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1 /* |
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2 |
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3 Copyright (C) 2002 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 <iostream> |
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28 #include <string> |
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29 |
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30 #include "DASRT.h" |
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31 #include "lo-mappers.h" |
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32 |
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33 #include "defun-dld.h" |
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34 #include "error.h" |
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35 #include "gripes.h" |
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36 #include "oct-obj.h" |
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37 #include "ov-fcn.h" |
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38 #include "pager.h" |
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39 #include "parse.h" |
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40 #include "unwind-prot.h" |
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41 #include "utils.h" |
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42 #include "variables.h" |
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43 |
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44 #include "DASRT-opts.cc" |
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45 |
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46 // Global pointers for user defined function required by dasrt. |
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47 static octave_function *dasrt_f; |
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48 static octave_function *dasrt_j; |
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49 static octave_function *dasrt_cf; |
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50 |
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51 // Have we warned about imaginary values returned from user function? |
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52 static bool warned_fcn_imaginary = false; |
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53 static bool warned_jac_imaginary = false; |
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54 static bool warned_cf_imaginary = false; |
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55 |
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56 // Is this a recursive call? |
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57 static int call_depth = 0; |
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58 |
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59 static ColumnVector |
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60 dasrt_user_f (const ColumnVector& x, const ColumnVector& xprime, |
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61 double t, int& ires) |
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62 { |
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63 ColumnVector retval; |
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64 |
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65 octave_value_list args; |
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66 |
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67 int n = x.length (); |
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68 |
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69 args(2) = t; |
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70 |
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71 if (n > 1) |
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72 { |
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73 args(1) = xprime; |
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74 args(0) = x; |
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75 } |
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76 else if (n == 1) |
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77 { |
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78 args(1) = xprime(0); |
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79 args(0) = x(0); |
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80 } |
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81 else |
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82 { |
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83 args(1) = Matrix (); |
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84 args(0) = Matrix (); |
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85 } |
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86 |
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87 if (dasrt_f) |
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88 { |
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89 octave_value_list tmp = dasrt_f->do_multi_index_op (1, args); |
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90 |
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91 if (error_state) |
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92 { |
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93 gripe_user_supplied_eval ("dasrt"); |
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94 return retval; |
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95 } |
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96 |
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97 if (tmp.length () > 0 && tmp(0).is_defined ()) |
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98 { |
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99 if (! warned_fcn_imaginary && tmp(0).is_complex_type ()) |
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100 { |
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101 warning ("dasrt: ignoring imaginary part returned from user-supplied function"); |
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102 warned_fcn_imaginary = true; |
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103 } |
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104 |
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105 retval = ColumnVector (tmp(0).vector_value ()); |
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106 |
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107 if (error_state || retval.length () == 0) |
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108 gripe_user_supplied_eval ("dasrt"); |
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109 } |
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110 else |
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111 gripe_user_supplied_eval ("dasrt"); |
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112 } |
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113 |
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114 return retval; |
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115 } |
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116 |
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117 static ColumnVector |
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118 dasrt_user_cf (const ColumnVector& x, double t) |
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119 { |
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120 ColumnVector retval; |
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121 |
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122 octave_value_list args; |
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123 |
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124 int n = x.length (); |
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125 |
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126 if (n > 1) |
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127 args(0) = x; |
