Mercurial > octave
annotate libinterp/corefcn/lsode.cc @ 29961:7d6709900da7
eliminate octave:: namespace tags in DEFUN and DEFMETHOD and more
Files affected: __betainc__.cc, __contourc__.cc, __eigs__.cc,
__expint__.cc, __ftp__.cc, __gammainc__.cc, __ichol__.cc, __ilu__.cc,
__magick_read__.cc, __pchip_deriv__.cc, __qp__.cc, amd.cc, balance.cc,
besselj.cc, bsxfun.cc, call-stack.cc, ccolamd.cc, cellfun.cc, chol.cc,
colamd.cc, colloc.cc, conv2.cc, daspk.cc, dasrt.cc, dassl.cc, data.cc,
defaults.cc, dirfns.cc, display.cc, dlmread.cc, dmperm.cc, dot.cc,
eig.cc, ellipj.cc, environment.cc, error.cc, event-manager.cc, fft.cc,
fft2.cc, fftn.cc, file-io.cc, find.cc, gcd.cc, getgrent.cc,
getpwent.cc, getrusage.cc, gsvd.cc, hash.cc, help.cc, hess.cc,
hex2num.cc, input.cc, inv.cc, jsondecode.cc, jsonencode.cc,
load-path.cc, load-save.cc, lookup.cc, lsode.cc, lu.cc, max.cc,
mgorth.cc, oct-hist.cc, ordqz.cc, ordschur.cc, pager.cc, pr-output.cc,
psi.cc, qr.cc, quad.cc, quadcc.cc, qz.cc, rand.cc, regexp.cc,
schur.cc, settings.cc, sighandlers.cc, sparse.cc, spparms.cc,
sqrtm.cc, stream-euler.cc, strfind.cc, strfns.cc, sub2ind.cc, svd.cc,
symbfact.cc, symtab.cc, syscalls.cc, sysdep.cc, time.cc, toplev.cc,
tril.cc, typecast.cc, urlwrite.cc, utils.cc, variables.cc,
__delaunayn__.cc, __fltk_uigetfile__.cc, __glpk__.cc,
__init_gnuplot__.cc, __ode15__.cc, __voronoi__.cc, audiodevinfo.cc,
audioread.cc, convhulln.cc, fftw.cc, gzip.cc, ov-cell.cc, ov-class.cc,
ov-classdef.cc, ov-fcn-handle.cc, ov-struct.cc, ov-typeinfo.cc,
ov-usr-fcn.cc, octave.cc, lex.ll, oct-parse.yy, profiler.cc,
andpt-eval.cc.
author | John W. Eaton <jwe@octave.org> |
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date | Sat, 14 Aug 2021 22:48:52 -0400 |
parents | 32c3a5805893 |
children | c4bc77a90fb5 |
rev | line source |
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1 //////////////////////////////////////////////////////////////////////// |
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2 // |
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3 // Copyright (C) 1996-2021 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 |
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6 // distribution or <https://octave.org/copyright/>. |
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7 // |
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8 // This file is part of Octave. |
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9 // |
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10 // Octave is free software: you can redistribute it and/or modify it |
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11 // under the terms of the GNU General Public License as published by |
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12 // the Free Software Foundation, either version 3 of the License, or |
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13 // (at your option) any later version. |
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14 // |
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15 // Octave is distributed in the hope that it will be useful, but |
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16 // WITHOUT ANY WARRANTY; without even the implied warranty of |
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17 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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18 // GNU General Public License for more details. |
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19 // |
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20 // You should have received a copy of the GNU General Public License |
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21 // along with Octave; see the file COPYING. If not, see |
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22 // <https://www.gnu.org/licenses/>. |
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23 // |
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24 //////////////////////////////////////////////////////////////////////// |
2928 | 25 |
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26 #if defined (HAVE_CONFIG_H) |
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27 # include "config.h" |
2928 | 28 #endif |
29 | |
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30 #include <list> |
2928 | 31 #include <string> |
32 | |
33 #include "LSODE.h" | |
34 #include "lo-mappers.h" | |
35 | |
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36 #include "defun.h" |
2928 | 37 #include "error.h" |
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38 #include "errwarn.h" |
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39 #include "interpreter-private.h" |
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40 #include "ovl.h" |
2968 | 41 #include "ov-fcn.h" |
5729 | 42 #include "ov-cell.h" |
2928 | 43 #include "pager.h" |
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44 #include "parse.h" |
3952 | 45 #include "pr-output.h" |
3243 | 46 #include "unwind-prot.h" |
2928 | 47 #include "utils.h" |
48 #include "variables.h" | |
49 | |
3998 | 50 #include "LSODE-opts.cc" |
51 | |
2928 | 52 // Global pointer for user defined function required by lsode. |
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53 static octave_value lsode_fcn; |
2928 | 54 |
55 // Global pointer for optional user defined jacobian function used by lsode. | |
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56 static octave_value lsode_jac; |
2928 | 57 |
4140 | 58 // Have we warned about imaginary values returned from user function? |
59 static bool warned_fcn_imaginary = false; | |
60 static bool warned_jac_imaginary = false; | |
61 | |
3243 | 62 // Is this a recursive call? |
63 static int call_depth = 0; | |
64 | |
2928 | 65 ColumnVector |
66 lsode_user_function (const ColumnVector& x, double t) | |
67 { | |
68 ColumnVector retval; | |
69 | |
70 octave_value_list args; | |
71 args(1) = t; | |
4628 | 72 args(0) = x; |
2928 | 73 |
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74 if (lsode_fcn.is_defined ()) |
2928 | 75 { |
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76 octave_value_list tmp; |
2928 | 77 |
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78 try |
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79 { |
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80 tmp = octave::feval (lsode_fcn, args, 1); |
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81 } |
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82 catch (octave::execution_exception& ee) |
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83 { |
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84 err_user_supplied_eval (ee, "lsode"); |
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85 } |
2928 | 86 |
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87 if (tmp.empty () || ! tmp(0).is_defined ()) |
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88 err_user_supplied_eval ("lsode"); |
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89 |
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90 if (! warned_fcn_imaginary && tmp(0).iscomplex ()) |
