annotate libinterp/corefcn/lsode.cc @ 28817:aef839f40da2

Replace unwind_protect with more efficient constructs (bug #59192). * __eigs__.cc, daspk.cc, dasrt.cc, dassl.cc, lsode.cc, quad.cc: Replace unwind_protect frame and protect_var() call for variable "call_depth" with unwind_protect_var().
author Rik <rik@octave.org>
date Tue, 29 Sep 2020 06:59:13 -0700
parents bd51beb6205e
children 8f67ad8b3103
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1 ////////////////////////////////////////////////////////////////////////
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2 //
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3 // Copyright (C) 1996-2020 The Octave Project Developers
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4 //
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5 // See the file COPYRIGHT.md in the top-level directory of this
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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 ////////////////////////////////////////////////////////////////////////
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25
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26 #if defined (HAVE_CONFIG_H)
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27 # include "config.h"
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28 #endif
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29
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30 #include <list>
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31 #include <string>
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32
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33 #include "LSODE.h"
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34 #include "lo-mappers.h"
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35
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36 #include "defun.h"
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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"
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41 #include "ov-fcn.h"
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42 #include "ov-cell.h"
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43 #include "pager.h"
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44 #include "parse.h"
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45 #include "pr-output.h"
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46 #include "unwind-prot.h"
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47 #include "utils.h"
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48 #include "variables.h"
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49
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50 #include "LSODE-opts.cc"
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51
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52 // Global pointer for user defined function required by lsode.
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53 static octave_value lsode_fcn;
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54
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55 // Global pointer for optional user defined jacobian function used by lsode.
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56 static octave_value lsode_jac;
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57
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58 // Have we warned about imaginary values returned from user function?
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59 static bool warned_fcn_imaginary = false;
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60 static bool warned_jac_imaginary = false;
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61
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62 // Is this a recursive call?
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63 static int call_depth = 0;
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64
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65 ColumnVector
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66 lsode_user_function (const ColumnVector& x, double t)
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67 {
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68 ColumnVector retval;
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69
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70 octave_value_list args;
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71 args(1) = t;
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72 args(0) = x;
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73
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74 if (lsode_fcn.is_defined ())
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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 = octave::feval (lsode_fcn, args, 1);
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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, "lsode");
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85 }
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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 }
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95
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96 retval = tmp(0).xvector_value ("lsode: expecting user supplied function to return numeric vector");
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97
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98 if (retval.isempty ())
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99 err_user_supplied_eval ("lsode");
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100 }
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101
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102 return retval;
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103 }
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104
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105 Matrix
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106 lsode_user_jacobian (const ColumnVector& x, double t)
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107 {
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108 Matrix retval;
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109
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110 octave_value_list args;
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111 args(1) = t;
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112 args(0) = x;
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113
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114 if (lsode_jac.is_defined ())
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115 {
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116 octave_value_list tmp;
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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& e)
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123 {
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124 err_user_supplied_eval (e, "lsode");
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125 }
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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 }
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135
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136 retval = tmp(0).xmatrix_value ("lsode: expecting user supplied jacobian function to return numeric array");
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137
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138 if (retval.isempty ())
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139 err_user_supplied_eval ("lsode");
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140 }
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141
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142 return retval;
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143 }
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144
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145 DEFMETHOD (lsode, interp, args, nargout,
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146 doc: /* -*- texinfo -*-
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147 @deftypefn {} {[@var{x}, @var{istate}, @var{msg}] =} lsode (@var{fcn}, @var{x_0}, @var{t})
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148 @deftypefnx {} {[@var{x}, @var{istate}, @var{msg}] =} lsode (@var{fcn}, @var{x_0}, @var{t}, @var{t_crit})
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149 Ordinary Differential Equation (ODE) solver.
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150
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151 The set of differential equations to solve is
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152 @tex
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153 $$ {dx \over dt} = f (x, t) $$
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154 with
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155 $$ x(t_0) = x_0 $$
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156 @end tex
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157 @ifnottex
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158
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159 @example
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160 @group
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161 dx
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162 -- = f (x, t)
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163 dt
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164 @end group
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165 @end example
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166
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167 @noindent
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168 with
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169
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170 @example
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171 x(t_0) = x_0
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172 @end example
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173
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174 @end ifnottex
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175 The solution is returned in the matrix @var{x}, with each row
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176 corresponding to an element of the vector @var{t}. The first element
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177 of @var{t} should be @math{t_0} and should correspond to the initial
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178 state of the system @var{x_0}, so that the first row of the output
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179 is @var{x_0}.
