rosenbrock_tableau.hpp

/*
 *    This file is part of CasADi.
 *
 *    CasADi -- A symbolic framework for dynamic optimization.
 *    Copyright (C) 2010-2026 Joel Andersson, Joris Gillis, Moritz Diehl,
 *                            KU Leuven. All rights reserved.
 *    Copyright (C) 2011-2014 Greg Horn
 *
 *    CasADi is free software; you can redistribute it and/or
 *    modify it under the terms of the GNU Lesser General Public
 *    License as published by the Free Software Foundation; either
 *    version 3 of the License, or (at your option) any later version.
 *
 *    CasADi is distributed in the hope that it will be useful,
 *    but WITHOUT ANY WARRANTY; without even the implied warranty of
 *    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
 *    Lesser General Public License for more details.
 *
 *    You should have received a copy of the GNU Lesser General Public
 *    License along with CasADi; if not, write to the Free Software
 *    Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
 *
 */
 
 
// Generated by a standalone construction tool (start 1980, seed 0): do not edit.
// Order conditions residual 2.738e-33, |R(iy)| <= 1 (embedded: <= 1),
// principal error coefficients (2-norm) 5.8068e-03
#ifndef CASADI_ROSENBROCK_TABLEAU_HPP
#define CASADI_ROSENBROCK_TABLEAU_HPP
 
namespace casadi {
namespace rosenbrock_tableau {
 
// Number of stages, order of the embedded method
const casadi_int n_stages = 8;
const casadi_int order_embedded = 4;
 
// Diagonal coefficient
const long double gamma = +3.323340443279714703335030188780199e-01L;
 
// Stage coefficients alpha_ij, strictly lower triangular
const long double alpha[8][8] = {
  {0, 0, 0, 0, 0, 0, 0, 0},
  {+9.970021329839144110005090566340597e-01L, 0, 0, 0, 0, 0, 0, 0},
  {+2.638072029217540558797397460845354e-01L,
   +1.627013513314058848476776539832963e-01L, 0, 0, 0, 0, 0, 0},
  {+1.156060581039499367639400112958590e-01L,
   +8.849875903703587803778131520274638e-02L,
   +7.610418638770641484510168422329190e-02L, 0, 0, 0, 0, 0},
  {+5.079789276294878329575954726112726e-01L,
   -1.081516929353128396606394679014294e-01L,
   +1.322441184323504463684453717109770e+00L,
   -1.011344004186509484005731086050250e+00L, 0, 0, 0, 0},
  {+1.442306973000468595103029656456783e+01L,
   -2.990151994401519797150967860943638e-01L,
   +4.480696617811057791413986706174910e+01L,
   -5.123820911570281499969325977872359e+01L,
   -6.692811592972296885761807061498985e+00L, 0, 0, 0},
  {-1.147313289489853671554442371416371e+00L,
   -2.809851424789066552136505098671165e-01L,
   -1.880528842992333693473483435809612e+00L,
   +3.249933561672380484209994634968282e+00L,
   +7.265596689607420656980786632467979e-01L,
   +3.323340443279714703335030188780199e-01L, 0, 0},
  {-1.134782246263643168472474903656345e-01L,
   -7.453293029201630167580394908620101e-02L,
   -3.915682092665757059096002357858872e-01L,
   +9.310123647864515507575475900484733e-01L,
   +4.913545744587709773830073710802730e-01L,
   -1.751216193882376740414063047690435e-01L,
   +3.323340443279714703335030188780199e-01L, 0}
};
 
