const Complex& z, double alpha, int kode, int& ierr); |
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184 |
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185 static inline Complex |
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186 zbesi (const Complex& z, double alpha, int kode, int& ierr); |
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187 |
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188 static inline Complex |
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189 zbesk (const Complex& z, double alpha, int kode, int& ierr); |
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190 |
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191 static inline Complex |
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192 zbesh1 (const Complex& z, double alpha, int kode, int& ierr); |
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193 |
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194 static inline Complex |
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195 zbesh2 (const Complex& z, double alpha, int kode, int& ierr); |
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196 |
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197 static inline Complex |
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198 bessel_return_value (const Complex& val, int ierr) |
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199 { |
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200 static const Complex inf_val = Complex (octave_Inf, octave_Inf); |
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201 static const Complex nan_val = Complex (octave_NaN, octave_NaN); |
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202 |
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203 Complex retval; |
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204 |
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205 switch (ierr) |
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206 { |
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207 case 0: |
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208 case 3: |
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209 retval = val; |
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210 break; |
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211 |
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212 case 2: |
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213 retval = inf_val; |
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214 break; |
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215 |
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216 default: |
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217 retval = nan_val; |
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218 break; |
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219 } |
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220 |
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221 return retval; |
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222 } |
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223 |
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224 static inline Complex |
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225 zbesj (const Complex& z, double alpha, int kode, int& ierr) |
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226 { |
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227 Complex retval; |
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228 |
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229 if (alpha >= 0.0) |
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230 { |
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231 double yr = 0.0; |
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232 double yi = 0.0; |
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233 |
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234 int nz; |
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235 |
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236 double zr = z.real (); |
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237 double zi = z.imag (); |
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238 |
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239 F77_FUNC (zbesj, ZBESJ) (zr, zi, alpha, 2, 1, &yr, &yi, nz, ierr); |
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240 |
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241 if (kode != 2) |
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242 { |
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243 double expz = exp (std::abs (zi)); |
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244 yr *= expz; |
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245 yi *= expz; |