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180
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181 The first argument, @var{fcn}, is a string, inline, or function handle
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182 that names the function @math{f} to call to compute the vector of right
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183 hand sides for the set of equations. The function must have the form
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184
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185 @example
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186 @var{xdot} = f (@var{x}, @var{t})
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187 @end example
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188
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189 @noindent
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190 in which @var{xdot} and @var{x} are vectors and @var{t} is a scalar.
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191
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192 If @var{fcn} is a two-element string array or a two-element cell array
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193 of strings, inline functions, or function handles, the first element names
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194 the function @math{f} described above, and the second element names a
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195 function to compute the Jacobian of @math{f}. The Jacobian function
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196 must have the form
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197
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198 @example
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199 @var{jac} = j (@var{x}, @var{t})
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200 @end example
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201
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202 @noindent
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203 in which @var{jac} is the matrix of partial derivatives
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204 @tex
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205 $$ J = {\partial f_i \over \partial x_j} = \left[\matrix{
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206 {\partial f_1 \over \partial x_1}
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207 & {\partial f_1 \over \partial x_2}
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208 & \cdots
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209 & {\partial f_1 \over \partial x_N} \cr
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210 {\partial f_2 \over \partial x_1}
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211 & {\partial f_2 \over \partial x_2}
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212 & \cdots
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213 & {\partial f_2 \over \partial x_N} \cr
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214 \vdots & \vdots & \ddots & \vdots \cr
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215 {\partial f_3 \over \partial x_1}
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216 & {\partial f_3 \over \partial x_2}
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217 & \cdots
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218 & {\partial f_3 \over \partial x_N} \cr}\right]$$
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219 @end tex
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220 @ifnottex
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221
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222 @example
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223 @group
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224 | df_1 df_1 df_1 |
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225 | ---- ---- ... ---- |
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226 | dx_1 dx_2 dx_N |
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227 | |
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228 | df_2 df_2 df_2 |
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229 | ---- ---- ... ---- |
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230 df_i | dx_1 dx_2 dx_N |
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231 jac = ---- = | |
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232 dx_j | . . . . |
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233 | . . . . |
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234 | . . . . |
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235 | |
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236 | df_N df_N df_N |
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237 | ---- ---- ... ---- |
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238 | dx_1 dx_2 dx_N |
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239 @end group
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240 @end example
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241
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242 @end ifnottex
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243
24412
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244 The second argument specifies the initial state of the system @math{x_0}. The
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245 third argument is a vector, @var{t}, specifying the time values for which a
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246 solution is sought.
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247
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248 The fourth argument is optional, and may be used to specify a set of
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249 times that the ODE solver should not integrate past. It is useful for
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250 avoiding difficulties with singularities and points where there is a
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251 discontinuity in the derivative.
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252
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253 After a successful computation, the value of @var{istate} will be 2
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254 (consistent with the Fortran version of @sc{lsode}).
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255
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256 If the computation is not successful, @var{istate} will be something
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257 other than 2 and @var{msg} will contain additional information.
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258
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259 You can use the function @code{lsode_options} to set optional
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260 parameters for @code{lsode}.
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261 @seealso{daspk, dassl, dasrt}
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262 @end deftypefn */)
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263 {
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264 int nargin = args.length ();
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265
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266 if (nargin < 3 || nargin > 4)
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267 print_usage ();
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268
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269 warned_fcn_imaginary = false;
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270 warned_jac_imaginary = false;
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271
28817
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272 octave::unwind_protect_var<int> restore_var (call_depth);
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273 call_depth++;
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274
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275 if (call_depth > 1)
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276 error ("lsode: invalid recursive call");
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277
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278 octave::symbol_table& symtab = interp.get_symbol_table ();
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279
20801
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280 std::string fcn_name, fname, jac_name, jname;
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diff changeset
281
041caa61ed34 use get_function_handle instead of extract_function
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diff changeset
282 lsode_fcn = octave_value ();
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diff changeset
283 lsode_jac = octave_value ();
20801
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diff changeset
284
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diff changeset
285 octave_value f_arg = args(0);
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diff changeset
286
26864
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diff changeset
287 std::list<std::string> parameter_names ({"x", "t"});
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parents: 26376
diff changeset
288
23576
00e518162fda maint: Deprecate is_cell and replace with iscell.
