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+// DAE.cc                                               -*- C++ -*-
+/*
+
+Copyright (C) 1992, 1993 John W. Eaton
+
+This file is part of Octave.
+
+Octave is free software; you can redistribute it and/or modify it
+under the terms of the GNU General Public License as published by the
+Free Software Foundation; either version 2, or (at your option) any
+later version.
+
+Octave 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 General Public License
+for more details.
+
+You should have received a copy of the GNU General Public License
+along with Octave; see the file COPYING.  If not, write to the Free
+Software Foundation, 675 Mass Ave, Cambridge, MA 02139, USA.
+
+*/
+
+#ifdef __GNUG__
+#pragma implementation
+#endif
+
+#include <iostream.h>
+#include "DAE.h"
+
+extern "C"
+{
+  int F77_FCN (ddassl) (int (*)(), const int*, double*, double*,
+			double*, double*, const int*, const double*,
+			const double*, int*, double*, const int*, 
+			int*, const int*, const double*, const int*,
+			int (*)());
+}
+
+static DAERHSFunc user_fun;
+static DAEJacFunc user_jac;
+static int nn;
+
+DAE::DAE (void)
+{
+  n = 0;
+  t = 0.0;
+
+  stop_time_set = 0;
+  stop_time = 0.0;
+
+  restart = 1;
+
+  DAEFunc::set_function (NULL);
+  DAEFunc::set_jacobian_function (NULL);
+
+  liw = 0;
+  lrw = 0;
+
+  info  = new int [15];
+  iwork = (int *) NULL;
+  rwork = (double *) NULL;
+
+  for (int i = 0; i < 15; i++)
+    info [i] = 0;
+}
+
+DAE::DAE (int size)
+{
+  n = size;
+  t = 0.0;
+
+  absolute_tolerance = 1.0e-6;
+  relative_tolerance = 1.0e-6;
+
+  stop_time_set = 0;
+  stop_time = 0.0;
+
+  restart = 1;
+
+  DAEFunc::set_function (NULL);
+  DAEFunc::set_jacobian_function (NULL);
+
+  liw = 20 + n;
+  lrw = 40 + 9*n + n*n;
+
+  info  = new int [15];
+  iwork = new int [liw];
+  rwork = new double [lrw];
+
+  for (int i = 0; i < 15; i++)
+    info [i] = 0;
+}
+
+DAE::DAE (Vector& state, double time, DAEFunc& f)
+{
+  n = state.capacity ();
+  t = time;
+  x = state;
+  xdot.resize (n, 0.0);
+
+  absolute_tolerance = 1.0e-6;
+  relative_tolerance = 1.0e-6;
+
+  stop_time_set = 0;
+  stop_time = 0.0;
+
+  restart = 1;
+
+  DAEFunc::set_function (f.function ());
+  DAEFunc::set_jacobian_function (f.jacobian_function ());
+
+  liw = 20 + n;
+  lrw = 40 + 9*n + n*n;
+
+  info  = new int [15];
+  iwork = new int [liw];
+  rwork = new double [lrw];
+
+  for (int i = 0; i < 15; i++)
+    info [i] = 0;
+}
+
+DAE::DAE (Vector& state, Vector& deriv, double time, DAEFunc& f)
+{
+  if (deriv.capacity () != state.capacity ())
+    {
+      cerr << "x, xdot size mismatch in DAE constructor";
+      exit (1);
+    }
+
+  n = state.capacity ();
+  t = time;
+  xdot = deriv;
+  x = state;
+
+  absolute_tolerance = 1.0e-6;
+  relative_tolerance = 1.0e-6;
+
+  stop_time_set = 0;
+  stop_time = 0.0;
+
+  DAEFunc::set_function (f.function ());
+  DAEFunc::set_jacobian_function (f.jacobian_function ());
+
+  liw = 20 + n;
+  lrw = 40 + 9*n + n*n;
+
+  info  = new int [15];
+  iwork = new int [liw];
+  rwork = new double [lrw];
+
+  for (int i = 0; i < 15; i++)
+    info [i] = 0;
+}
+
+DAE::~DAE (void)
+{
+  delete info;
+  delete rwork;
+  delete iwork;
+}
+
+Vector
+DAE::deriv (void)
+{
+  return xdot;
+}
+
+void
+DAE::initialize (Vector& state, double time)
+{
+  restart = 1;
+  x = state;
+  int nx = x.capacity ();
+  xdot.resize (nx, 0.0);
+  t = time;
+}
+
+void
+DAE::initialize (Vector& state, Vector& deriv, double time)
+{
+  restart = 1;
+  xdot = deriv;
+  x = state;
+  t = time;
+}
+
+int
+ddassl_f (double *time, double *state, double *deriv, double *delta,
+	  int *ires, double *rpar, int *ipar)
+{
+  Vector tmp_deriv (nn);
+  Vector tmp_state (nn);
+  Vector tmp_delta (nn);
+
+  for (int i = 0; i < nn; i++)
+    {
+      tmp_deriv.elem (i) = deriv [i];
+      tmp_state.elem (i) = state [i];
+    }
+
+  tmp_delta = user_fun (tmp_state, tmp_deriv, *time);
+
+  for (i = 0; i < nn; i++)
+    delta [i] = tmp_delta.elem (i);
+
+  return 0;
+}
+
+int
+ddassl_j (double *time, double *state, double *deriv, double *pd,
+	  double *cj, double *rpar, int *ipar)
+{
+  Vector tmp_state (nn);
+  Vector tmp_deriv (nn);
+
+// XXX FIXME XXX
+
+  Matrix tmp_dfdxdot (nn, nn);
+  Matrix tmp_dfdx (nn, nn);
+
+  DAEJac tmp_jac;
+  tmp_jac.dfdxdot = &tmp_dfdxdot;
+  tmp_jac.dfdx    = &tmp_dfdx;
+
+  tmp_jac = user_jac (tmp_state, tmp_deriv, *time);
+
+  // Fix up the matrix of partial derivatives for dassl.