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246 } |
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247 |
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248 if (zi == 0.0 && zr >= 0.0) |
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249 yi = 0.0; |
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250 |
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251 retval = bessel_return_value (Complex (yr, yi), ierr); |
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252 } |
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253 else |
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254 { |
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255 alpha = -alpha; |
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256 |
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257 Complex tmp = cos (M_PI * alpha) * zbesj (z, alpha, kode, ierr); |
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258 |
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259 if (ierr == 0 || ierr == 3) |
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260 { |
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261 tmp -= sin (M_PI * alpha) * zbesy (z, alpha, kode, ierr); |
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262 |
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263 retval = bessel_return_value (tmp, ierr); |
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264 } |
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265 else |
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266 retval = Complex (octave_NaN, octave_NaN); |
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267 } |
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268 |
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269 return retval; |
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270 } |
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271 |
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272 static inline Complex |
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273 zbesy (const Complex& z, double alpha, int kode, int& ierr) |
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274 { |
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275 Complex retval; |
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276 |
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277 if (alpha >= 0.0) |
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278 { |
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279 double yr = 0.0; |
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280 double yi = 0.0; |
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281 |
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282 int nz; |
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283 |
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284 double wr, wi; |
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285 |
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286 double zr = z.real (); |
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287 double zi = z.imag (); |
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288 |
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289 ierr = 0; |
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290 |
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291 if (zr == 0.0 && zi == 0.0) |
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292 { |
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293 yr = -octave_Inf; |
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294 yi = 0.0; |
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295 } |
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296 else |
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297 { |
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298 F77_FUNC (zbesy, ZBESY) (zr, zi, alpha, 2, 1, &yr, &yi, nz, |
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299 &wr, &wi, ierr); |
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300 |
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301 if (kode != 2) |
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302 { |
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303 double expz = exp (std::abs (zi)); |
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304 yr *= expz; |
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305 yi *= expz; |
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306 } |
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307 |
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308 if (zi == 0.0 && zr >= 0.0) |
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309 yi = 0.0; |
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310 } |