Rik <rik@octave.org>
parents: 23473
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289 if (f_arg.iscell ())
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diff changeset
290 {
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diff changeset
291 Cell c = f_arg.cell_value ();
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diff changeset
292 if (c.numel () == 1)
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diff changeset
293 f_arg = c(0);
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diff changeset
294 else if (c.numel () == 2)
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parents: 20785
diff changeset
295 {
26864
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diff changeset
296 lsode_fcn = octave::get_function_handle (interp, c(0),
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diff changeset
297 parameter_names);
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diff changeset
298
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diff changeset
299 if (lsode_fcn.is_defined ())
20801
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parents: 20785
diff changeset
300 {
26864
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diff changeset
301 lsode_jac = octave::get_function_handle (interp, c(1),
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parents: 26376
diff changeset
302 parameter_names);
20801
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parents: 20785
diff changeset
303
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diff changeset
304 if (lsode_jac.is_undefined ())
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parents: 26376
diff changeset
305 lsode_fcn = octave_value ();
20801
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parents: 20785
diff changeset
306 }
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parents: 20785
diff changeset
307 }
a542a9bf177e eliminate return statements after calls to print_usage
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parents: 20785
diff changeset
308 else
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John W. Eaton <jwe@octave.org>
parents: 20785
diff changeset
309 error ("lsode: incorrect number of elements in cell array");
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parents: 20785
diff changeset
310 }
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parents: 20785
diff changeset
311
26864
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John W. Eaton <jwe@octave.org>
parents: 26376
diff changeset
312 if (lsode_fcn.is_undefined () && ! f_arg.iscell ())
20801
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diff changeset
313 {
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diff changeset
314 if (f_arg.is_function_handle () || f_arg.is_inline_function ())
26864
041caa61ed34 use get_function_handle instead of extract_function
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parents: 26376
diff changeset
315 lsode_fcn = f_arg;
20801
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parents: 20785
diff changeset
316 else
10154
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 10066
diff changeset
317 {
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John W. Eaton <jwe@octave.org>
parents: 20785
diff changeset
318 switch (f_arg.rows ())
10154
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 10066
diff changeset
319 {
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parents: 20785
diff changeset
320 case 1:
26864
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John W. Eaton <jwe@octave.org>
parents: 26376
diff changeset
321 lsode_fcn = octave::get_function_handle (interp, f_arg,
041caa61ed34 use get_function_handle instead of extract_function
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parents: 26376
diff changeset
322 parameter_names);
20801
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parents: 20785
diff changeset
323 break;
11586
12df7854fa7c strip trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 11553
diff changeset
324
20801
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John W. Eaton <jwe@octave.org>
parents: 20785
diff changeset
325 case 2:
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John W. Eaton <jwe@octave.org>
parents: 20785
diff changeset
326 {
20990
fc9cca99b2de Deprecate all_strings, replace with string_vector_value.
