Mercurial > octave
annotate libinterp/corefcn/dassl.cc @ 23220:092078913d54
maint: Merge stable to default.
author | John W. Eaton <jwe@octave.org> |
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date | Wed, 22 Feb 2017 12:58:07 -0500 |
parents | ef4d915df748 3ac9f9ecfae5 |
children | 55916f99b8b6 |
rev | line source |
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2928 | 1 /* |
2 | |
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3 Copyright (C) 1996-2017 John W. Eaton |
2928 | 4 |
5 This file is part of Octave. | |
6 | |
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 |
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9 the Free Software Foundation; either version 3 of the License, or |
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10 (at your option) any later version. |
2928 | 11 |
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12 Octave is distributed in the hope that it will be useful, but |
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13 WITHOUT ANY WARRANTY; without even the implied warranty of |
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14 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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15 GNU General Public License for more details. |
2928 | 16 |
17 You should have received a copy of the GNU General Public License | |
7016 | 18 along with Octave; see the file COPYING. If not, see |
19 <http://www.gnu.org/licenses/>. | |
2928 | 20 |
21 */ | |
22 | |
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23 #if defined (HAVE_CONFIG_H) |
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24 # include "config.h" |
2928 | 25 #endif |
26 | |
27 #include <string> | |
28 | |
3567 | 29 #include <iomanip> |
3523 | 30 #include <iostream> |
2928 | 31 |
32 #include "DASSL.h" | |
33 | |
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34 #include "defun.h" |
2928 | 35 #include "error.h" |
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36 #include "errwarn.h" |
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37 #include "ovl.h" |
2968 | 38 #include "ov-fcn.h" |
5729 | 39 #include "ov-cell.h" |
2928 | 40 #include "pager.h" |
3243 | 41 #include "unwind-prot.h" |
2928 | 42 #include "utils.h" |
43 #include "variables.h" | |
44 | |
3998 | 45 #include "DASSL-opts.cc" |
46 | |
2928 | 47 // Global pointer for user defined function required by dassl. |
2968 | 48 static octave_function *dassl_fcn; |
2928 | 49 |
3991 | 50 // Global pointer for optional user defined jacobian function. |
51 static octave_function *dassl_jac; | |
52 | |
4140 | 53 // Have we warned about imaginary values returned from user function? |
54 static bool warned_fcn_imaginary = false; | |
55 static bool warned_jac_imaginary = false; | |
56 | |
3243 | 57 // Is this a recursive call? |
58 static int call_depth = 0; | |
59 | |
2928 | 60 ColumnVector |
3849 | 61 dassl_user_function (const ColumnVector& x, const ColumnVector& xdot, |
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62 double t, octave_idx_type& ires) |
2928 | 63 { |
64 ColumnVector retval; | |
65 | |
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66 assert (x.numel () == xdot.numel ()); |
2928 | 67 |
68 octave_value_list args; | |
4628 | 69 |
2928 | 70 args(2) = t; |
4628 | 71 args(1) = xdot; |
72 args(0) = x; | |
2928 | 73 |
74 if (dassl_fcn) | |
75 { | |
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76 octave_value_list tmp; |
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77 |
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78 try |
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79 { |
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80 tmp = dassl_fcn->do_multi_index_op (1, args); |
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81 } |
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82 catch (octave::execution_exception& e) |
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83 { |
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84 err_user_supplied_eval (e, "dassl"); |
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85 } |
2928 | 86 |
3849 | 87 int tlen = tmp.length (); |
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88 if (tlen == 0 || ! tmp(0).is_defined ()) |
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89 err_user_supplied_eval ("dassl"); |
4140 | 90 |
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91 if (! warned_fcn_imaginary && tmp(0).is_complex_type ()) |
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92 { |
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93 warning ("dassl: ignoring imaginary part returned from user-supplied function"); |
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94 warned_fcn_imaginary = true; |
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95 } |
3849 | 96 |
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97 retval = tmp(0).vector_value (); |
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98 |
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99 if (tlen > 1) |
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100 ires = tmp(1).int_value (); |
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101 |
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102 if (retval.is_empty ()) |
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103 err_user_supplied_eval ("dassl"); |
2928 | 104 } |
105 | |
106 return retval; | |
107 } | |
108 | |
3991 | 109 Matrix |
110 dassl_user_jacobian (const ColumnVector& x, const ColumnVector& xdot, | |
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111 double t, double cj) |
3991 | 112 { |
113 Matrix retval; | |
114 | |
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115 assert (x.numel () == xdot.numel ()); |
3991 | 116 |
117 octave_value_list args; | |
118 | |
119 args(3) = cj; | |
120 args(2) = t; | |
4628 | 121 args(1) = xdot; |
122 args(0) = x; | |
3991 | 123 |
124 if (dassl_jac) | |
125 { | |
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126 octave_value_list tmp; |
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127 |
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128 try |
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129 { |
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130 tmp = dassl_jac->do_multi_index_op (1, args); |
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131 } |
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132 catch (octave::execution_exception& e) |
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133 { |
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134 err_user_supplied_eval (e, "dassl"); |
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135 } |
3991 | 136 |
137 int tlen = tmp.length (); | |
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138 if (tlen == 0 || ! tmp(0).is_defined ()) |
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139 err_user_supplied_eval ("dassl"); |
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140 |
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141 if (! warned_jac_imaginary && tmp(0).is_complex_type ()) |
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142 { |
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143 warning ("dassl: ignoring imaginary part returned from user-supplied jacobian function"); |