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311 |
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312 return bessel_return_value (Complex (yr, yi), ierr); |
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313 } |
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314 else |
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315 { |
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316 alpha = -alpha; |
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317 |
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318 Complex tmp = cos (M_PI * alpha) * zbesy (z, alpha, kode, ierr); |
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319 |
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320 if (ierr == 0 || ierr == 3) |
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321 { |
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322 tmp += sin (M_PI * alpha) * zbesj (z, alpha, kode, ierr); |
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323 |
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324 retval = bessel_return_value (tmp, ierr); |
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325 } |
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326 else |
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327 retval = Complex (octave_NaN, octave_NaN); |
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328 } |
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329 |
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330 return retval; |
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331 } |
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332 |
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333 static inline Complex |
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334 zbesi (const Complex& z, double alpha, int kode, int& ierr) |
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335 { |
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336 Complex retval; |
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337 |
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338 if (alpha >= 0.0) |
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339 { |
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340 double yr = 0.0; |
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341 double yi = 0.0; |
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342 |
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343 int nz; |
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344 |
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345 double zr = z.real (); |
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346 double zi = z.imag (); |
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347 |
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348 F77_FUNC (zbesi, ZBESI) (zr, zi, alpha, 2, 1, &yr, &yi, nz, ierr); |
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349 |
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350 if (kode != 2) |
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351 { |
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352 double expz = exp (std::abs (zr)); |
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353 yr *= expz; |
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354 yi *= expz; |
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355 } |
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356 |
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357 if (zi == 0.0 && zr >= 0.0) |
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358 yi = 0.0; |
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359 |
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360 retval = bessel_return_value (Complex (yr, yi), ierr); |
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361 } |
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362 else |
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363 { |
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364 alpha = -alpha; |
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365 |
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366 Complex tmp = zbesi (z, alpha, kode, ierr); |
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367 |
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368 if (ierr == 0 || ierr == 3) |
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369 { |
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370 tmp += (2.0 / M_PI) * sin (M_PI * alpha) |
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371 * zbesk (z, alpha, kode, ierr); |
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372 |
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373 retval = bessel_return_value (tmp, ierr); |
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374 } |