Rik <rik@octave.org>
parents: 20974
diff changeset
327 string_vector tmp = f_arg.string_vector_value ();
2928
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parents:
diff changeset
328
26864
041caa61ed34 use get_function_handle instead of extract_function
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parents: 26376
diff changeset
329 lsode_fcn = octave::get_function_handle (interp, tmp(0),
041caa61ed34 use get_function_handle instead of extract_function
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parents: 26376
diff changeset
330 parameter_names);
2928
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jwe
parents:
diff changeset
331
26864
041caa61ed34 use get_function_handle instead of extract_function
John W. Eaton <jwe@octave.org>
parents: 26376
diff changeset
332 if (lsode_fcn.is_defined ())
10154
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 10066
diff changeset
333 {
26864
041caa61ed34 use get_function_handle instead of extract_function
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parents: 26376
diff changeset
334 lsode_jac = octave::get_function_handle (interp, tmp(1),
041caa61ed34 use get_function_handle instead of extract_function
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parents: 26376
diff changeset
335 parameter_names);
5729
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jwe
parents: 5694
diff changeset
336
26864
041caa61ed34 use get_function_handle instead of extract_function
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parents: 26376
diff changeset
337 if (lsode_jac.is_undefined ())
041caa61ed34 use get_function_handle instead of extract_function
John W. Eaton <jwe@octave.org>
parents: 26376
diff changeset
338 lsode_fcn = octave_value ();
10154
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 10066
diff changeset
339 }
20801
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John W. Eaton <jwe@octave.org>
parents: 20785
diff changeset
340 }
a542a9bf177e eliminate return statements after calls to print_usage
John W. Eaton <jwe@octave.org>
parents: 20785
diff changeset
341 break;
2928
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
342
20801
a542a9bf177e eliminate return statements after calls to print_usage
John W. Eaton <jwe@octave.org>
parents: 20785
diff changeset
343 default:
a542a9bf177e eliminate return statements after calls to print_usage
John W. Eaton <jwe@octave.org>
parents: 20785
diff changeset
344 error ("lsode: first arg should be a string or 2-element string array");
10154
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 10066
diff changeset
345 }
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 10066
diff changeset
346 }
20801
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parents: 20785
diff changeset
347 }
2928
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
348
26864
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parents: 26376
diff changeset
349 if (lsode_fcn.is_undefined ())
20801
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John W. Eaton <jwe@octave.org>
parents: 20785
diff changeset
350 error ("lsode: FCN argument is not a valid function name or handle");
20687
5f04bfc7c17a backout changeset 18f38ed43962
John W. Eaton <jwe@octave.org>
parents: 20682
diff changeset
351
20801
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John W. Eaton <jwe@octave.org>
parents: 20785
diff changeset
352 ColumnVector state = args(1).xvector_value ("lsode: initial state X_0 must be a vector");
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John W. Eaton <jwe@octave.org>
parents: 20785
diff changeset
353 ColumnVector out_times = args(2).xvector_value ("lsode: output time variable T must be a vector");
2928
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jwe
parents:
diff changeset
354
20801
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John W. Eaton <jwe@octave.org>
parents: 20785
diff changeset
355 ColumnVector crit_times;
2928
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
356
20801
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diff changeset
357 int crit_times_set = 0;
a542a9bf177e eliminate return statements after calls to print_usage
John W. Eaton <jwe@octave.org>
parents: 20785
diff changeset
358 if (nargin > 3)
a542a9bf177e eliminate return statements after calls to print_usage
John W. Eaton <jwe@octave.org>
parents: 20785
diff changeset
359 {
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John W. Eaton <jwe@octave.org>
parents: 20785
diff changeset
360 crit_times = args(3).xvector_value ("lsode: list of critical times T_CRIT must be a vector");
2928
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
361
20801
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John W. Eaton <jwe@octave.org>
parents: 20785
diff changeset
362 crit_times_set = 1;
a542a9bf177e eliminate return statements after calls to print_usage
John W. Eaton <jwe@octave.org>
parents: 20785
diff changeset
363 }
2928