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144 warned_jac_imaginary = true; |
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145 } |
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147 retval = tmp(0).matrix_value (); |
3991 | 148 |
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149 if (retval.is_empty ()) |
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150 err_user_supplied_eval ("dassl"); |
3991 | 151 } |
152 | |
153 return retval; | |
154 } | |
155 | |
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156 DEFUN (dassl, args, nargout, |
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157 doc: /* -*- texinfo -*- |
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158 @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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159 Solve the set of differential-algebraic equations |
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160 @tex |
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161 $$ 0 = f (x, \dot{x}, t) $$ |
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162 with |
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163 $$ x(t_0) = x_0, \dot{x}(t_0) = \dot{x}_0 $$ |
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164 @end tex |
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165 @ifnottex |
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166 |
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167 @example |
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168 0 = f (x, xdot, t) |
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169 @end example |
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170 |
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171 @noindent |
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172 with |
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173 |
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174 @example |
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175 x(t_0) = x_0, xdot(t_0) = xdot_0 |
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176 @end example |
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177 |
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178 @end ifnottex |
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179 The solution is returned in the matrices @var{x} and @var{xdot}, |
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180 with each row in the result matrices corresponding to one of the |
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181 elements in the vector @var{t}. The first element of @var{t} |
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182 should be @math{t_0} and correspond to the initial state of the |
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183 system @var{x_0} and its derivative @var{xdot_0}, so that the first |
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184 row of the output @var{x} is @var{x_0} and the first row |
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185 of the output @var{xdot} is @var{xdot_0}. |
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186 |
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187 The first argument, @var{fcn}, is a string, inline, or function handle |
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188 that names the function @math{f} to call to compute the vector of |
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189 residuals for the set of equations. It must have the form |
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190 |
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191 @example |
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192 @var{res} = f (@var{x}, @var{xdot}, @var{t}) |
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193 @end example |
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194 |
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195 @noindent |
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196 in which @var{x}, @var{xdot}, and @var{res} are vectors, and @var{t} is a |
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197 scalar. |
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198 |
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199 If @var{fcn} is a two-element string array or a two-element cell array |
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200 of strings, inline functions, or function handles, the first element names |
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201 the function @math{f} described above, and the second element names a |
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202 function to compute the modified Jacobian |
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203 |
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204 @tex |
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205 $$ |
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206 J = {\partial f \over \partial x} |
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207 + c {\partial f \over \partial \dot{x}} |
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208 $$ |
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209 @end tex |
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210 @ifnottex |
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211 |
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212 @example |
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213 @group |
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214 df df |
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215 jac = -- + c ------ |
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216 dx d xdot |
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217 @end group |
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218 @end example |
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219 |
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220 @end ifnottex |
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221 |
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222 The modified Jacobian function must have the form |
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223 |
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224 @example |
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225 @group |
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226 |
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227 @var{jac} = j (@var{x}, @var{xdot}, @var{t}, @var{c}) |
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228 |
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229 @end group |
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230 @end example |
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231 |
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232 The second and third arguments to @code{dassl} specify the initial |
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233 condition of the states and their derivatives, and the fourth argument |
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234 specifies a vector of output times at which the solution is desired, |
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235 including the time corresponding to the initial condition. |
