Mercurial > octave
annotate libinterp/corefcn/dassl.cc @ 27919:1891570abac8
update Octave Project Developers copyright for the new year
In files that have the "Octave Project Developers" copyright notice,
update for 2020.
author | John W. Eaton <jwe@octave.org> |
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date | Mon, 06 Jan 2020 22:29:51 -0500 |
parents | b442ec6dda5c |
children | bd51beb6205e |
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2928 | 1 /* |
2 | |
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update Octave Project Developers copyright for the new year
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3 Copyright (C) 1996-2020 The Octave Project Developers |
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4 |
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5 See the file COPYRIGHT.md in the top-level directory of this distribution |
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6 or <https://octave.org/COPYRIGHT.html/>. |
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7 |
2928 | 8 |
9 This file is part of Octave. | |
10 | |
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11 Octave is free software: you can redistribute it and/or modify it |
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12 under the terms of the GNU General Public License as published by |
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13 the Free Software Foundation, either version 3 of the License, or |
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14 (at your option) any later version. |
2928 | 15 |
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16 Octave is distributed in the hope that it will be useful, but |
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17 WITHOUT ANY WARRANTY; without even the implied warranty of |
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18 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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19 GNU General Public License for more details. |
2928 | 20 |
21 You should have received a copy of the GNU General Public License | |
7016 | 22 along with Octave; see the file COPYING. If not, see |
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23 <https://www.gnu.org/licenses/>. |
2928 | 24 |
25 */ | |
26 | |
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27 #if defined (HAVE_CONFIG_H) |
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28 # include "config.h" |
2928 | 29 #endif |
30 | |
31 #include <string> | |
32 | |
33 #include "DASSL.h" | |
34 | |
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35 #include "defun.h" |
2928 | 36 #include "error.h" |
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37 #include "errwarn.h" |
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38 #include "interpreter-private.h" |
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39 #include "ovl.h" |
2968 | 40 #include "ov-fcn.h" |
5729 | 41 #include "ov-cell.h" |
2928 | 42 #include "pager.h" |
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43 #include "parse.h" |
3243 | 44 #include "unwind-prot.h" |
2928 | 45 #include "utils.h" |
46 #include "variables.h" | |
47 | |
3998 | 48 #include "DASSL-opts.cc" |
49 | |
2928 | 50 // Global pointer for user defined function required by dassl. |
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51 static octave_value dassl_fcn; |
2928 | 52 |
3991 | 53 // Global pointer for optional user defined jacobian function. |
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54 static octave_value dassl_jac; |
3991 | 55 |
4140 | 56 // Have we warned about imaginary values returned from user function? |
57 static bool warned_fcn_imaginary = false; | |
58 static bool warned_jac_imaginary = false; | |
59 | |
3243 | 60 // Is this a recursive call? |
61 static int call_depth = 0; | |
62 | |
2928 | 63 ColumnVector |
3849 | 64 dassl_user_function (const ColumnVector& x, const ColumnVector& xdot, |
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65 double t, octave_idx_type& ires) |
2928 | 66 { |
67 ColumnVector retval; | |
68 | |
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69 assert (x.numel () == xdot.numel ()); |
2928 | 70 |
71 octave_value_list args; | |
4628 | 72 |
2928 | 73 args(2) = t; |
4628 | 74 args(1) = xdot; |
75 args(0) = x; | |
2928 | 76 |
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77 if (dassl_fcn.is_defined ()) |
2928 | 78 { |
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79 octave_value_list tmp; |
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80 |
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81 try |
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82 { |
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83 tmp = octave::feval (dassl_fcn, args, 1); |
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84 } |
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85 catch (octave::execution_exception& e) |
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86 { |
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87 err_user_supplied_eval (e, "dassl"); |
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88 } |
2928 | 89 |
3849 | 90 int tlen = tmp.length (); |
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91 if (tlen == 0 || ! tmp(0).is_defined ()) |
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92 err_user_supplied_eval ("dassl"); |
4140 | 93 |
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94 if (! warned_fcn_imaginary && tmp(0).iscomplex ()) |
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95 { |
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96 warning ("dassl: ignoring imaginary part returned from user-supplied function"); |
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97 warned_fcn_imaginary = true; |
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98 } |
3849 | 99 |
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100 retval = tmp(0).vector_value (); |
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101 |
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102 if (tlen > 1) |
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103 ires = tmp(1).int_value (); |
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104 |
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105 if (retval.isempty ()) |
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106 err_user_supplied_eval ("dassl"); |
2928 | 107 } |
108 | |
109 return retval; | |
110 } | |
111 | |
3991 | 112 Matrix |
113 dassl_user_jacobian (const ColumnVector& x, const ColumnVector& xdot, | |
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114 double t, double cj) |
3991 | 115 { |
116 Matrix retval; | |
117 | |
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118 assert (x.numel () == xdot.numel ()); |
3991 | 119 |
120 octave_value_list args; | |
121 | |
122 args(3) = cj; | |
123 args(2) = t; | |
4628 | 124 args(1) = xdot; |
125 args(0) = x; | |
3991 | 126 |
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127 if (dassl_jac.is_defined ()) |
3991 | 128 { |
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129 octave_value_list tmp; |
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130 |
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131 try |
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132 { |
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133 tmp = octave::feval (dassl_jac, args, 1); |
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134 } |
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135 catch (octave::execution_exception& e) |
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136 { |
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137 err_user_supplied_eval (e, "dassl"); |
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138 } |
3991 | 139 |
140 int tlen = tmp.length (); | |
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141 if (tlen == 0 || ! tmp(0).is_defined ()) |
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142 err_user_supplied_eval ("dassl"); |
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143 |
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144 if (! warned_jac_imaginary && tmp(0).iscomplex ()) |
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145 { |
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146 warning ("dassl: ignoring imaginary part returned from user-supplied jacobian function"); |
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147 warned_jac_imaginary = true; |
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148 } |
4140 | 149 |