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128 else if (n == 1) |
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129 args(0) = x(0); |
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130 else |
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131 args(0) = Matrix (); |
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132 |
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133 args(1) = t; |
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134 |
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135 if (dasrt_cf) |
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136 { |
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137 octave_value_list tmp = dasrt_cf->do_multi_index_op (1, args); |
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138 |
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139 if (error_state) |
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140 { |
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141 gripe_user_supplied_eval ("dasrt"); |
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142 return retval; |
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143 } |
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144 |
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145 if (tmp.length () > 0 && tmp(0).is_defined ()) |
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146 { |
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147 if (! warned_cf_imaginary && tmp(0).is_complex_type ()) |
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148 { |
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149 warning ("dasrt: ignoring imaginary part returned from user-supplied constraint function"); |
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150 warned_cf_imaginary = true; |
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151 } |
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152 |
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153 retval = ColumnVector (tmp(0).vector_value ()); |
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154 |
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155 if (error_state || retval.length () == 0) |
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156 gripe_user_supplied_eval ("dasrt"); |
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157 } |
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158 else |
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159 gripe_user_supplied_eval ("dasrt"); |
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160 } |
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161 |
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162 return retval; |
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163 } |
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164 |
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165 static Matrix |
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166 dasrt_user_j (const ColumnVector& x, const ColumnVector& xdot, |
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167 double t, double cj) |
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168 { |
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169 Matrix retval; |
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170 |
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171 int nstates = x.capacity (); |
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172 |
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173 assert (nstates == xdot.capacity ()); |
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174 |
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175 octave_value_list args; |
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176 |
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177 args(3) = cj; |
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178 args(2) = t; |
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179 |
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180 if (nstates > 1) |
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181 { |
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182 Matrix m1 (nstates, 1); |
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183 Matrix m2 (nstates, 1); |
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184 for (int i = 0; i < nstates; i++) |
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185 { |
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186 m1 (i, 0) = x (i); |
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187 m2 (i, 0) = xdot (i); |
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188 } |
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189 octave_value state (m1); |
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190 octave_value deriv (m2); |
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191 args(1) = deriv; |
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192 args(0) = state; |
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193 } |
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194 else |
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195 { |
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196 double d1 = x (0); |
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197 double d2 = xdot (0); |
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198 octave_value state (d1); |
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199 octave_value deriv (d2); |
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200 args(1) = deriv; |
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201 args(0) = state; |
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202 } |
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203 |
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204 if (dasrt_j) |
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205 { |
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206 octave_value_list tmp = dasrt_j->do_multi_index_op (1, args); |
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207 |
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208 if (error_state) |
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209 { |
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210 gripe_user_supplied_eval ("dasrt"); |
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211 return retval; |
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212 } |
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213 |
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214 int tlen = tmp.length (); |
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215 if (tlen > 0 && tmp(0).is_defined ()) |
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216 { |
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217 if (! warned_jac_imaginary && tmp(0).is_complex_type ()) |
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218 { |
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219 warning ("dasrt: ignoring imaginary part returned from user-supplied jacobian function"); |
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220 warned_jac_imaginary = true; |
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221 } |
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222 |
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223 retval = tmp(0).matrix_value (); |
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224 |
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225 if (error_state || retval.length () == 0) |
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226 gripe_user_supplied_eval ("dasrt"); |
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227 } |
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228 else |
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229 gripe_user_supplied_eval ("dasrt"); |
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230 } |
