Mercurial > octave
annotate libinterp/corefcn/lsode.cc @ 24412:6e1d3ad32ed1 stable
doc: Fix documentation of third input to lsode() (bug #52664).
* lsode.cc (Flsode): Rewrite documentation for third input t.
author | Rik <rik@octave.org> |
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date | Thu, 14 Dec 2017 14:38:33 -0800 |
parents | 3ac9f9ecfae5 |
children | 2adff1743db7 |
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 | |
8 under the terms of the GNU General Public License as published by the | |
7016 | 9 Free Software Foundation; either version 3 of the License, or (at your |
10 option) any later version. | |
2928 | 11 |
12 Octave is distributed in the hope that it will be useful, but WITHOUT | |
13 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or | |
14 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License | |
15 for more details. | |
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 "LSODE.h" | |
33 #include "lo-mappers.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 "ovl.h" |
2968 | 39 #include "ov-fcn.h" |
5729 | 40 #include "ov-cell.h" |
2928 | 41 #include "pager.h" |
3952 | 42 #include "pr-output.h" |
3243 | 43 #include "unwind-prot.h" |
2928 | 44 #include "utils.h" |
45 #include "variables.h" | |
46 | |
3998 | 47 #include "LSODE-opts.cc" |
48 | |
2928 | 49 // Global pointer for user defined function required by lsode. |
2968 | 50 static octave_function *lsode_fcn; |
2928 | 51 |
52 // Global pointer for optional user defined jacobian function used by lsode. | |
2968 | 53 static octave_function *lsode_jac; |
2928 | 54 |
4140 | 55 // Have we warned about imaginary values returned from user function? |
56 static bool warned_fcn_imaginary = false; | |
57 static bool warned_jac_imaginary = false; | |
58 | |
3243 | 59 // Is this a recursive call? |
60 static int call_depth = 0; | |
61 | |
2928 | 62 ColumnVector |
63 lsode_user_function (const ColumnVector& x, double t) | |
64 { | |
65 ColumnVector retval; | |
66 | |
67 octave_value_list args; | |
68 args(1) = t; | |
4628 | 69 args(0) = x; |
2928 | 70 |
71 if (lsode_fcn) | |
72 { | |
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73 octave_value_list tmp; |
2928 | 74 |
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75 try |
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76 { |
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77 tmp = lsode_fcn->do_multi_index_op (1, args); |
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78 } |
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79 catch (octave::execution_exception& e) |
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80 { |
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81 err_user_supplied_eval (e, "lsode"); |
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82 } |
2928 | 83 |
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84 if (tmp.empty () || ! tmp(0).is_defined ()) |
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85 err_user_supplied_eval ("lsode"); |
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86 |
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87 if (! warned_fcn_imaginary && tmp(0).is_complex_type ()) |
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88 { |
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89 warning ("lsode: ignoring imaginary part returned from user-supplied function"); |
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90 warned_fcn_imaginary = true; |
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91 } |
4140 | 92 |
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93 retval = tmp(0).xvector_value ("lsode: expecting user supplied function to return numeric vector"); |
2928 | 94 |
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95 if (retval.is_empty ()) |
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96 err_user_supplied_eval ("lsode"); |
2928 | 97 } |
98 | |
99 return retval; | |
100 } | |
101 | |
102 Matrix | |
103 lsode_user_jacobian (const ColumnVector& x, double t) | |
104 { | |
105 Matrix retval; | |
106 | |
107 octave_value_list args; | |
108 args(1) = t; | |
4628 | 109 args(0) = x; |
2928 | 110 |
111 if (lsode_jac) | |
112 { | |
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113 octave_value_list tmp; |
2928 | 114 |
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115 try |
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116 { |
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117 tmp = lsode_jac->do_multi_index_op (1, args); |
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118 } |
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119 catch (octave::execution_exception& e) |
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120 { |
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121 err_user_supplied_eval (e, "lsode"); |
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122 } |
2928 | 123 |
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124 if (tmp.empty () || ! tmp(0).is_defined ()) |
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125 err_user_supplied_eval ("lsode"); |
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126 |
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127 if (! warned_jac_imaginary && tmp(0).is_complex_type ()) |
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128 { |
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129 warning ("lsode: ignoring imaginary part returned from user-supplied jacobian function"); |
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130 warned_jac_imaginary = true; |
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131 } |
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133 retval = tmp(0).xmatrix_value ("lsode: expecting user supplied jacobian function to return numeric array"); |
2928 | 134 |
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135 if (retval.is_empty ()) |
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136 err_user_supplied_eval ("lsode"); |
2928 | 137 } |
138 | |
139 return retval; | |
140 } | |
141 | |
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142 DEFUN (lsode, args, nargout, |
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143 doc: /* -*- texinfo -*- |
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144 @deftypefn {} {[@var{x}, @var{istate}, @var{msg}] =} lsode (@var{fcn}, @var{x_0}, @var{t}) |
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145 @deftypefnx {} {[@var{x}, @var{istate}, @var{msg}] =} lsode (@var{fcn}, @var{x_0}, @var{t}, @var{t_crit}) |
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146 Ordinary Differential Equation (ODE) solver. |
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147 |
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148 The set of differential equations to solve is |
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149 @tex |
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150 $$ {dx \over dt} = f (x, t) $$ |
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151 with |
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152 $$ x(t_0) = x_0 $$ |
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153 @end tex |
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154 @ifnottex |
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155 |
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156 @example |
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157 @group |
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158 dx |
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159 -- = f (x, t) |
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160 dt |
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161 @end group |
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162 @end example |
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163 |
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164 @noindent |
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165 with |
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166 |
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167 @example |
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168 x(t_0) = x_0 |
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169 @end example |
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170 |
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171 @end ifnottex |
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172 The solution is returned in the matrix @var{x}, with each row |