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150 retval = tmp(0).matrix_value (); |
3991 | 151 |
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152 if (retval.isempty ()) |
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153 err_user_supplied_eval ("dassl"); |
3991 | 154 } |
155 | |
156 return retval; | |
157 } | |
158 | |
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159 DEFMETHOD (dassl, interp, args, nargout, |
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160 doc: /* -*- texinfo -*- |
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161 @deftypefn {} {[@var{x}, @var{xdot}, @var{istate}, @var{msg}] =} dassl (@var{fcn}, @var{x_0}, @var{xdot_0}, @var{t}, @var{t_crit}) |
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162 Solve a set of differential-algebraic equations. |
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163 |
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164 @code{dassl} solves the set of equations |
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165 @tex |
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166 $$ 0 = f (x, \dot{x}, t) $$ |
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167 with |
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168 $$ x(t_0) = x_0, \dot{x}(t_0) = \dot{x}_0 $$ |
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169 @end tex |
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170 @ifnottex |
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171 |
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172 @example |
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173 0 = f (x, xdot, t) |
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174 @end example |
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175 |
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176 @noindent |
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177 with |
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178 |
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179 @example |
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180 x(t_0) = x_0, xdot(t_0) = xdot_0 |
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181 @end example |
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182 |
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183 @end ifnottex |
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184 The solution is returned in the matrices @var{x} and @var{xdot}, |
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185 with each row in the result matrices corresponding to one of the |
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186 elements in the vector @var{t}. The first element of @var{t} |
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187 should be @math{t_0} and correspond to the initial state of the |
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188 system @var{x_0} and its derivative @var{xdot_0}, so that the first |
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189 row of the output @var{x} is @var{x_0} and the first row |
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190 of the output @var{xdot} is @var{xdot_0}. |
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191 |
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192 The first argument, @var{fcn}, is a string, inline, or function handle |
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193 that names the function @math{f} to call to compute the vector of |
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194 residuals for the set of equations. It must have the form |
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195 |
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196 @example |
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197 @var{res} = f (@var{x}, @var{xdot}, @var{t}) |
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198 @end example |
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199 |
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200 @noindent |
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201 in which @var{x}, @var{xdot}, and @var{res} are vectors, and @var{t} is a |
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202 scalar. |
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203 |
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204 If @var{fcn} is a two-element string array or a two-element cell array |
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205 of strings, inline functions, or function handles, the first element names |
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206 the function @math{f} described above, and the second element names a |
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207 function to compute the modified Jacobian |
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208 |
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209 @tex |
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210 $$ |
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211 J = {\partial f \over \partial x} |
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212 + c {\partial f \over \partial \dot{x}} |
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213 $$ |
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214 @end tex |
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215 @ifnottex |
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216 |
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217 @example |
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218 @group |
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219 df df |
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220 jac = -- + c ------ |
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221 dx d xdot |
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222 @end group |
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223 @end example |
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224 |
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225 @end ifnottex |
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226 |
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227 The modified Jacobian function must have the form |
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228 |
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229 @example |
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230 @group |
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231 |
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232 @var{jac} = j (@var{x}, @var{xdot}, @var{t}, @var{c}) |
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233 |
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234 @end group |
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235 @end example |
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236 |
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237 The second and third arguments to @code{dassl} specify the initial |
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238 condition of the states and their derivatives, and the fourth argument |
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239 specifies a vector of output times at which the solution is desired, |
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240 including the time corresponding to the initial condition. |
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241 |
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242 The set of initial states and derivatives are not strictly required to |
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243 be consistent. In practice, however, @sc{dassl} is not very good at |
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244 determining a consistent set for you, so it is best if you ensure that |
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245 the initial values result in the function evaluating to zero. |
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246 |
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247 The fifth argument is optional, and may be used to specify a set of |
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248 times that the DAE solver should not integrate past. It is useful for |
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249 avoiding difficulties with singularities and points where there is a |
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250 discontinuity in the derivative. |
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251 |
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252 After a successful computation, the value of @var{istate} will be |
