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