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231 |
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232 return retval; |
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233 } |
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234 |
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235 #define DASRT_ABORT \ |
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236 do \ |
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237 { \ |
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238 unwind_protect::run_frame ("Fdasrt"); \ |
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239 return retval; \ |
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240 } \ |
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241 while (0) |
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242 |
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243 #define DASRT_ABORT1(msg) \ |
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244 do \ |
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245 { \ |
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246 ::error ("dasrt: " msg); \ |
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247 DASRT_ABORT; \ |
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248 } \ |
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249 while (0) |
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250 |
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251 #define DASRT_ABORT2(fmt, arg) \ |
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252 do \ |
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253 { \ |
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254 ::error ("dasrt: " fmt, arg); \ |
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255 DASRT_ABORT; \ |
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256 } \ |
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257 while (0) |
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258 |
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259 DEFUN_DLD (dasrt, args, nargout, |
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260 "-*- texinfo -*-\n\ |
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261 @deftypefn {Loadable Function} {[@var{x}, @var{xdot}, @var{t_out}, @var{istat}, @var{msg}] =} dasrt (@var{fcn} [, @var{g}], @var{x_0}, @var{xdot_0}, @var{t} [, @var{t_crit}])\n\ |
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262 Solve the set of differential-algebraic equations\n\ |
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263 @tex\n\ |
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264 $$ 0 = f (\\dot{x}, x, t) $$\n\ |
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265 with\n\ |
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266 $$ x(t_0) = x_0, \\dot{x}(t_0) = \\dot{x}_0 $$\n\ |
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267 @end tex\n\ |
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268 @ifinfo\n\ |
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269 \n\ |
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270 @example\n\ |
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271 0 = f (xdot, x, t)\n\ |
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272 @end example\n\ |
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273 \n\ |
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274 with\n\ |
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275 \n\ |
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276 @example\n\ |
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277 x(t_0) = x_0, xdot(t_0) = xdot_0\n\ |
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278 @end example\n\ |
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279 \n\ |
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280 @end ifinfo\n\ |
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281 with functional stopping criteria (root solving).\n\ |
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282 \n\ |
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283 The solution is returned in the matrices @var{x} and @var{xdot},\n\ |
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284 with each row in the result matrices corresponding to one of the\n\ |
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285 elements in the vector @var{t_out}. The first element of @var{t}\n\ |
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286 should be @math{t_0} and correspond to the initial state of the\n\ |
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287 system @var{x_0} and its derivative @var{xdot_0}, so that the first\n\ |
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288 row of the output @var{x} is @var{x_0} and the first row\n\ |
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289 of the output @var{xdot} is @var{xdot_0}.\n\ |
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290 \n\ |
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291 The vector @var{t} provides an upper limit on the length of the\n\ |
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292 integration. If the stopping condition is met, the vector\n\ |
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293 @var{t_out} will be shorter than @var{t}, and the final element of\n\ |
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294 @var{t_out} will be the point at which the stopping condition was met,\n\ |
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295 and may not correspond to any element of the vector @var{t}.\n\ |
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296 \n\ |
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297 The first argument, @var{fcn}, is a string that names the function to\n\ |
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298 call to compute the vector of residuals for the set of equations.\n\ |
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299 It must have the form\n\ |
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300 \n\ |
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301 @example\n\ |
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302 @var{res} = f (@var{x}, @var{xdot}, @var{t})\n\ |
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303 @end example\n\ |
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304 \n\ |
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305 @noindent\n\ |
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306 in which @var{x}, @var{xdot}, and @var{res} are vectors, and @var{t} is a\n\ |
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307 scalar.\n\ |
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308 \n\ |
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309 If @var{fcn} is a two-element string array, the first element names\n\ |
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310 the function @math{f} described above, and the second element names\n\ |
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311 a function to compute the modified Jacobian\n\ |
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312 \n\ |
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313 @tex\n\ |
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314 $$\n\ |
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315 J = {\\partial f \\over \\partial x}\n\ |
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316 + c {\\partial f \\over \\partial \\dot{x}}\n\ |
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317 $$\n\ |
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318 @end tex\n\ |
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319 @ifinfo\n\ |
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320 \n\ |
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321 @example\n\ |
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322 df df\n\ |