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173 corresponding to an element of the vector @var{t}. The first element |
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174 of @var{t} should be @math{t_0} and should correspond to the initial |
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175 state of the system @var{x_0}, so that the first row of the output |
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176 is @var{x_0}. |
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177 |
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178 The first argument, @var{fcn}, is a string, inline, or function handle |
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179 that names the function @math{f} to call to compute the vector of right |
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180 hand sides for the set of equations. The function must have the form |
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181 |
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182 @example |
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183 @var{xdot} = f (@var{x}, @var{t}) |
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184 @end example |
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185 |
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186 @noindent |
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187 in which @var{xdot} and @var{x} are vectors and @var{t} is a scalar. |
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188 |
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189 If @var{fcn} is a two-element string array or a two-element cell array |
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190 of strings, inline functions, or function handles, the first element names |
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191 the function @math{f} described above, and the second element names a |
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192 function to compute the Jacobian of @math{f}. The Jacobian function |
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193 must have the form |
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194 |
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195 @example |
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196 @var{jac} = j (@var{x}, @var{t}) |
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197 @end example |
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198 |
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199 @noindent |
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200 in which @var{jac} is the matrix of partial derivatives |
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201 @tex |
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202 $$ J = {\partial f_i \over \partial x_j} = \left[\matrix{ |
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203 {\partial f_1 \over \partial x_1} |
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204 & {\partial f_1 \over \partial x_2} |
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205 & \cdots |
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206 & {\partial f_1 \over \partial x_N} \cr |
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207 {\partial f_2 \over \partial x_1} |
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208 & {\partial f_2 \over \partial x_2} |
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209 & \cdots |
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210 & {\partial f_2 \over \partial x_N} \cr |
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211 \vdots & \vdots & \ddots & \vdots \cr |
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212 {\partial f_3 \over \partial x_1} |
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213 & {\partial f_3 \over \partial x_2} |
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214 & \cdots |
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215 & {\partial f_3 \over \partial x_N} \cr}\right]$$ |
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216 @end tex |
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217 @ifnottex |
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218 |
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219 @example |
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220 @group |
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221 | df_1 df_1 df_1 | |
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222 | ---- ---- ... ---- | |
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223 | dx_1 dx_2 dx_N | |
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224 | | |
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225 | df_2 df_2 df_2 | |
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226 | ---- ---- ... ---- | |
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227 df_i | dx_1 dx_2 dx_N | |
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228 jac = ---- = | | |
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229 dx_j | . . . . | |
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230 | . . . . | |
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231 | . . . . | |
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232 | | |
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233 | df_N df_N df_N | |
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234 | ---- ---- ... ---- | |
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235 | dx_1 dx_2 dx_N | |
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236 @end group |
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237 @end example |
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238 |
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239 @end ifnottex |
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240 |
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241 The second argument specifies the initial state of the system @math{x_0}. The |
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242 third argument is a vector, @var{t}, specifying the time values for which a |
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243 solution is sought. |
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244 |
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245 The fourth argument is optional, and may be used to specify a set of |
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246 times that the ODE solver should not integrate past. It is useful for |
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247 avoiding difficulties with singularities and points where there is a |
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248 discontinuity in the derivative. |
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249 |
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250 After a successful computation, the value of @var{istate} will be 2 |
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251 (consistent with the Fortran version of @sc{lsode}). |
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252 |
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253 If the computation is not successful, @var{istate} will be something |
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254 other than 2 and @var{msg} will contain additional information. |
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255 |
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256 You can use the function @code{lsode_options} to set optional |
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257 parameters for @code{lsode}. |
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258 @seealso{daspk, dassl, dasrt} |
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259 @end deftypefn */) |
2928 | 260 { |
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261 int nargin = args.length (); |
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262 |
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263 if (nargin < 3 || nargin > 4) |
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264 print_usage (); |
2928 | 265 |
4140 | 266 warned_fcn_imaginary = false; |
267 warned_jac_imaginary = false; | |
268 | |
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269 octave::unwind_protect frame; |
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271 frame.protect_var (call_depth); |
3243 | 272 call_depth++; |
273 | |
274 if (call_depth > 1) | |
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275 error ("lsode: invalid recursive call"); |