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375 else |
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376 retval = Complex (octave_NaN, octave_NaN); |
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377 } |
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378 |
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379 return retval; |
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380 } |
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381 |
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382 static inline Complex |
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383 zbesk (const Complex& z, double alpha, int kode, int& ierr) |
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384 { |
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385 Complex retval; |
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386 |
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387 if (alpha >= 0.0) |
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388 { |
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389 double yr = 0.0; |
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390 double yi = 0.0; |
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391 |
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392 int nz; |
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393 |
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394 double zr = z.real (); |
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395 double zi = z.imag (); |
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396 |
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397 ierr = 0; |
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398 |
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399 if (zr == 0.0 && zi == 0.0) |
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400 { |
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401 yr = octave_Inf; |
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402 yi = 0.0; |
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403 } |
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404 else |
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405 { |
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406 F77_FUNC (zbesk, ZBESK) (zr, zi, alpha, 2, 1, &yr, &yi, nz, ierr); |
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407 |
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408 if (kode != 2) |
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409 { |
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410 Complex expz = exp (-z); |
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411 |
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412 double rexpz = real (expz); |
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413 double iexpz = imag (expz); |
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414 |
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415 double tmp = yr*rexpz - yi*iexpz; |
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416 |
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417 yi = yr*iexpz + yi*rexpz; |
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418 yr = tmp; |
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419 } |
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420 |
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421 if (zi == 0.0 && zr >= 0.0) |
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422 yi = 0.0; |
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423 } |
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424 |
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425 retval = bessel_return_value (Complex (yr, yi), ierr); |
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426 } |
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427 else |
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428 { |
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429 Complex tmp = zbesk (z, -alpha, kode, ierr); |
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430 |
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431 retval = bessel_return_value (tmp, ierr); |
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432 } |
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433 |
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434 return retval; |
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435 } |
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436 |
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437 static inline Complex |
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438 zbesh1 (const Complex& z, double alpha, int kode, int& ierr) |
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439 { |