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
364
20801
a542a9bf177e eliminate return statements after calls to print_usage
John W. Eaton <jwe@octave.org>
parents: 20785
diff changeset
365 double tzero = out_times (0);
3243
dd00769643ae [project @ 1999-05-28 04:19:00 by jwe]
jwe
parents: 3131
diff changeset
366
20801
a542a9bf177e eliminate return statements after calls to print_usage
John W. Eaton <jwe@octave.org>
parents: 20785
diff changeset
367 ODEFunc func (lsode_user_function);
26864
041caa61ed34 use get_function_handle instead of extract_function
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parents: 26376
diff changeset
368
041caa61ed34 use get_function_handle instead of extract_function
John W. Eaton <jwe@octave.org>
parents: 26376
diff changeset
369 if (lsode_jac.is_defined ())
20801
a542a9bf177e eliminate return statements after calls to print_usage
John W. Eaton <jwe@octave.org>
parents: 20785
diff changeset
370 func.set_jacobian_function (lsode_user_jacobian);
2928
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
371
20801
a542a9bf177e eliminate return statements after calls to print_usage
John W. Eaton <jwe@octave.org>
parents: 20785
diff changeset
372 LSODE ode (state, tzero, func);
3243
dd00769643ae [project @ 1999-05-28 04:19:00 by jwe]
jwe
parents: 3131
diff changeset
373
20801
a542a9bf177e eliminate return statements after calls to print_usage
John W. Eaton <jwe@octave.org>
parents: 20785
diff changeset
374 ode.set_options (lsode_opts);
3243
dd00769643ae [project @ 1999-05-28 04:19:00 by jwe]
jwe
parents: 3131
diff changeset
375
20801
a542a9bf177e eliminate return statements after calls to print_usage
John W. Eaton <jwe@octave.org>
parents: 20785
diff changeset
376 Matrix output;
a542a9bf177e eliminate return statements after calls to print_usage
John W. Eaton <jwe@octave.org>
parents: 20785
diff changeset
377 if (crit_times_set)
a542a9bf177e eliminate return statements after calls to print_usage
John W. Eaton <jwe@octave.org>
parents: 20785
diff changeset
378 output = ode.integrate (out_times, crit_times);
a542a9bf177e eliminate return statements after calls to print_usage
John W. Eaton <jwe@octave.org>
parents: 20785
diff changeset
379 else
a542a9bf177e eliminate return statements after calls to print_usage
John W. Eaton <jwe@octave.org>
parents: 20785
diff changeset
380 output = ode.integrate (out_times);
5729
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jwe
parents: 5694
diff changeset
381
20801
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John W. Eaton <jwe@octave.org>
parents: 20785
diff changeset
382 if (fcn_name.length ())
23699
b29904962d2d deprecate some global functions that access the symbol table
John W. Eaton <jwe@octave.org>
parents: 23581
diff changeset
383 symtab.clear_function (fcn_name);
20801
a542a9bf177e eliminate return statements after calls to print_usage
John W. Eaton <jwe@octave.org>
parents: 20785
diff changeset
384 if (jac_name.length ())
23699
b29904962d2d deprecate some global functions that access the symbol table
John W. Eaton <jwe@octave.org>
parents: 23581
diff changeset
385 symtab.clear_function (jac_name);
3997
d4091aff6468 [project @ 2002-07-17 18:00:06 by jwe]
jwe
parents: 3991
diff changeset
386
20801
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John W. Eaton <jwe@octave.org>
parents: 20785
diff changeset
387 std::string msg = ode.error_message ();
a542a9bf177e eliminate return statements after calls to print_usage
John W. Eaton <jwe@octave.org>
parents: 20785
diff changeset
388
20898
8da80da1ac37 maint: Use ovl() more places in the code.
Rik <rik@octave.org>
parents: 20892
diff changeset
389 octave_value_list retval (3);
8da80da1ac37 maint: Use ovl() more places in the code.
Rik <rik@octave.org>
parents: 20892
diff changeset
390
20801
a542a9bf177e eliminate return statements after calls to print_usage
John W. Eaton <jwe@octave.org>
parents: 20785
diff changeset
391 if (ode.integration_ok ())
a542a9bf177e eliminate return statements after calls to print_usage
John W. Eaton <jwe@octave.org>
parents: 20785
diff changeset
392 retval(0) = output;
20892
c07bee629973 2015 Code Sprint: use ovl ().
Rik <rik@octave.org>
parents: 20853
diff changeset
393 else if (nargout < 2)
c07bee629973 2015 Code Sprint: use ovl ().
Rik <rik@octave.org>
parents: 20853
diff changeset
394 error ("lsode: %s", msg.c_str ());
20801
a542a9bf177e eliminate return statements after calls to print_usage
John W. Eaton <jwe@octave.org>
parents: 20785
diff changeset
395 else
20892
c07bee629973 2015 Code Sprint: use ovl ().
Rik <rik@octave.org>
parents: 20853
diff changeset
396 retval(0) = Matrix ();
3959
5a848097fe4a [project @ 2002-05-24 17:58:16 by jwe]
jwe
parents: 3957
diff changeset
397
20892
c07bee629973 2015 Code Sprint: use ovl ().
Rik <rik@octave.org>
parents: 20853
diff changeset
398 retval(1) = static_cast<double> (ode.integration_state ());
c07bee629973 2015 Code Sprint: use ovl ().