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253 greater than zero (consistent with the Fortran version of @sc{dassl}). |
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254 |
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255 If the computation is not successful, the value of @var{istate} will be |
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256 less than zero and @var{msg} will contain additional information. |
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257 |
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258 You can use the function @code{dassl_options} to set optional |
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259 parameters for @code{dassl}. |
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260 @seealso{daspk, dasrt, lsode} |
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261 @end deftypefn */) |
2928 | 262 { |
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263 int nargin = args.length (); |
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264 |
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265 if (nargin < 4 || nargin > 5) |
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266 print_usage (); |
2928 | 267 |
4140 | 268 warned_fcn_imaginary = false; |
269 warned_jac_imaginary = false; | |
270 | |
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271 octave_value_list retval (4); |
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272 |
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273 octave::unwind_protect frame; |
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275 frame.protect_var (call_depth); |
3243 | 276 call_depth++; |
2928 | 277 |
3243 | 278 if (call_depth > 1) |
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279 error ("dassl: invalid recursive call"); |
2928 | 280 |
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281 std::string fcn_name, fname, jac_name, jname; |
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282 |
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283 dassl_fcn = octave_value (); |
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284 dassl_jac = octave_value (); |
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285 |
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286 octave_value f_arg = args(0); |
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287 |
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288 std::list<std::string> fcn_param_names ({"x", "xdot", "t"}); |
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289 std::list<std::string> jac_param_names ({"x", "xdot", "t", "cj"}); |
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290 |
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291 if (f_arg.iscell ()) |
2928 | 292 { |
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293 Cell c = f_arg.cell_value (); |
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294 if (c.numel () == 1) |
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295 f_arg = c(0); |
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296 else if (c.numel () == 2) |
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297 { |
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298 dassl_fcn = octave::get_function_handle (interp, c(0), |
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299 fcn_param_names); |
3991 | 300 |
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301 if (dassl_fcn.is_defined ()) |
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302 { |
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303 dassl_jac = octave::get_function_handle (interp, c(1), |
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304 jac_param_names); |
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305 |
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306 if (dassl_jac.is_undefined ()) |
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307 dassl_fcn = octave_value (); |
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308 } |
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309 } |
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310 else |
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311 error ("dassl: incorrect number of elements in cell array"); |
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312 } |
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313 |
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314 if (dassl_fcn.is_undefined () && ! f_arg.iscell ()) |
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315 { |
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316 if (f_arg.is_function_handle () || f_arg.is_inline_function ()) |
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317 dassl_fcn = f_arg; |
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318 else |
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319 { |
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320 switch (f_arg.rows ()) |
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321 { |
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322 case 1: |
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323 dassl_fcn = octave::get_function_handle (interp, f_arg, |
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324 fcn_param_names); |
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325 break; |
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326 |
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327 case 2: |
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328 { |
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329 string_vector tmp = f_arg.string_vector_value (); |
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331 dassl_fcn = octave::get_function_handle (interp, tmp(0), |
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332 fcn_param_names); |
3991 | 333 |
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334 if (dassl_fcn.is_defined ()) |
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335 { |
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336 dassl_jac = octave::get_function_handle (interp, tmp(1), |
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337 jac_param_names); |
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339 if (dassl_jac.is_undefined ()) |
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340 dassl_fcn = octave_value (); |
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341 } |
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342 } |
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343 break; |
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344 |
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345 default: |
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346 error ("dassl: first arg should be a string or 2-element string array"); |
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347 } |
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348 } |
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349 } |
3243 | 350 |
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351 if (dassl_fcn.is_undefined ()) |
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352 error ("dassl: FCN argument is not a valid function name or handle"); |
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354 ColumnVector state = args(1).xvector_value ("dassl: initial state X_0 must be a vector"); |
2928 | 355 |
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356 ColumnVector deriv = args(2).xvector_value ("dassl: initial derivatives XDOT_0 must be a vector"); |
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357 |
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358 ColumnVector out_times = args(3).xvector_value ("dassl: output time variable T must be a vector"); |
2928 | 359 |
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360 ColumnVector crit_times; |
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361 int crit_times_set = 0; |
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362 if (nargin > 4) |
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363 { |
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364 crit_times = args(4).xvector_value ("dassl: list of critical times T_CRIT must be a vector"); |
2928 | 365 |
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366 crit_times_set = 1; |
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367 } |
3991 | 368 |
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369 if (state.numel () != deriv.numel ()) |
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370 error ("dassl: X and XDOT_0 must have the same size"); |
3991 | 371 |
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372 double tzero = out_times (0); |