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440 Complex retval; |
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441 |
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442 if (alpha >= 0.0) |
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443 { |
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444 double yr = 0.0; |
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445 double yi = 0.0; |
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446 |
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447 int nz; |
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448 |
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449 double zr = z.real (); |
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450 double zi = z.imag (); |
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451 |
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452 F77_FUNC (zbesh, ZBESH) (zr, zi, alpha, 2, 1, 1, &yr, &yi, nz, ierr); |
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453 |
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454 if (kode != 2) |
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455 { |
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456 Complex expz = exp (Complex (0.0, 1.0) * z); |
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457 |
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458 double rexpz = real (expz); |
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459 double iexpz = imag (expz); |
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460 |
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461 double tmp = yr*rexpz - yi*iexpz; |
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462 |
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463 yi = yr*iexpz + yi*rexpz; |
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464 yr = tmp; |
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465 } |
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466 |
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467 retval = bessel_return_value (Complex (yr, yi), ierr); |
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468 } |
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469 else |
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470 { |
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471 alpha = -alpha; |
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472 |
|
|
473 static const Complex eye = Complex (0.0, 1.0); |
|
3146
|
474 |
|
3220
|
475 Complex tmp = exp (M_PI * alpha * eye) * zbesh1 (z, alpha, kode, ierr); |
|
3146
|
476 |
|
3220
|
477 retval = bessel_return_value (tmp, ierr); |
|
|
478 } |
|
3146
|
479 |
|
3220
|
480 return retval; |
|
|
481 } |
|
3146
|
482 |
|
3220
|
483 static inline Complex |
|
|
484 zbesh2 (const Complex& z, double alpha, int kode, int& ierr) |
|
|
485 { |
|
|
486 Complex retval; |
|
3146
|
487 |
|
3220
|
488 if (alpha >= 0.0) |
|
|
489 { |
|
|
490 double yr = 0.0; |
|
|
491 double yi = 0.0; |
|
|
492 |
|
|
493 int nz; |
|
3146
|
494 |
|
3220
|
495 double zr = z.real (); |
|
|
496 double zi = z.imag (); |
|
3146
|
497 |
|
4506
|
498 F77_FUNC (zbesh, ZBESH) (zr, zi, alpha, 2, 2, 1, &yr, &yi, nz, ierr); |
|
|
499 |
|
|
500 if (kode != 2) |
|
|
501 { |
|
|
502 Complex expz = exp (-Complex (0.0, 1.0) * z); |
|
|
503 |
|
|
504 double rexpz = real (expz); |
|
|
505 double iexpz = imag (expz); |
|
|
506 |
|
|
507 double tmp = yr*rexpz - yi*iexpz; |
|
|
508 |
|
|
509 yi = yr*iexpz + yi*rexpz; |
|
|
510 yr = tmp; |
|
|
511 } |
|
3220
|
512 |
|
|
513 retval = bessel_return_value (Complex (yr, yi), ierr); |
|
3146
|
514 } |
|
|
515 else |
|
3220
|
516 { |
|
|
517 alpha = -alpha; |
|
|
518 |
|
|
519 static const Complex eye = Complex (0.0, 1.0); |
|
|
520 |
|
|
521 Complex tmp = exp (-M_PI * alpha * eye) * zbesh2 (z, alpha, kode, ierr); |
|
|
522 |
|
|
523 retval = bessel_return_value (tmp, ierr); |
|
|
524 } |
|
|
525 |
|
|
526 return retval; |
|
|
527 } |
|
|
528 |
|
|
529 typedef Complex (*fptr) (const Complex&, double, int, int&); |
|
|
530 |
|
|
531 static inline Complex |
|
|
532 do_bessel (fptr f, const char *, double alpha, const Complex& x, |
|
|
533 bool scaled, int& ierr) |
|
|
534 { |
|
|
535 Complex retval; |
|
|
536 |
|
|
537 retval = f (x, alpha, (scaled ? 2 : 1), ierr); |
|
|
538 |
|
|
539 return retval; |
|
|
540 } |
|
|
541 |
|
|
542 static inline ComplexMatrix |
|
|
543 do_bessel (fptr f, const char *, double alpha, const ComplexMatrix& x, |
|
|
544 bool scaled, Array2<int>& ierr) |
|
|
545 { |
|
|
546 int nr = x.rows (); |
|
|
547 int nc = x.cols (); |
|
|
548 |
|
|
549 ComplexMatrix retval (nr, nc); |
|
|
550 |
|
|
551 ierr.resize (nr, nc); |
|
|
552 |
|
|
553 for (int j = 0; j < nc; j++) |
|
|
554 for (int i = 0; i < nr; i++) |
|
|