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91 { |
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92 warning ("lsode: ignoring imaginary part returned from user-supplied function"); |
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93 warned_fcn_imaginary = true; |
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94 } |
4140 | 95 |
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96 retval = tmp(0).xvector_value ("lsode: expecting user supplied function to return numeric vector"); |
2928 | 97 |
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98 if (retval.isempty ()) |
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99 err_user_supplied_eval ("lsode"); |
2928 | 100 } |
101 | |
102 return retval; | |
103 } | |
104 | |
105 Matrix | |
106 lsode_user_jacobian (const ColumnVector& x, double t) | |
107 { | |
108 Matrix retval; | |
109 | |
110 octave_value_list args; | |
111 args(1) = t; | |
4628 | 112 args(0) = x; |
2928 | 113 |
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114 if (lsode_jac.is_defined ()) |
2928 | 115 { |
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116 octave_value_list tmp; |
2928 | 117 |
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118 try |
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119 { |
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120 tmp = octave::feval (lsode_jac, args, 1); |
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121 } |
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122 catch (octave::execution_exception& ee) |
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123 { |
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124 err_user_supplied_eval (ee, "lsode"); |
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125 } |
2928 | 126 |
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127 if (tmp.empty () || ! tmp(0).is_defined ()) |
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128 err_user_supplied_eval ("lsode"); |
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129 |
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130 if (! warned_jac_imaginary && tmp(0).iscomplex ()) |
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131 { |
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132 warning ("lsode: ignoring imaginary part returned from user-supplied jacobian function"); |
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133 warned_jac_imaginary = true; |
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134 } |
4140 | 135 |
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136 retval = tmp(0).xmatrix_value ("lsode: expecting user supplied jacobian function to return numeric array"); |
2928 | 137 |
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138 if (retval.isempty ()) |
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139 err_user_supplied_eval ("lsode"); |
2928 | 140 } |
141 | |
142 return retval; | |
143 } | |
144 | |
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145 OCTAVE_NAMESPACE_BEGIN |
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146 |
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147 DEFMETHOD (lsode, interp, args, nargout, |
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148 doc: /* -*- texinfo -*- |
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149 @deftypefn {} {[@var{x}, @var{istate}, @var{msg}] =} lsode (@var{fcn}, @var{x_0}, @var{t}) |
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150 @deftypefnx {} {[@var{x}, @var{istate}, @var{msg}] =} lsode (@var{fcn}, @var{x_0}, @var{t}, @var{t_crit}) |
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151 Ordinary Differential Equation (ODE) solver. |
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152 |
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153 The set of differential equations to solve is |
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154 @tex |
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155 $$ {dx \over dt} = f (x, t) $$ |
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156 with |
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157 $$ x(t_0) = x_0 $$ |
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158 @end tex |
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159 @ifnottex |
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160 |
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161 @example |
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162 @group |
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163 dx |
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164 -- = f (x, t) |
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165 dt |
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166 @end group |
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167 @end example |
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168 |
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169 @noindent |
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170 with |
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171 |
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172 @example |
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173 x(t_0) = x_0 |
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174 @end example |
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175 |
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176 @end ifnottex |
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177 The solution is returned in the matrix @var{x}, with each row |
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178 corresponding to an element of the vector @var{t}. The first element |
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179 of @var{t} should be @math{t_0} and should correspond to the initial |
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180 state of the system @var{x_0}, so that the first row of the output |
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181 is @var{x_0}. |
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182 |
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183 The first argument, @var{fcn}, is a string, inline, or function handle |
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184 that names the function @math{f} to call to compute the vector of right |
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185 hand sides for the set of equations. The function must have the form |
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186 |
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187 @example |
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188 @var{xdot} = f (@var{x}, @var{t}) |
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189 @end example |
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190 |
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191 @noindent |
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192 in which @var{xdot} and @var{x} are vectors and @var{t} is a scalar. |
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193 |
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194 If @var{fcn} is a two-element string array or a two-element cell array |