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277 std::string fcn_name, fname, jac_name, jname; |
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278 lsode_fcn = 0; |
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279 lsode_jac = 0; |
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280 |
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281 octave_value f_arg = args(0); |
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282 |
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283 if (f_arg.is_cell ()) |
2928 | 284 { |
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285 Cell c = f_arg.cell_value (); |
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286 if (c.numel () == 1) |
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287 f_arg = c(0); |
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288 else if (c.numel () == 2) |
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289 { |
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290 if (c(0).is_function_handle () || c(0).is_inline_function ()) |
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291 lsode_fcn = c(0).function_value (); |
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292 else |
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293 { |
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294 fcn_name = unique_symbol_name ("__lsode_fcn__"); |
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295 fname = "function y = "; |
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296 fname.append (fcn_name); |
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297 fname.append (" (x, t) y = "); |
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298 lsode_fcn = extract_function (c(0), "lsode", fcn_name, fname, |
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299 "; endfunction"); |
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300 } |
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302 if (lsode_fcn) |
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303 { |
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304 if (c(1).is_function_handle () || c(1).is_inline_function ()) |
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305 lsode_jac = c(1).function_value (); |
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306 else |
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307 { |
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308 jac_name = unique_symbol_name ("__lsode_jac__"); |
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309 jname = "function jac = "; |
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310 jname.append (jac_name); |
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311 jname.append (" (x, t) jac = "); |
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312 lsode_jac = extract_function (c(1), "lsode", jac_name, |
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313 jname, "; endfunction"); |
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314 |
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315 if (! lsode_jac) |
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316 { |
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317 if (fcn_name.length ()) |
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318 clear_function (fcn_name); |
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319 lsode_fcn = 0; |
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320 } |
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321 } |
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322 } |
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323 } |
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324 else |
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325 error ("lsode: incorrect number of elements in cell array"); |
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326 } |
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327 |
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328 if (! lsode_fcn && ! f_arg.is_cell ()) |
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329 { |
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330 if (f_arg.is_function_handle () || f_arg.is_inline_function ()) |
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331 lsode_fcn = f_arg.function_value (); |
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332 else |
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333 { |
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334 switch (f_arg.rows ()) |
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335 { |
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336 case 1: |
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337 do |
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338 { |
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339 fcn_name = unique_symbol_name ("__lsode_fcn__"); |
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340 fname = "function y = "; |
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341 fname.append (fcn_name); |
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342 fname.append (" (x, t) y = "); |
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343 lsode_fcn = extract_function (f_arg, "lsode", fcn_name, |
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344 fname, "; endfunction"); |
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345 } |
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346 while (0); |
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347 break; |
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348 |
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349 case 2: |
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350 { |
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351 string_vector tmp = f_arg.string_vector_value (); |
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353 fcn_name = unique_symbol_name ("__lsode_fcn__"); |
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354 fname = "function y = "; |
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355 fname.append (fcn_name); |
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356 fname.append (" (x, t) y = "); |
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357 lsode_fcn = extract_function (tmp(0), "lsode", fcn_name, |
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358 fname, "; endfunction"); |
2928 | 359 |
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360 if (lsode_fcn) |
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361 { |
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362 jac_name = unique_symbol_name ("__lsode_jac__"); |
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363 jname = "function jac = "; |
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364 jname.append (jac_name); |
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365 jname.append (" (x, t) jac = "); |
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366 lsode_jac = extract_function (tmp(1), "lsode", |
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367 jac_name, jname, |
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368 "; endfunction"); |
5729 | 369 |
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370 if (! lsode_jac) |
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371 { |
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372 if (fcn_name.length ()) |
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373 clear_function (fcn_name); |
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374 lsode_fcn = 0; |
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375 } |
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376 } |
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377 } |
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378 break; |
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380 default: |
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381 error ("lsode: first arg should be a string or 2-element string array"); |
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382 } |
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383 } |
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384 } |
2928 | 385 |
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386 if (! lsode_fcn) |
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387 error ("lsode: FCN argument is not a valid function name or handle"); |
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388 |
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389 ColumnVector state = args(1).xvector_value ("lsode: initial state X_0 must be a vector"); |