555 retval(i,j) = f (x(i,j), alpha, (scaled ? 2 : 1), ierr(i,j)); |
|
|
556 |
|
|
557 return retval; |
|
|
558 } |
|
|
559 |
|
|
560 static inline ComplexMatrix |
|
|
561 do_bessel (fptr f, const char *, const Matrix& alpha, const Complex& x, |
|
|
562 bool scaled, Array2<int>& ierr) |
|
|
563 { |
|
|
564 int nr = alpha.rows (); |
|
|
565 int nc = alpha.cols (); |
|
|
566 |
|
|
567 ComplexMatrix retval (nr, nc); |
|
|
568 |
|
|
569 ierr.resize (nr, nc); |
|
|
570 |
|
|
571 for (int j = 0; j < nc; j++) |
|
|
572 for (int i = 0; i < nr; i++) |
|
|
573 retval(i,j) = f (x, alpha(i,j), (scaled ? 2 : 1), ierr(i,j)); |
|
3146
|
574 |
|
|
575 return retval; |
|
|
576 } |
|
|
577 |
|
3220
|
578 static inline ComplexMatrix |
|
|
579 do_bessel (fptr f, const char *fn, const Matrix& alpha, |
|
|
580 const ComplexMatrix& x, bool scaled, Array2<int>& ierr) |
|
3146
|
581 { |
|
3220
|
582 ComplexMatrix retval; |
|
|
583 |
|
|
584 int x_nr = x.rows (); |
|
|
585 int x_nc = x.cols (); |
|
|
586 |
|
|
587 int alpha_nr = alpha.rows (); |
|
|
588 int alpha_nc = alpha.cols (); |
|
|
589 |
|
|
590 if (x_nr == alpha_nr && x_nc == alpha_nc) |
|
|
591 { |
|
|
592 int nr = x_nr; |
|
|
593 int nc = x_nc; |
|
|
594 |
|
|
595 retval.resize (nr, nc); |
|
|
596 |
|
|
597 ierr.resize (nr, nc); |
|
|
598 |
|
|
599 for (int j = 0; j < nc; j++) |
|
|
600 for (int i = 0; i < nr; i++) |
|
|
601 retval(i,j) = f (x(i,j), alpha(i,j), (scaled ? 2 : 1), ierr(i,j)); |
|
|
602 } |
|
|
603 else |
|
|
604 (*current_liboctave_error_handler) |
|
|
605 ("%s: the sizes of alpha and x must conform", fn); |
|
|
606 |
|
|
607 return retval; |
|
3146
|
608 } |
|
|
609 |
|
3220
|
610 static inline ComplexMatrix |
|
|
611 do_bessel (fptr f, const char *, const RowVector& alpha, |
|
|
612 const ComplexColumnVector& x, bool scaled, Array2<int>& ierr) |
|
3146
|
613 { |
|
3220
|
614 int nr = x.length (); |
|
|
615 int nc = alpha.length (); |
|
|
616 |
|
|
617 ComplexMatrix retval (nr, nc); |
|
3146
|
618 |
|
3220
|
619 ierr.resize (nr, nc); |
|
|
620 |
|
|
621 for (int j = 0; j < nc; j++) |
|
|
622 for (int i = 0; i < nr; i++) |
|
|
623 retval(i,j) = f (x(i), alpha(j), (scaled ? 2 : 1), ierr(i,j)); |
|
|
624 |
|
|
625 return retval; |
|
3146
|
626 } |
|
|
627 |
|
3220
|
628 #define SS_BESSEL(name, fcn) \ |
|
|
629 Complex \ |
|
|
630 name (double alpha, const Complex& x, bool scaled, int& ierr) \ |
|
|
631 { \ |
|
|
632 return do_bessel (fcn, #name, alpha, x, scaled, ierr); \ |
|
|
633 } |
|
|
634 |
|
|
635 #define SM_BESSEL(name, fcn) \ |
|
|
636 ComplexMatrix \ |
|
|
637 name (double alpha, const ComplexMatrix& x, bool scaled, \ |
|
|
638 Array2<int>& ierr) \ |
|
|
639 { \ |
|
|
640 return do_bessel (fcn, #name, alpha, x, scaled, ierr); \ |
|
|
641 } |
|
|
642 |
|
|
643 #define MS_BESSEL(name, fcn) \ |
|
|
644 ComplexMatrix \ |
|
|
645 name (const Matrix& alpha, const Complex& x, bool scaled, \ |
|
|
646 Array2<int>& ierr) \ |
|
|
647 { \ |
|
|
648 return do_bessel (fcn, #name, alpha, x, scaled, ierr); \ |
|
|
649 } |
|
|
650 |
|
|
651 #define MM_BESSEL(name, fcn) \ |
|
|
652 ComplexMatrix \ |
|
|
653 name (const Matrix& alpha, const ComplexMatrix& x, bool scaled, \ |
|
|
654 Array2<int>& ierr) \ |
|
|
655 { \ |
|
|
656 return do_bessel (fcn, #name, alpha, x, scaled, ierr); \ |
|
|
657 } |
|
|
658 |
|
|
659 #define RC_BESSEL(name, fcn) \ |
|
|
660 ComplexMatrix \ |
|
|
661 name (const RowVector& alpha, const ComplexColumnVector& x, bool scaled, \ |
|
|
662 Array2<int>& ierr) \ |
|
|
663 { \ |
|
|
664 return do_bessel (fcn, #name, alpha, x, scaled, ierr); \ |
|
|
665 } |
|
|
666 |
|
|
667 #define ALL_BESSEL(name, fcn) \ |
|
|
668 SS_BESSEL (name, fcn) \ |
|
|
669 SM_BESSEL (name, fcn) \ |
|
|
670 MS_BESSEL (name, fcn) \ |
|
|
671 MM_BESSEL (name, fcn) \ |
|
|
672 RC_BESSEL (name, fcn) |
|
|
673 |
|
|
674 ALL_BESSEL (besselj, zbesj) |
|
|
675 ALL_BESSEL (bessely, zbesy) |
|
|
676 ALL_BESSEL (besseli, zbesi) |
|
|
677 ALL_BESSEL (besselk, zbesk) |
|
|
678 ALL_BESSEL (besselh1, zbesh1) |
|
|
679 ALL_BESSEL (besselh2, zbesh2) |
|
|
680 |
|
|
681 Complex |
|
|
682 airy (const Complex& z, bool deriv, bool scaled, int& ierr) |
|
3146
|
683 { |
|
3220
|
684 double ar = 0.0; |
|
|
685 double ai = 0.0; |
|
|
686 |
|
|
687 int nz; |
|
|
688 |
|
|
689 double zr = z.real (); |
|
|
690 double zi = z.imag (); |
|
3146
|
691 |
|
3220
|
692 int id = deriv ? 1 : 0; |
|
|
693 |
|
4506
|
694 F77_FUNC (zairy, ZAIRY) (zr, zi, id, 2, ar, ai, nz, ierr); |
|
|
695 |
|
|
696 if (! scaled) |
|
|
697 { |
|
|
698 Complex expz = exp (- 2.0 / 3.0 * z * sqrt(z)); |
|
3220
|
699 |
|
4506
|
700 double rexpz = real (expz); |
|
|
701 double iexpz = imag (expz); |
|
|
702 |
|
|
703 double tmp = ar*rexpz - ai*iexpz; |
|
|
704 |
|
|
705 ai = ar*iexpz + ai*rexpz; |