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323 jac = -- + c ------\n\ |
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324 dx d xdot\n\ |
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325 @end example\n\ |
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326 \n\ |
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327 @end ifinfo\n\ |
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328 \n\ |
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329 The modified Jacobian function must have the form\n\ |
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330 \n\ |
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331 @example\n\ |
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332 \n\ |
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333 @var{jac} = j (@var{x}, @var{xdot}, @var{t}, @var{c})\n\ |
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334 \n\ |
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335 @end example\n\ |
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336 \n\ |
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337 The optional second argument names a function that defines the\n\ |
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338 constraint functions whose roots are desired during the integration.\n\ |
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339 This function must have the form\n\ |
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340 \n\ |
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341 @example\n\ |
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342 @var{g_out} = g (@var{x}, @var{t})\n\ |
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343 @end example\n\ |
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344 \n\ |
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345 and return a vector of the constraint function values.\n\ |
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346 If the value of any of the constraint functions changes sign, @sc{Dasrt}\n\ |
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347 will attempt to stop the integration at the point of the sign change.\n\ |
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348 \n\ |
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349 If the name of the constraint function is omitted, @code{dasrt} solves\n\ |
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350 the saem problem as @code{daspk} or @code{dassl}.\n\ |
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351 \n\ |
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352 Note that because of numerical errors in the constraint functions\n\ |
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353 due to roundoff and integration error, @sc{Dasrt} may return false\n\ |
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354 roots, or return the same root at two or more nearly equal values of\n\ |
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355 @var{T}. If such false roots are suspected, the user should consider\n\ |
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356 smaller error tolerances or higher precision in the evaluation of the\n\ |
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357 constraint functions.\n\ |
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358 \n\ |
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359 If a root of some constraint function defines the end of the problem,\n\ |
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360 the input to @sc{Dasrt} should nevertheless allow integration to a\n\ |
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361 point slightly past that root, so that @sc{Dasrt} can locate the root\n\ |
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362 by interpolation.\n\ |
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363 \n\ |
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364 The third and fourth arguments to @code{dasrt} specify the initial\n\ |
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365 condition of the states and their derivatives, and the fourth argument\n\ |
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366 specifies a vector of output times at which the solution is desired,\n\ |
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367 including the time corresponding to the initial condition.\n\ |
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368 \n\ |
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369 The set of initial states and derivatives are not strictly required to\n\ |
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370 be consistent. In practice, however, @sc{Dassl} is not very good at\n\ |
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371 determining a consistent set for you, so it is best if you ensure that\n\ |
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372 the initial values result in the function evaluating to zero.\n\ |
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373 \n\ |
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374 The sixth argument is optional, and may be used to specify a set of\n\ |
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375 times that the DAE solver should not integrate past. It is useful for\n\ |
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376 avoiding difficulties with singularities and points where there is a\n\ |
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377 discontinuity in the derivative.\n\ |
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378 \n\ |
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379 After a successful computation, the value of @var{istate} will be\n\ |
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380 greater than zero (consistent with the Fortran version of @sc{Dassl}).\n\ |
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381 \n\ |
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382 If the computation is not successful, the value of @var{istate} will be\n\ |
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383 less than zero and @var{msg} will contain additional information.\n\ |
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384 \n\ |
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385 You can use the function @code{dasrt_options} to set optional\n\ |
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386 parameters for @code{dasrt}.\n\ |
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387 @end deftypefn\n\ |
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388 @seealso{daspk, dasrt, lsode, odessa}") |
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389 { |
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390 octave_value_list retval; |
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391 |
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392 warned_fcn_imaginary = false; |
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393 warned_jac_imaginary = false; |
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394 warned_cf_imaginary = false; |
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395 |
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396 unwind_protect::begin_frame ("Fdasrt"); |
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397 |
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398 unwind_protect_int (call_depth); |
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399 call_depth++; |
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400 |
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401 if (call_depth > 1) |
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402 DASRT_ABORT1 ("invalid recursive call"); |
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403 |
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404 int argp = 0; |