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236 |
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237 The set of initial states and derivatives are not strictly required to |
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238 be consistent. In practice, however, @sc{dassl} is not very good at |
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239 determining a consistent set for you, so it is best if you ensure that |
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240 the initial values result in the function evaluating to zero. |
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241 |
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242 The fifth argument is optional, and may be used to specify a set of |
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243 times that the DAE solver should not integrate past. It is useful for |
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244 avoiding difficulties with singularities and points where there is a |
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245 discontinuity in the derivative. |
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246 |
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247 After a successful computation, the value of @var{istate} will be |
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248 greater than zero (consistent with the Fortran version of @sc{dassl}). |
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249 |
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250 If the computation is not successful, the value of @var{istate} will be |
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251 less than zero and @var{msg} will contain additional information. |
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252 |
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253 You can use the function @code{dassl_options} to set optional |
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254 parameters for @code{dassl}. |
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255 @seealso{daspk, dasrt, lsode} |
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256 @end deftypefn */) |
2928 | 257 { |
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258 int nargin = args.length (); |
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259 |
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260 if (nargin < 4 || nargin > 5) |
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261 print_usage (); |
2928 | 262 |
4140 | 263 warned_fcn_imaginary = false; |
264 warned_jac_imaginary = false; | |
265 | |
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266 octave_value_list retval (4); |
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267 |
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268 octave::unwind_protect frame; |
2928 | 269 |
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270 frame.protect_var (call_depth); |
3243 | 271 call_depth++; |
2928 | 272 |
3243 | 273 if (call_depth > 1) |
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274 error ("dassl: invalid recursive call"); |
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276 std::string fcn_name, fname, jac_name, jname; |
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277 dassl_fcn = 0; |
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278 dassl_jac = 0; |
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279 |
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280 octave_value f_arg = args(0); |
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281 |
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282 if (f_arg.is_cell ()) |
2928 | 283 { |
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284 Cell c = f_arg.cell_value (); |
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285 if (c.numel () == 1) |
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286 f_arg = c(0); |
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287 else if (c.numel () == 2) |
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288 { |
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289 if (c(0).is_function_handle () || c(0).is_inline_function ()) |
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290 dassl_fcn = c(0).function_value (); |
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291 else |
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292 { |
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293 fcn_name = unique_symbol_name ("__dassl_fcn__"); |
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294 fname = "function y = "; |
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295 fname.append (fcn_name); |
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296 fname.append (" (x, xdot, t) y = "); |
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297 dassl_fcn = extract_function (c(0), "dassl", fcn_name, fname, |
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298 "; endfunction"); |
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299 } |
3991 | 300 |
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301 if (dassl_fcn) |
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302 { |
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303 if (c(1).is_function_handle () || c(1).is_inline_function ()) |
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304 dassl_jac = c(1).function_value (); |
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305 else |
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306 { |
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307 jac_name = unique_symbol_name ("__dassl_jac__"); |
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308 jname = "function jac = "; |
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309 jname.append (jac_name); |
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310 jname.append (" (x, xdot, t, cj) jac = "); |
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311 dassl_jac = extract_function (c(1), "dassl", jac_name, |
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312 jname, "; endfunction"); |
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313 |
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314 if (! dassl_jac) |
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315 { |
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316 if (fcn_name.length ()) |
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317 clear_function (fcn_name); |
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318 dassl_fcn = 0; |
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319 } |
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320 } |
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321 } |
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322 } |
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323 else |
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324 error ("dassl: incorrect number of elements in cell array"); |
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325 } |
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326 |
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327 if (! dassl_fcn && ! f_arg.is_cell ()) |
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328 { |