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195 of strings, inline functions, or function handles, the first element names |
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196 the function @math{f} described above, and the second element names a |
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197 function to compute the Jacobian of @math{f}. The Jacobian function |
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198 must have the form |
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199 |
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200 @example |
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201 @var{jac} = j (@var{x}, @var{t}) |
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202 @end example |
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203 |
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204 @noindent |
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205 in which @var{jac} is the matrix of partial derivatives |
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206 @tex |
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207 $$ J = {\partial f_i \over \partial x_j} = \left[\matrix{ |
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208 {\partial f_1 \over \partial x_1} |
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209 & {\partial f_1 \over \partial x_2} |
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210 & \cdots |
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211 & {\partial f_1 \over \partial x_N} \cr |
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212 {\partial f_2 \over \partial x_1} |
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213 & {\partial f_2 \over \partial x_2} |
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214 & \cdots |
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215 & {\partial f_2 \over \partial x_N} \cr |
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216 \vdots & \vdots & \ddots & \vdots \cr |
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217 {\partial f_3 \over \partial x_1} |
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218 & {\partial f_3 \over \partial x_2} |
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219 & \cdots |
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220 & {\partial f_3 \over \partial x_N} \cr}\right]$$ |
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221 @end tex |
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222 @ifnottex |
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223 |
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224 @example |
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225 @group |
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226 | df_1 df_1 df_1 | |
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227 | ---- ---- ... ---- | |
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228 | dx_1 dx_2 dx_N | |
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229 | | |
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230 | df_2 df_2 df_2 | |
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231 | ---- ---- ... ---- | |
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232 df_i | dx_1 dx_2 dx_N | |
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233 jac = ---- = | | |
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234 dx_j | . . . . | |
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235 | . . . . | |
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236 | . . . . | |
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237 | | |
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238 | df_N df_N df_N | |
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239 | ---- ---- ... ---- | |
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240 | dx_1 dx_2 dx_N | |
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241 @end group |
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242 @end example |
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243 |
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244 @end ifnottex |
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245 |
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246 The second argument specifies the initial state of the system @math{x_0}. The |
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247 third argument is a vector, @var{t}, specifying the time values for which a |
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248 solution is sought. |
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249 |
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250 The fourth argument is optional, and may be used to specify a set of |
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251 times that the ODE solver should not integrate past. It is useful for |
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252 avoiding difficulties with singularities and points where there is a |
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253 discontinuity in the derivative. |
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254 |
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255 After a successful computation, the value of @var{istate} will be 2 |
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256 (consistent with the Fortran version of @sc{lsode}). |
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257 |
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258 If the computation is not successful, @var{istate} will be something |
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259 other than 2 and @var{msg} will contain additional information. |
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260 |
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261 You can use the function @code{lsode_options} to set optional |
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262 parameters for @code{lsode}. |
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263 |
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264 See @nospell{Alan C. Hindmarsh}, |
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265 @cite{ODEPACK, A Systematized Collection of ODE Solvers}, |
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266 in Scientific Computing, @nospell{R. S. Stepleman}, editor, (1983) |
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267 or @url{https://computing.llnl.gov/projects/odepack} |
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268 for more information about the inner workings of @code{lsode}. |
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269 |
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270 Example: Solve the @nospell{Van der Pol} equation |
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271 |
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272 @example |
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273 @group |
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274 fvdp = @@(@var{y},@var{t}) [@var{y}(2); (1 - @var{y}(1)^2) * @var{y}(2) - @var{y}(1)]; |
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275 @var{t} = linspace (0, 20, 100); |