2928 | 373 |
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374 DAEFunc func (dassl_user_function); |
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375 if (dassl_jac.is_defined ()) |
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376 func.set_jacobian_function (dassl_user_jacobian); |
3243 | 377 |
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378 DASSL dae (state, deriv, tzero, func); |
2928 | 379 |
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380 dae.set_options (dassl_opts); |
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382 Matrix output; |
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383 Matrix deriv_output; |
3997 | 384 |
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385 if (crit_times_set) |
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386 output = dae.integrate (out_times, deriv_output, crit_times); |
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387 else |
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388 output = dae.integrate (out_times, deriv_output); |
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389 |
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390 std::string msg = dae.error_message (); |
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391 |
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392 if (dae.integration_ok ()) |
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393 { |
20892 | 394 retval(0) = output; |
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395 retval(1) = deriv_output; |
2928 | 396 } |
3243 | 397 else |
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398 { |
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399 if (nargout < 3) |
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400 error ("dassl: %s", msg.c_str ()); |
20892 | 401 |
402 retval(0) = Matrix (); | |
403 retval(1) = Matrix (); | |
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404 } |
3243 | 405 |
20892 | 406 retval(2) = static_cast<double> (dae.integration_state ()); |
407 retval(3) = msg; | |
408 | |
2928 | 409 return retval; |
410 } | |
411 | |
412 /* | |
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413 ## dassl-1.m |
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414 ## |
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415 ## Test dassl() function |
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416 ## |
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417 ## Author: David Billinghurst (David.Billinghurst@riotinto.com.au) |
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418 ## Comalco Research and Technology |
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419 ## 20 May 1998 |
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420 ## |
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421 ## Problem |
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422 ## |
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423 ## y1' = -y2, y1(0) = 1 |
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424 ## y2' = y1, y2(0) = 0 |
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425 ## |
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426 ## Solution |
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427 ## |
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428 ## y1(t) = cos(t) |
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429 ## y2(t) = sin(t) |
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430 ## |
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431 %!function res = __f (x, xdot, t) |
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432 %! res = [xdot(1)+x(2); xdot(2)-x(1)]; |
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433 %!endfunction |
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434 |
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435 %!test |
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436 %! |
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437 %! x0 = [1; 0]; |
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438 %! xdot0 = [0; 1]; |
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439 %! t = (0:1:10)'; |
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440 %! |
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441 %! tol = 100 * dassl_options ("relative tolerance"); |
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442 %! |
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443 %! [x, xdot] = dassl ("__f", x0, xdot0, t); |
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444 %! |
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445 %! y = [cos(t), sin(t)]; |
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446 %! |
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447 %! assert (x, y, tol); |
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448 |
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449 ## dassl-2.m |
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450 ## |
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451 ## Test dassl() function |
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452 ## |
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453 ## Author: David Billinghurst (David.Billinghurst@riotinto.com.au) |
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454 ## Comalco Research and Technology |
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455 ## 20 May 1998 |
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456 ## |
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457 ## Based on SLATEC quick check for DASSL by Linda Petzold |
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458 ## |
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459 ## Problem |
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460 ## |
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461 ## x1' + 10*x1 = 0, x1(0) = 1 |
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462 ## x1 + x2 = 1, x2(0) = 0 |
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463 ## |
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464 ## |
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465 ## Solution |
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466 ## |
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467 ## x1(t) = exp(-10*t) |
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468 ## x2(t) = 1 - x(1) |
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469 ## |
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470 %!function res = __f (x, xdot, t) |
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471 %! res = [xdot(1)+10*x(1); x(1)+x(2)-1]; |
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472 %!endfunction |
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473 |
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474 %!test |
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475 %! |
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476 %! x0 = [1; 0]; |
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477 %! xdot0 = [-10; 10]; |
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478 %! t = (0:0.2:1)'; |
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479 %! |
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480 %! tol = 500 * dassl_options ("relative tolerance"); |
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481 %! |
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482 %! [x, xdot] = dassl ("__f", x0, xdot0, t); |
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483 %! |
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484 %! y = [exp(-10*t), 1-exp(-10*t)]; |
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485 %! |
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486 %! assert (x, y, tol); |
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487 |
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488 %!test |
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489 %! old_tol = dassl_options ("absolute tolerance"); |
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490 %! dassl_options ("absolute tolerance", eps); |
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491 %! assert (dassl_options ("absolute tolerance") == eps); |
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492 %! ## Restore old value of tolerance |
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493 %! dassl_options ("absolute tolerance", old_tol); |
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494 |
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495 %!error dassl_options ("foo", 1, 2) |
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496 */ |