|
|
706 ar = tmp; |
|
|
707 } |
|
3220
|
708 |
|
4490
|
709 if (zi == 0.0 && (! scaled || zr >= 0.0)) |
|
3225
|
710 ai = 0.0; |
|
|
711 |
|
3220
|
712 return bessel_return_value (Complex (ar, ai), ierr); |
|
3146
|
713 } |
|
|
714 |
|
3220
|
715 Complex |
|
|
716 biry (const Complex& z, bool deriv, bool scaled, int& ierr) |
|
3146
|
717 { |
|
3220
|
718 double ar = 0.0; |
|
|
719 double ai = 0.0; |
|
|
720 |
|
|
721 double zr = z.real (); |
|
|
722 double zi = z.imag (); |
|
|
723 |
|
|
724 int id = deriv ? 1 : 0; |
|
|
725 |
|
4506
|
726 F77_FUNC (zbiry, ZBIRY) (zr, zi, id, 2, ar, ai, ierr); |
|
|
727 |
|
|
728 if (! scaled) |
|
|
729 { |
|
|
730 Complex expz = exp (std::abs (real (2.0 / 3.0 * z * sqrt (z)))); |
|
3220
|
731 |
|
4506
|
732 double rexpz = real (expz); |
|
|
733 double iexpz = imag (expz); |
|
|
734 |
|
|
735 double tmp = ar*rexpz - ai*iexpz; |
|
|
736 |
|
|
737 ai = ar*iexpz + ai*rexpz; |
|
|
738 ar = tmp; |
|
|
739 } |
|
3220
|
740 |
|
4490
|
741 if (zi == 0.0 && (! scaled || zr >= 0.0)) |
|
3225
|
742 ai = 0.0; |
|
|
743 |
|
3220
|
744 return bessel_return_value (Complex (ar, ai), ierr); |
|
3146
|
745 } |
|
|
746 |
|
3220
|
747 ComplexMatrix |
|
|
748 airy (const ComplexMatrix& z, bool deriv, bool scaled, Array2<int>& ierr) |
|
3146
|
749 { |
|
3220
|
750 int nr = z.rows (); |
|
|
751 int nc = z.cols (); |
|
|
752 |
|
|
753 ComplexMatrix retval (nr, nc); |
|
|
754 |
|
|
755 ierr.resize (nr, nc); |
|
|
756 |
|
|
757 for (int j = 0; j < nc; j++) |
|
|
758 for (int i = 0; i < nr; i++) |
|
|
759 retval(i,j) = airy (z(i,j), deriv, scaled, ierr(i,j)); |
|
|
760 |
|
|
761 return retval; |
|
3146
|
762 } |
|
|
763 |
|
3220
|
764 ComplexMatrix |
|
|
765 biry (const ComplexMatrix& z, bool deriv, bool scaled, Array2<int>& ierr) |
|
3146
|
766 { |
|
3220
|
767 int nr = z.rows (); |
|
|
768 int nc = z.cols (); |
|
|
769 |
|
|
770 ComplexMatrix retval (nr, nc); |
|
|
771 |
|
|
772 ierr.resize (nr, nc); |
|
|
773 |
|
|
774 for (int j = 0; j < nc; j++) |
|
|
775 for (int i = 0; i < nr; i++) |
|
|
776 retval(i,j) = biry (z(i,j), deriv, scaled, ierr(i,j)); |
|
|
777 |
|
|
778 return retval; |
|
3146
|
779 } |
|
|
780 |
|
|
781 static void |
|
|
782 gripe_betainc_nonconformant (int r1, int c1, int r2, int c2, int r3, |
|
|
783 int c3) |
|
|
784 { |
|
|
785 (*current_liboctave_error_handler) |
|
|
786 ("betainc: nonconformant arguments (x is %dx%d, a is %dx%d, b is %dx%d)", |
|
|
787 r1, c1, r2, c2, r3, c3); |
|
|
788 } |
|
|
789 |
|
|
790 double |
|
|
791 betainc (double x, double a, double b) |
|
|
792 { |
|
|
793 double retval; |
|
4180
|
794 F77_FUNC (xdbetai, XDBETAI) (x, a, b, retval); |
|
3146
|
795 return retval; |
|
|
796 } |
|
|
797 |
|
|
798 Matrix |
|
|
799 betainc (double x, double a, const Matrix& b) |
|
|
800 { |
|
|
801 int nr = b.rows (); |
|
|
802 int nc = b.cols (); |
|
|
803 |
|
|
804 Matrix retval (nr, nc); |
|
|
805 |
|
|
806 for (int j = 0; j < nc; j++) |
|
|
807 for (int i = 0; i < nr; i++) |
|
|
808 retval(i,j) = betainc (x, a, b(i,j)); |
|
|
809 |
|
|
810 return retval; |
|
|
811 } |
|
|
812 |
|
|
813 Matrix |
|
|
814 betainc (double x, const Matrix& a, double b) |
|
|
815 { |
|
|
816 int nr = a.rows (); |
|
|
817 int nc = a.cols (); |
|
|
818 |
|
|
819 Matrix retval (nr, nc); |
|
|
820 |
|
|
821 for (int j = 0; j < nc; j++) |
|
|
822 for (int i = 0; i < nr; i++) |
|
|
823 retval(i,j) = betainc (x, a(i,j), b); |
|
|
824 |
|
|
825 return retval; |
|
|
826 } |
|
|
827 |
|
|
828 Matrix |
|
|
829 betainc (double x, const Matrix& a, const Matrix& b) |
|
|
830 { |
|
|
831 Matrix retval; |
|
|
832 |
|
|
833 int a_nr = a.rows (); |
|
|
834 int a_nc = a.cols (); |
|
|
835 |
|
|
836 int b_nr = b.rows (); |
|
|
837 int b_nc = b.cols (); |
|
|
838 |
|
|
839 if (a_nr == b_nr && a_nc == b_nc) |
|
|
840 { |
|
|
841 retval.resize (a_nr, a_nc); |
|
|
842 |
|
|
843 for (int j = 0; j < a_nc; j++) |
|
|
844 for (int i = 0; i < a_nr; i++) |
|
|
845 retval(i,j) = betainc (x, a(i,j), b(i,j)); |
|
|
846 } |
|
|
847 else |
|
|
848 gripe_betainc_nonconformant (1, 1, a_nr, a_nc, b_nr, b_nc); |
|
|
849 |
|
|
850 return retval; |
|
|
851 } |
|
|
852 |
|
|
853 Matrix |
|
|
854 betainc (const Matrix& x, double a, double b) |
|
|
855 { |
|
|
856 int nr = x.rows (); |
|
|
857 int nc = x.cols (); |
|
|
858 |
|
|
859 Matrix retval (nr, nc); |
|
|
860 |
|
|
861 for (int j = 0; j < nc; j++) |
|
|
862 for (int i = 0; i < nr; i++) |
|
|
863 retval(i,j) = betainc (x(i,j), a, b); |
|
|
864 |
|
|
865 return retval; |
|
|
866 } |
|
|
867 |
|
|
868 Matrix |
|
|
869 betainc (const Matrix& x, double a, const Matrix& b) |
|
|
870 { |
|
|
871 Matrix retval; |
|
|
872 |
|
|
873 int nr = x.rows (); |
|
|
874 int nc = x.cols (); |
|
|
875 |
|
|
876 int b_nr = b.rows (); |
|
|