// Jacobian coefficients gamma_ij, strictly lower triangular
const long double gamma_ij[8][8] = {
  {0, 0, 0, 0, 0, 0, 0, 0},
  {-9.970021329839144110005090566340597e-01L, 0, 0, 0, 0, 0, 0, 0},
  {-3.856110112711767863395217338472314e-01L,
   -1.975024394312409506933296504869237e-01L, 0, 0, 0, 0, 0, 0},
  {-1.952826569204796837464846028343990e-01L,
   -8.750397230074750386580553195554704e-02L,
   -1.846691337664499790266824702321781e-01L, 0, 0, 0, 0, 0},
  {-6.968271726399242952522176809867906e-01L,
   +8.355942910782911108307852857318821e-02L,
   -1.985808753725242047682602689587963e+00L,
   +2.245751523485942359976526105005181e+00L, 0, 0, 0, 0},
  {-1.557038301949453962258473893598421e+01L,
   +1.803005696124532450144627622724727e-02L,
   -4.668749502110291160761335049755871e+01L,
   +5.448814267737519548390325441369187e+01L,
   +7.419371261933038951459885724745782e+00L, 0, 0, 0},
  {+1.033835064863489354707194881050737e+00L,
   +2.064522121868903535378465607809155e-01L,
   +1.488960633725757987563883200023725e+00L,
   -2.318921196885928933452447044919809e+00L,
   -2.352050945019710883150712921665248e-01L,
   -5.074556637162091443749093236470635e-01L, 0, 0},
  {+1.952575184071690387449604107499247e-01L,
   +3.267512070526884502974939523672930e-02L,
   +3.294287070687737160715761073941538e-01L,
   -4.769964306458966402191620048745044e-01L,
   -5.137939773755217818071084976791899e-02L,
   +1.618173127390534927321312784064486e-01L,
   -5.231368748647877445120473560228528e-01L, 0}
};
 
// Weights of the method and of the embedded method
const long double b[8] = {
  +8.177929378080472189771292038429022e-02L,
  -4.185780958674745664605455384947171e-02L,
  -6.213950219780198983802412839173343e-02L,
  +4.540159341405549105383855851739690e-01L,
  +4.399751767212187992022965213123540e-01L,
  -1.330430664918418130927502636259496e-02L,
  -1.908028305368162741785443371448330e-01L,
  +3.323340443279714703335030188780199e-01L
};
const long double bhat[8] = {
  -1.134782246263643168472474903656345e-01L,
  -7.453293029201630167580394908620101e-02L,
  -3.915682092665757059096002357858872e-01L,
  +9.310123647864515507575475900484733e-01L,
  +4.913545744587709773830073710802730e-01L,
  -1.751216193882376740414063047690435e-01L,
  +3.323340443279714703335030188780199e-01L,
  +0.000000000000000000000000000000000e+00L
};
 
// Dense output y(t0 + theta h) = y0 + sum_i b_i(theta) k_i of order 4 for ODEs,
// b_i(theta) = sum_q b_dense[q][i] theta^(q+1), b_i(1) = b_i
const casadi_int n_dense = 4;
const long double b_dense[4][8] = {
  {+3.406325963613571003017122804434047e+00L,
   +3.743382641202619078318739636244204e-01L,
   +6.663701611940329047314122301439193e+00L,
   -7.536615299688077194623620110969959e+00L,
   -1.850466028568891337709183424990081e+00L,
   -2.402537070053669389152549738175418e+00L,
   +5.641467071381775625459357777196518e+00L,
   -3.296214512745299662137123572558722e+00L},
  {-1.555184079474766844584505161922799e+01L,
   -1.494900137650647618708564664023459e+00L,
   -3.541030247536027146149692850162404e+01L,
   +4.383826169766790973631824050677370e+01L,
   +8.357308236344859521694256803012683e+00L,
   +1.284408784047791741063676817531173e+01L,
   -2.869652893378900003722332910270068e+01L,
   +1.611391456705690089462460840247805e+01L},
  {+2.022596425676281653943419036255626e+01L,
   +1.534377324770742427195294696445902e+00L,
   +4.891765419101144501101339658571605e+01L,
   -6.084225534523747444460371390505954e+01L,
   -9.143902730799331837423018865414151e+00L,
   -1.935079847509495428458957285484914e+01L,
   +4.211816379551040947781757878376280e+01L,
   -2.345920301692365288884415480315818e+01L},
  {-7.998670131847914374708548627378026e+00L,
   -4.556732608271041729646585498963194e-01L,
   -2.023319282978930458666861451392295e+01L,
   +2.499462488139819681344747909442977e+01L,
   +3.077035699744582452640242008703903e+00L,
   +8.895943398021522081796079391350222e+00L,
   -1.925390476364000134023215179540346e+01L,
   +1.097383700694002312669017299211686e+01L}
};
 
} // namespace rosenbrock_tableau
} // namespace casadi
 
#endif // CASADI_ROSENBROCK_TABLEAU_HPP