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276 @var{y} = lsode (fvdp, [2; 0], @var{t}); |
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277 @end group |
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278 @end example |
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279 @seealso{daspk, dassl, dasrt} |
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280 @end deftypefn */) |
2928 | 281 { |
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282 int nargin = args.length (); |
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283 |
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284 if (nargin < 3 || nargin > 4) |
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285 print_usage (); |
2928 | 286 |
4140 | 287 warned_fcn_imaginary = false; |
288 warned_jac_imaginary = false; | |
289 | |
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290 unwind_protect_var<int> restore_var (call_depth); |
3243 | 291 call_depth++; |
292 | |
293 if (call_depth > 1) | |
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294 error ("lsode: invalid recursive call"); |
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296 symbol_table& symtab = interp.get_symbol_table (); |
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297 |
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298 std::string fcn_name, fname, jac_name, jname; |
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299 |
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300 lsode_fcn = octave_value (); |
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301 lsode_jac = octave_value (); |
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302 |
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303 octave_value f_arg = args(0); |
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304 |
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305 std::list<std::string> parameter_names ({"x", "t"}); |
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306 |
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307 if (f_arg.iscell ()) |
2928 | 308 { |
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309 Cell c = f_arg.cell_value (); |
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310 if (c.numel () == 1) |
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311 f_arg = c(0); |
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312 else if (c.numel () == 2) |
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313 { |
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314 lsode_fcn = get_function_handle (interp, c(0), parameter_names); |
2928 | 315 |
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316 if (lsode_fcn.is_defined ()) |
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317 { |
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318 lsode_jac = get_function_handle (interp, c(1), parameter_names); |
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319 |
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320 if (lsode_jac.is_undefined ()) |
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321 lsode_fcn = octave_value (); |
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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.is_undefined () && ! f_arg.iscell ()) |
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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; |
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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 lsode_fcn = get_function_handle (interp, f_arg, parameter_names); |
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338 break; |
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339 |
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340 case 2: |
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341 { |
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342 string_vector tmp = f_arg.string_vector_value (); |
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344 lsode_fcn = get_function_handle (interp, tmp(0), |
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345 parameter_names); |
2928 | 346 |
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347 if (lsode_fcn.is_defined ()) |
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348 { |
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349 lsode_jac = get_function_handle (interp, tmp(1), |
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350 parameter_names); |
5729 | 351 |
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352 if (lsode_jac.is_undefined ()) |
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353 lsode_fcn = octave_value (); |
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354 } |
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355 } |
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356 break; |
2928 | 357 |
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358 default: |
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359 error ("lsode: first arg should be a string or 2-element string array"); |
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360 } |
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361 } |
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362 } |
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364 if (lsode_fcn.is_undefined ()) |
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365 error ("lsode: FCN argument is not a valid function name or handle"); |
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366 |
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367 ColumnVector state = args(1).xvector_value ("lsode: initial state X_0 must be a vector"); |
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368 ColumnVector out_times = args(2).xvector_value ("lsode: output time variable T must be a vector"); |
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370 ColumnVector crit_times; |
2928 | 371 |
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372 int crit_times_set = 0; |
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373 if (nargin > 3) |
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374 { |
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375 crit_times = args(3).xvector_value ("lsode: list of critical times T_CRIT must be a vector"); |
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377 crit_times_set = 1; |
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378 } |
2928 | 379 |
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380 double tzero = out_times (0); |
3243 | 381 |
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382 ODEFunc func (lsode_user_function); |
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383 |
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384 if (lsode_jac.is_defined ()) |
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385 func.set_jacobian_function (lsode_user_jacobian); |
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387 LSODE ode (state, tzero, func); |
3243 | 388 |
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389 ode.set_options (lsode_opts); |
3243 | 390 |