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390 ColumnVector out_times = args(2).xvector_value ("lsode: output time variable T must be a vector"); |
2928 | 391 |
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392 ColumnVector crit_times; |
2928 | 393 |
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394 int crit_times_set = 0; |
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395 if (nargin > 3) |
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396 { |
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397 crit_times = args(3).xvector_value ("lsode: list of critical times T_CRIT must be a vector"); |
2928 | 398 |
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399 crit_times_set = 1; |
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400 } |
2928 | 401 |
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402 double tzero = out_times (0); |
3243 | 403 |
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404 ODEFunc func (lsode_user_function); |
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405 if (lsode_jac) |
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406 func.set_jacobian_function (lsode_user_jacobian); |
2928 | 407 |
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408 LSODE ode (state, tzero, func); |
3243 | 409 |
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410 ode.set_options (lsode_opts); |
3243 | 411 |
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412 Matrix output; |
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413 if (crit_times_set) |
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414 output = ode.integrate (out_times, crit_times); |
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415 else |
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416 output = ode.integrate (out_times); |
5729 | 417 |
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418 if (fcn_name.length ()) |
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419 clear_function (fcn_name); |
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420 if (jac_name.length ()) |
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421 clear_function (jac_name); |
3997 | 422 |
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423 std::string msg = ode.error_message (); |
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424 |
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425 octave_value_list retval (3); |
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426 |
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427 if (ode.integration_ok ()) |
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428 retval(0) = output; |
20892 | 429 else if (nargout < 2) |
430 error ("lsode: %s", msg.c_str ()); | |
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431 else |
20892 | 432 retval(0) = Matrix (); |
3959 | 433 |
20892 | 434 retval(1) = static_cast<double> (ode.integration_state ()); |
435 retval(2) = msg; | |
2928 | 436 |
437 return retval; | |
438 } | |
439 | |
440 /* | |
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441 |
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442 ## dassl-1.m |
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443 ## |
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444 ## Test lsode() function |
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445 ## |
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446 ## Author: David Billinghurst (David.Billinghurst@riotinto.com.au) |
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447 ## Comalco Research and Technology |
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448 ## 20 May 1998 |
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449 ## |
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450 ## Problem |
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451 ## |
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452 ## y1' = -y2, y1(0) = 1 |
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453 ## y2' = y1, y2(0) = 0 |
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454 ## |
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455 ## Solution |
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456 ## |
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457 ## y1(t) = cos(t) |
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458 ## y2(t) = sin(t) |
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459 ## |
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460 %!function xdot = __f (x, t) |
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461 %! xdot = [-x(2); x(1)]; |
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462 %!endfunction |
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463 %!test |
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464 %! |
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465 %! x0 = [1; 0]; |
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466 %! xdot0 = [0; 1]; |
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467 %! t = (0:1:10)'; |
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468 %! |
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469 %! tol = 500 * lsode_options ("relative tolerance"); |
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470 %! |
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471 %! x = lsode ("__f", x0, t); |
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472 %! |
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473 %! y = [cos(t), sin(t)]; |
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474 %! |
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475 %! assert (x, y, tol); |
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476 |
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477 %!function xdotdot = __f (x, t) |
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478 %! xdotdot = [x(2); -x(1)]; |
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479 %!endfunction |
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480 %!test |
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481 %! |
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482 %! x0 = [1; 0]; |
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483 %! t = [0; 2*pi]; |
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484 %! tol = 100 * dassl_options ("relative tolerance"); |
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485 %! |
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486 %! x = lsode ("__f", x0, t); |
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487 %! |
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488 %! y = [1, 0; 1, 0]; |
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489 %! |
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490 %! assert (x, y, tol); |
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491 |
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492 %!function xdot = __f (x, t) |
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493 %! xdot = x; |
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494 %!endfunction |
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495 %!test |
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496 %! |
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497 %! x0 = 1; |
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498 %! t = [0; 1]; |
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499 %! tol = 100 * dassl_options ("relative tolerance"); |
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500 %! |
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501 %! x = lsode ("__f", x0, t); |
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502 %! |
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503 %! y = [1; e]; |
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504 %! |
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505 %! assert (x, y, tol); |
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506 |
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507 %!test |
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508 %! lsode_options ("absolute tolerance", eps); |
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509 %! assert (lsode_options ("absolute tolerance") == eps); |
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510 |
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511 %!error lsode_options ("foo", 1, 2) |
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512 */ |