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329 if (f_arg.is_function_handle () || f_arg.is_inline_function ()) |
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330 dassl_fcn = f_arg.function_value (); |
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331 else |
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332 { |
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333 switch (f_arg.rows ()) |
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334 { |
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335 case 1: |
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336 do |
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337 { |
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338 fcn_name = unique_symbol_name ("__dassl_fcn__"); |
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339 fname = "function y = "; |
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340 fname.append (fcn_name); |
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341 fname.append (" (x, xdot, t) y = "); |
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342 dassl_fcn = extract_function (f_arg, "dassl", fcn_name, |
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343 fname, "; endfunction"); |
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344 } |
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345 while (0); |
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346 break; |
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347 |
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348 case 2: |
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349 { |
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350 string_vector tmp = f_arg.string_vector_value (); |
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352 fcn_name = unique_symbol_name ("__dassl_fcn__"); |
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353 fname = "function y = "; |
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354 fname.append (fcn_name); |
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355 fname.append (" (x, xdot, t) y = "); |
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356 dassl_fcn = extract_function (tmp(0), "dassl", fcn_name, |
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357 fname, "; endfunction"); |
3991 | 358 |
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359 if (dassl_fcn) |
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360 { |
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361 jac_name = unique_symbol_name ("__dassl_jac__"); |
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362 jname = "function jac = "; |
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363 jname.append (jac_name); |
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364 jname.append (" (x, xdot, t, cj) jac = "); |
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365 dassl_jac = extract_function (tmp(1), "dassl", |
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366 jac_name, jname, |
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367 "; endfunction"); |
5729 | 368 |
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369 if (! dassl_jac) |
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370 { |
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371 if (fcn_name.length ()) |
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372 clear_function (fcn_name); |
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373 dassl_fcn = 0; |
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374 } |
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375 } |
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376 } |
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377 } |
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378 } |
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379 } |
3243 | 380 |
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381 if (! dassl_fcn) |
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382 return retval; |
3243 | 383 |
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384 ColumnVector state = args(1).xvector_value ("dassl: initial state X_0 must be a vector"); |
2928 | 385 |
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386 ColumnVector deriv = args(2).xvector_value ("dassl: initial derivatives XDOT_0 must be a vector"); |
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387 |
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388 ColumnVector out_times = args(3).xvector_value ("dassl: output time variable T must be a vector"); |
2928 | 389 |
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390 ColumnVector crit_times; |
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391 int crit_times_set = 0; |
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392 if (nargin > 4) |
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393 { |
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394 crit_times = args(4).xvector_value ("dassl: list of critical times T_CRIT must be a vector"); |
2928 | 395 |
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396 crit_times_set = 1; |
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397 } |
3991 | 398 |
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399 if (state.numel () != deriv.numel ()) |
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400 error ("dassl: X and XDOT_0 must have the same size"); |
3991 | 401 |
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402 double tzero = out_times (0); |
2928 | 403 |
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404 DAEFunc func (dassl_user_function); |
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405 if (dassl_jac) |
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406 func.set_jacobian_function (dassl_user_jacobian); |
3243 | 407 |
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408 DASSL dae (state, deriv, tzero, func); |
2928 | 409 |
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410 dae.set_options (dassl_opts); |
5729 | 411 |
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412 Matrix output; |
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413 Matrix deriv_output; |
3997 | 414 |
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415 if (crit_times_set) |
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416 output = dae.integrate (out_times, deriv_output, crit_times); |
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417 else |
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418 output = dae.integrate (out_times, deriv_output); |
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419 |
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420 if (fcn_name.length ()) |
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421 clear_function (fcn_name); |
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422 if (jac_name.length ()) |
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423 clear_function (jac_name); |
3997 | 424 |
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425 std::string msg = dae.error_message (); |
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426 |
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427 if (dae.integration_ok ()) |