877 int b_nc = b.cols (); |
|
|
878 |
|
|
879 if (nr == b_nr && nc == b_nc) |
|
|
880 { |
|
|
881 retval.resize (nr, nc); |
|
|
882 |
|
|
883 for (int j = 0; j < nc; j++) |
|
|
884 for (int i = 0; i < nr; i++) |
|
|
885 retval(i,j) = betainc (x(i,j), a, b(i,j)); |
|
|
886 } |
|
|
887 else |
|
|
888 gripe_betainc_nonconformant (nr, nc, 1, 1, b_nr, b_nc); |
|
|
889 |
|
|
890 return retval; |
|
|
891 } |
|
|
892 |
|
|
893 Matrix |
|
|
894 betainc (const Matrix& x, const Matrix& a, double b) |
|
|
895 { |
|
|
896 Matrix retval; |
|
|
897 |
|
|
898 int nr = x.rows (); |
|
|
899 int nc = x.cols (); |
|
|
900 |
|
|
901 int a_nr = a.rows (); |
|
|
902 int a_nc = a.cols (); |
|
|
903 |
|
|
904 if (nr == a_nr && nc == a_nc) |
|
|
905 { |
|
|
906 retval.resize (nr, nc); |
|
|
907 |
|
|
908 for (int j = 0; j < nc; j++) |
|
|
909 for (int i = 0; i < nr; i++) |
|
|
910 retval(i,j) = betainc (x(i,j), a(i,j), b); |
|
|
911 } |
|
|
912 else |
|
|
913 gripe_betainc_nonconformant (nr, nc, a_nr, a_nc, 1, 1); |
|
|
914 |
|
|
915 return retval; |
|
|
916 } |
|
|
917 |
|
|
918 Matrix |
|
|
919 betainc (const Matrix& x, const Matrix& a, const Matrix& b) |
|
|
920 { |
|
|
921 Matrix retval; |
|
|
922 |
|
|
923 int nr = x.rows (); |
|
|
924 int nc = x.cols (); |
|
|
925 |
|
|
926 int a_nr = a.rows (); |
|
|
927 int a_nc = a.cols (); |
|
|
928 |
|
|
929 int b_nr = b.rows (); |
|
|
930 int b_nc = b.cols (); |
|
|
931 |
|
|
932 if (nr == a_nr && nr == b_nr && nc == a_nc && nc == b_nc) |
|
|
933 { |
|
|
934 retval.resize (nr, nc); |
|
|
935 |
|
|
936 for (int j = 0; j < nc; j++) |
|
|
937 for (int i = 0; i < nr; i++) |
|
|
938 retval(i,j) = betainc (x(i,j), a(i,j), b(i,j)); |
|
|
939 } |
|
|
940 else |
|
|
941 gripe_betainc_nonconformant (nr, nc, a_nr, a_nc, b_nr, b_nc); |
|
|
942 |
|
|
943 return retval; |
|
|
944 } |
|
|
945 |
|
3164
|
946 // XXX FIXME XXX -- there is still room for improvement here... |
|
|
947 |
|
3146
|
948 double |
|
4004
|
949 gammainc (double x, double a, bool& err) |
|
3146
|
950 { |
|
|
951 double retval; |
|
3164
|
952 |
|
4004
|
953 err = false; |
|
3164
|
954 |
|
4004
|
955 if (a < 0.0 || x < 0.0) |
|
|
956 { |
|
|
957 (*current_liboctave_error_handler) |
|
|
958 ("gammainc: A and X must be non-negative"); |
|
|
959 |
|
|
960 err = true; |
|
|
961 } |
|
|
962 else |
|
4180
|
963 F77_FUNC (xgammainc, XGAMMAINC) (a, x, retval); |
|
3164
|
964 |
|
3146
|
965 return retval; |
|
|
966 } |
|
|
967 |
|
|
968 Matrix |
|
|
969 gammainc (double x, const Matrix& a) |
|
|
970 { |
|
|
971 int nr = a.rows (); |
|
|
972 int nc = a.cols (); |
|
|
973 |
|
4004
|
974 Matrix result (nr, nc); |
|
|
975 Matrix retval; |
|
|
976 |
|
|
977 bool err; |
|
3146
|
978 |
|
|
979 for (int j = 0; j < nc; j++) |
|
|
980 for (int i = 0; i < nr; i++) |
|
4004
|
981 { |
|
|
982 result(i,j) = gammainc (x, a(i,j), err); |
|
|
983 |
|
|
984 if (err) |
|
|
985 goto done; |
|
|
986 } |
|
|
987 |
|
|
988 retval = result; |
|
|
989 |
|
|
990 done: |
|
3146
|
991 |
|
|
992 return retval; |
|
|
993 } |
|
|
994 |
|
|
995 Matrix |
|
|
996 gammainc (const Matrix& x, double a) |
|
|
997 { |
|
|
998 int nr = x.rows (); |
|
|
999 int nc = x.cols (); |
|
|
1000 |
|
4004
|
1001 Matrix result (nr, nc); |
|
|
1002 Matrix retval; |
|
|
1003 |
|
|
1004 bool err; |
|
3146
|
1005 |
|
|
1006 for (int j = 0; j < nc; j++) |
|
|
1007 for (int i = 0; i < nr; i++) |
|
4004
|
1008 { |
|
|
1009 result(i,j) = gammainc (x(i,j), a, err); |
|
|
1010 |
|
|
1011 if (err) |
|
|
1012 goto done; |
|
|
1013 } |
|
|
1014 |
|
|
1015 retval = result; |
|
|
1016 |
|
|
1017 done: |
|
3146
|
1018 |
|
|
1019 return retval; |
|
|
1020 } |
|
|
1021 |
|
|
1022 Matrix |
|
|
1023 gammainc (const Matrix& x, const Matrix& a) |
|
|
1024 { |
|
4004
|
1025 Matrix result; |
|
3146
|
1026 Matrix retval; |
|
|
1027 |
|
|
1028 int nr = x.rows (); |
|
|
1029 int nc = x.cols (); |
|
|
1030 |
|
|
1031 int a_nr = a.rows (); |
|
|
1032 int a_nc = a.cols (); |
|
|
1033 |
|
|
1034 if (nr == a_nr && nc == a_nc) |
|
|
1035 { |
|
4004
|
1036 result.resize (nr, nc); |
|
|
1037 |
|
|
1038 bool err; |
|
3146
|
1039 |
|
|
1040 for (int j = 0; j < nc; j++) |
|
|
1041 for (int i = 0; i < nr; i++) |
|
4004
|
1042 { |
|
|
1043 result(i,j) = gammainc (x(i,j), a(i,j), err); |
|
|
1044 |
|
|
1045 if (err) |
|
|
1046 goto done; |
|
|
1047 } |
|
|
1048 |
|
|
1049 retval = result; |
|
3146
|
1050 } |
|
|
1051 else |
|
|
1052 (*current_liboctave_error_handler) |
|
|
1053 ("gammainc: nonconformant arguments (arg 1 is %dx%d, arg 2 is %dx%d)", |
|
|
1054 nr, nc, a_nr, a_nc); |
|
|
1055 |
|
4004
|
1056 done: |
|
|
1057 |
|
3146
|
1058 return retval; |
|
|
1059 } |
|
|
1060 |
|
|
1061 /* |
|
|
1062 ;;; Local Variables: *** |
|
|
1063 ;;; mode: C++ *** |
|
|
1064 ;;; End: *** |
|
|
1065 */ |