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405 |
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406 int nargin = args.length (); |
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407 |
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408 if (nargin < 4 || nargin > 6) |
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409 { |
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410 print_usage ("dasrt"); |
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411 unwind_protect::run_frame ("Fdasrt"); |
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412 return retval; |
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413 } |
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414 |
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415 dasrt_f = 0; |
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416 dasrt_j = 0; |
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417 dasrt_cf = 0; |
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418 |
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419 // Check all the arguments. Are they the right animals? |
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420 |
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421 // Here's where I take care of f and j in one shot: |
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422 |
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423 octave_value f_arg = args(0); |
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424 |
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425 switch (f_arg.rows ()) |
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426 { |
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427 case 1: |
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428 dasrt_f = extract_function |
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429 (args(0), "dasrt", "__dasrt_fcn__", |
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430 "function res = __dasrt_fcn__ (x, xdot, t) res = ", |
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431 "; endfunction"); |
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432 break; |
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433 |
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434 case 2: |
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435 { |
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436 string_vector tmp = args(0).all_strings (); |
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437 |
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438 if (! error_state) |
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439 { |
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440 dasrt_f = extract_function |
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441 (tmp(0), "dasrt", "__dasrt_fcn__", |
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442 "function res = __dasrt_fcn__ (x, xdot, t) res = ", |
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443 "; endfunction"); |
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444 |
|
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445 if (dasrt_f) |
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446 { |
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447 dasrt_j = extract_function |
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448 (tmp(1), "dasrt", "__dasrt_jac__", |
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449 "function jac = __dasrt_jac__ (x, xdot, t, cj) jac = ", |
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450 "; endfunction"); |
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451 |
|
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452 if (! dasrt_j) |
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453 dasrt_f = 0; |
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454 } |
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455 } |
|
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456 } |
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457 break; |
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458 |
|
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459 default: |
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460 DASRT_ABORT1 |
|
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461 ("first arg should be a string or 2-element string array"); |
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462 } |
|
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463 |
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464 if (error_state || (! dasrt_f)) |
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465 DASRT_ABORT; |
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466 |
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467 DAERTFunc func (dasrt_user_f); |
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468 |
|
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469 argp++; |
|
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470 |
|
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471 if (args(1).is_string ()) |
|
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472 { |
|
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473 dasrt_cf = is_valid_function (args(1), "dasrt", true); |
|
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474 |
|
|
475 if (! dasrt_cf) |
|
3992
|
476 DASRT_ABORT1 ("expecting function name as argument 2"); |
|
3990
|
477 |
|
|
478 argp++; |
|
|
479 |
|
|
480 func.set_constraint_function (dasrt_user_cf); |
|
|
481 } |
|
|
482 |
|
|
483 ColumnVector state (args(argp++).vector_value ()); |
|
|
484 |
|
|
485 if (error_state) |
|
|
486 DASRT_ABORT2 ("expecting state vector as argument %d", argp); |
|
|
487 |
|
3992
|
488 ColumnVector stateprime (args(argp++).vector_value ()); |
|
3990
|
489 |
|
|
490 if (error_state) |
|
|
491 DASRT_ABORT2 |
|
|
492 ("expecting time derivative of state vector as argument %d", argp); |
|
|
493 |
|
3994
|
494 ColumnVector out_times (args(argp++).vector_value ()); |
|
3990
|
495 |
|
|
496 if (error_state) |
|
|
497 DASRT_ABORT2 |
|
|
498 ("expecting output time vector as %s argument %d", argp); |
|
|
499 |
|
3994
|
500 double tzero = out_times (0); |
|
3990
|
501 |
|
|
502 ColumnVector crit_times; |
|
|
503 |
|
|
504 bool crit_times_set = false; |
|
|
505 |
|
|
506 if (argp < nargin) |
|
|
507 { |
|
|
508 crit_times = ColumnVector (args(argp++).vector_value ()); |
|
|
509 |
|
|
510 if (error_state) |
|
|
511 DASRT_ABORT2 |
|
|
512 ("expecting critical time vector as argument %d", argp); |
|
|
513 |
|
|
514 crit_times_set = true; |
|
|
515 } |
|
|
516 |
|
|
517 if (dasrt_j) |
|
|
518 func.set_jacobian_function (dasrt_user_j); |
|
|
519 |
|
|
520 DASRT_result output; |
|
|
521 |
|
3992
|
522 DASRT dae = DASRT (state, stateprime, tzero, func); |
|
3990
|
523 |
|
4122
|
524 dae.set_options (dasrt_opts); |
|
3990
|
525 |
|
|
526 if (crit_times_set) |
|
|
527 output = dae.integrate (out_times, crit_times); |
|
|
528 else |
|
|
529 output = dae.integrate (out_times); |
|
|
530 |
|
|
531 if (! error_state) |
|
|
532 { |
|
3997
|
533 std::string msg = dae.error_message (); |
|
|
534 |
|
|
535 retval(4) = msg; |
|
|
536 retval(3) = static_cast<double> (dae.integration_state ()); |
|
|
537 |
|
|
538 if (dae.integration_ok ()) |
|
|
539 { |
|
|
540 retval(2) = output.times (); |
|
|
541 retval(1) = output.deriv (); |
|
|
542 retval(0) = output.state (); |
|
|
543 } |
|
|
544 else |
|
|
545 { |
|
|
546 retval(2) = Matrix (); |
|
|
547 retval(1) = Matrix (); |
|
|
548 retval(0) = Matrix (); |
|
|
549 |
|
|
550 if (nargout < 4) |
|
|
551 error ("dasrt: %s", msg.c_str ()); |
|
|
552 } |
|
3990
|
553 } |
|
|
554 |
|
|
555 unwind_protect::run_frame ("Fdasrt"); |
|
|
556 |
|
|
557 return retval; |
|
|
558 } |
|
|
559 |
|
|
560 /* |
|
|
561 ;;; Local Variables: *** |
|
|
562 ;;; mode: C++ *** |
|
|
563 ;;; End: *** |
|
|
564 */ |