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428 { |
20892 | 429 retval(0) = output; |
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430 retval(1) = deriv_output; |
2928 | 431 } |
3243 | 432 else |
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433 { |
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434 if (nargout < 3) |
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435 error ("dassl: %s", msg.c_str ()); |
20892 | 436 |
437 retval(0) = Matrix (); | |
438 retval(1) = Matrix (); | |
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439 } |
3243 | 440 |
20892 | 441 retval(2) = static_cast<double> (dae.integration_state ()); |
442 retval(3) = msg; | |
443 | |
2928 | 444 return retval; |
445 } | |
446 | |
447 /* | |
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448 ## dassl-1.m |
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449 ## |
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450 ## Test dassl() function |
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451 ## |
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452 ## Author: David Billinghurst (David.Billinghurst@riotinto.com.au) |
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453 ## Comalco Research and Technology |
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454 ## 20 May 1998 |
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455 ## |
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456 ## Problem |
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457 ## |
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458 ## y1' = -y2, y1(0) = 1 |
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459 ## y2' = y1, y2(0) = 0 |
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460 ## |
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461 ## Solution |
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462 ## |
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463 ## y1(t) = cos(t) |
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464 ## y2(t) = sin(t) |
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465 ## |
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466 %!function res = __f (x, xdot, t) |
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467 %! res = [xdot(1)+x(2); xdot(2)-x(1)]; |
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468 %!endfunction |
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469 |
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470 %!test |
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471 %! |
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472 %! x0 = [1; 0]; |
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473 %! xdot0 = [0; 1]; |
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474 %! t = (0:1:10)'; |
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475 %! |
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476 %! tol = 100 * dassl_options ("relative tolerance"); |
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477 %! |
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478 %! [x, xdot] = dassl ("__f", x0, xdot0, t); |
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479 %! |
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480 %! y = [cos(t), sin(t)]; |
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481 %! |
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482 %! assert (x, y, tol); |
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483 |
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484 ## dassl-2.m |
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485 ## |
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486 ## Test dassl() function |
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487 ## |
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488 ## Author: David Billinghurst (David.Billinghurst@riotinto.com.au) |
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489 ## Comalco Research and Technology |
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490 ## 20 May 1998 |
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491 ## |
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492 ## Based on SLATEC quick check for DASSL by Linda Petzold |
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493 ## |
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494 ## Problem |
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495 ## |
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496 ## x1' + 10*x1 = 0, x1(0) = 1 |
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497 ## x1 + x2 = 1, x2(0) = 0 |
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498 ## |
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499 ## |
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500 ## Solution |
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501 ## |
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502 ## x1(t) = exp(-10*t) |
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503 ## x2(t) = 1 - x(1) |
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504 ## |
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505 %!function res = __f (x, xdot, t) |
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506 %! res = [xdot(1)+10*x(1); x(1)+x(2)-1]; |
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507 %!endfunction |
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508 |
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509 %!test |
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510 %! |
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511 %! x0 = [1; 0]; |
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512 %! xdot0 = [-10; 10]; |
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513 %! t = (0:0.2:1)'; |
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514 %! |
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515 %! tol = 500 * dassl_options ("relative tolerance"); |
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516 %! |
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517 %! [x, xdot] = dassl ("__f", x0, xdot0, t); |
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518 %! |
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519 %! y = [exp(-10*t), 1-exp(-10*t)]; |
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520 %! |
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521 %! assert (x, y, tol); |
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522 |
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523 %!test |
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524 %! old_tol = dassl_options ("absolute tolerance"); |
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525 %! dassl_options ("absolute tolerance", eps); |
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526 %! assert (dassl_options ("absolute tolerance") == eps); |
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527 %! ## Restore old value of tolerance |
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528 %! dassl_options ("absolute tolerance", old_tol); |
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529 |
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530 %!error dassl_options ("foo", 1, 2) |
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531 */ |