Rik <rik@octave.org>
parents: 20853
diff changeset
399 retval(2) = msg;
2928
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
400
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
401 return retval;
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
402 }
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
403
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
404 /*
7562
c827f5673321 move tests to individual source files
John W. Eaton <jwe@octave.org>
parents: 7017
diff changeset
405
14501
60e5cf354d80 Update %!tests in DLD-FUNCTIONS/ directory with Octave coding conventions.
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
406 ## dassl-1.m
60e5cf354d80 Update %!tests in DLD-FUNCTIONS/ directory with Octave coding conventions.
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
407 ##
60e5cf354d80 Update %!tests in DLD-FUNCTIONS/ directory with Octave coding conventions.
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
408 ## Test lsode() function
60e5cf354d80 Update %!tests in DLD-FUNCTIONS/ directory with Octave coding conventions.
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
409 ##
60e5cf354d80 Update %!tests in DLD-FUNCTIONS/ directory with Octave coding conventions.
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
410 ## Author: David Billinghurst (David.Billinghurst@riotinto.com.au)
60e5cf354d80 Update %!tests in DLD-FUNCTIONS/ directory with Octave coding conventions.
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
411 ## Comalco Research and Technology
60e5cf354d80 Update %!tests in DLD-FUNCTIONS/ directory with Octave coding conventions.
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
412 ## 20 May 1998
60e5cf354d80 Update %!tests in DLD-FUNCTIONS/ directory with Octave coding conventions.
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
413 ##
60e5cf354d80 Update %!tests in DLD-FUNCTIONS/ directory with Octave coding conventions.
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
414 ## Problem
60e5cf354d80 Update %!tests in DLD-FUNCTIONS/ directory with Octave coding conventions.
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
415 ##
60e5cf354d80 Update %!tests in DLD-FUNCTIONS/ directory with Octave coding conventions.
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
416 ## y1' = -y2, y1(0) = 1
60e5cf354d80 Update %!tests in DLD-FUNCTIONS/ directory with Octave coding conventions.
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
417 ## y2' = y1, y2(0) = 0
60e5cf354d80 Update %!tests in DLD-FUNCTIONS/ directory with Octave coding conventions.
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
418 ##
60e5cf354d80 Update %!tests in DLD-FUNCTIONS/ directory with Octave coding conventions.
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
419 ## Solution
60e5cf354d80 Update %!tests in DLD-FUNCTIONS/ directory with Octave coding conventions.
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
420 ##
60e5cf354d80 Update %!tests in DLD-FUNCTIONS/ directory with Octave coding conventions.
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
421 ## y1(t) = cos(t)
60e5cf354d80 Update %!tests in DLD-FUNCTIONS/ directory with Octave coding conventions.
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
422 ## y2(t) = sin(t)
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423 ##
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424 %!function xdot = __f (x, t)
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425 %! xdot = [-x(2); x(1)];
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426 %!endfunction
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427 %!test
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428 %!
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429 %! x0 = [1; 0];
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430 %! xdot0 = [0; 1];
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431 %! t = (0:1:10)';
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432 %!
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433 %! tol = 500 * lsode_options ("relative tolerance");
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434 %!
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435 %! x = lsode ("__f", x0, t);
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436 %!
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437 %! y = [cos(t), sin(t)];
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438 %!
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439 %! assert (x, y, tol);
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440
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441 %!function xdotdot = __f (x, t)
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442 %! xdotdot = [x(2); -x(1)];
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443 %!endfunction
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444 %!test
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445 %!
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446 %! x0 = [1; 0];
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447 %! t = [0; 2*pi];
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448 %! tol = 100 * dassl_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 = [1, 0; 1, 0];
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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 xdot = __f (x, t)
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457 %! xdot = x;
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458 %!endfunction
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459 %!test
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460 %!
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461 %! x0 = 1;
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462 %! t = [0; 1];
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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; e];
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468 %!
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469 %! assert (x, y, tol);
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470
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471 %!test
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472 %! lsode_options ("absolute tolerance", eps);
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473 %! assert (lsode_options ("absolute tolerance") == eps);
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474
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475 %!error lsode_options ("foo", 1, 2)
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476 */