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391 Matrix output; |
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392 if (crit_times_set) |
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393 output = ode.integrate (out_times, crit_times); |
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394 else |
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395 output = ode.integrate (out_times); |
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397 if (fcn_name.length ()) |
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398 symtab.clear_function (fcn_name); |
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399 if (jac_name.length ()) |
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400 symtab.clear_function (jac_name); |
3997 | 401 |
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402 std::string msg = ode.error_message (); |
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403 |
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404 octave_value_list retval (3); |
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405 |
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406 if (ode.integration_ok ()) |
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407 retval(0) = output; |
20892 | 408 else if (nargout < 2) |
409 error ("lsode: %s", msg.c_str ()); | |
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410 else |
20892 | 411 retval(0) = Matrix (); |
3959 | 412 |
20892 | 413 retval(1) = static_cast<double> (ode.integration_state ()); |
414 retval(2) = msg; | |
2928 | 415 |
416 return retval; | |
417 } | |
418 | |
419 /* | |
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420 |
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421 ## dassl-1.m |
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422 ## |
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423 ## Test lsode() function |
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424 ## |
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425 ## Author: David Billinghurst (David.Billinghurst@riotinto.com.au) |
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426 ## Comalco Research and Technology |
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427 ## 20 May 1998 |
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428 ## |
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429 ## Problem |
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430 ## |
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431 ## y1' = -y2, y1(0) = 1 |
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432 ## y2' = y1, y2(0) = 0 |
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433 ## |
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434 ## Solution |
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435 ## |
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436 ## y1(t) = cos(t) |
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437 ## y2(t) = sin(t) |
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438 ## |
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439 %!function xdot = __f (x, t) |
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440 %! xdot = [-x(2); x(1)]; |
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441 %!endfunction |
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442 %!test |
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443 %! |
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444 %! x0 = [1; 0]; |
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445 %! xdot0 = [0; 1]; |
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446 %! t = (0:1:10)'; |
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447 %! |
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448 %! tol = 500 * lsode_options ("relative tolerance"); |
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449 %! |
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450 %! x = lsode ("__f", x0, t); |
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451 %! |
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452 %! y = [cos(t), sin(t)]; |
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453 %! |
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454 %! assert (x, y, tol); |
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455 |
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456 %!function xdotdot = __f (x, t) |
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457 %! xdotdot = [x(2); -x(1)]; |
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458 %!endfunction |
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459 %!test |
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460 %! |
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461 %! x0 = [1; 0]; |
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462 %! t = [0; 2*pi]; |
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463 %! tol = 100 * dassl_options ("relative tolerance"); |
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464 %! |
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465 %! x = lsode ("__f", x0, t); |
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466 %! |
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467 %! y = [1, 0; 1, 0]; |
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468 %! |
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469 %! assert (x, y, tol); |
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470 |
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471 %!function xdot = __f (x, t) |
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472 %! xdot = x; |
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473 %!endfunction |
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474 %!test |
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475 %! |
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476 %! x0 = 1; |
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477 %! t = [0; 1]; |
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478 %! tol = 100 * dassl_options ("relative tolerance"); |
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479 %! |
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480 %! x = lsode ("__f", x0, t); |
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481 %! |
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482 %! y = [1; e]; |
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483 %! |
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484 %! assert (x, y, tol); |
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485 |
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486 %!test |
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487 %! lsode_options ("absolute tolerance", eps); |
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488 %! assert (lsode_options ("absolute tolerance") == eps); |
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489 |
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490 %!error lsode_options ("foo", 1, 2) |
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491 */ |
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492 |
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493 OCTAVE_NAMESPACE_END |