+
+  tmp_dfdx = tmp_dfdx + (*cj * tmp_dfdxdot);
+
+  for (int j = 0; j < nn; j++)
+    for (int i = 0; i < nn; i++)
+      pd [nn * j + i] = tmp_dfdx.elem (i, j);
+
+  return 0;
+}
+
+Vector
+DAE::integrate (double tout)
+{
+  if (DAEFunc::jac == NULL)
+    iwork [4] = 0;
+  else
+    iwork [4] = 1;
+
+  double *px    = x.fortran_vec ();
+  double *pxdot = xdot.fortran_vec ();
+
+  nn = n;
+  user_fun = DAEFunc::fun;
+  user_jac = DAEFunc::jac;
+
+  if (stop_time_set)
+    {
+      info [3] = 1;
+      rwork [0] = stop_time;
+    }
+  else
+    info [3] = 0;
+
+  double dummy;
+  int idummy;
+
+  if (restart)
+    {
+      restart = 0;
+      info[0] = 0;
+    }
+
+ again:
+
+  F77_FCN (ddassl) (ddassl_f, &n, &t, px, pxdot, &tout, info,
+		    &relative_tolerance, &absolute_tolerance, &idid,
+		    rwork, &lrw, iwork, &liw, &dummy, &idummy,
+		    ddassl_j);
+
+  switch (idid)
+    {
+    case 1: // A step was successfully taken in the
+	    // intermediate-output mode. The code has not yet reached
+	    // TOUT.
+      break;
+    case 2: // The integration to TSTOP was successfully completed
+	    // (T=TSTOP) by stepping exactly to TSTOP.
+      break;
+    case 3: // The integration to TOUT was successfully completed
+	    // (T=TOUT) by stepping past TOUT.  Y(*) is obtained by
+	    // interpolation.  YPRIME(*) is obtained by interpolation.
+      break;
+    case -1: // A large amount of work has been expended.  (About 500 steps).
+      break;
+    case -2: // The error tolerances are too stringent.
+      break;
+    case -3: // The local error test cannot be satisfied because you
+	     // specified a zero component in ATOL and the
+	     // corresponding computed solution component is zero.
+	     // Thus, a pure relative error test is impossible for
+	     // this component.
+      break;
+    case -6: // DDASSL had repeated error test failures on the last
+	     // attempted step.
+      break;
+    case -7: // The corrector could not converge.
+      break;
+    case -8: // The matrix of partial derivatives is singular.
+      break;
+    case -9: // The corrector could not converge.  There were repeated
+	     // error test failures in this step.
+      break;
+    case -10: // The corrector could not converge because IRES was
+	      // equal to minus one.
+      break;
+    case -11: // IRES equal to -2 was encountered and control is being
+	      // returned to the calling program.
+      break;
+    case -12: // DDASSL failed to compute the initial YPRIME.
+      break;
+    case -33: // The code has encountered trouble from which it cannot
+	      // recover. A message is printed explaining the trouble
+	      // and control is returned to the calling program. For
+	      // example, this occurs when invalid input is detected.
+      break;
+    default:
+      // Error?
+      break;
+    }
+
+  t = tout;
+
+  return x;
+}
+
+Matrix
+DAE::integrate (const Vector& tout, Matrix& xdot_out)
+{
+  Matrix retval;
+  int n_out = tout.capacity ();
+
+  if (n_out > 0 && n > 0)
+    {
+      retval.resize (n_out, n);
+      xdot_out.resize (n_out, n);
+
+      for (int i = 0; i < n; i++)
+	{
+	  retval.elem (0, i) = x.elem (i);
+	  xdot_out.elem (0, i) = xdot.elem (i);
+	}
+
+      for (int j = 1; j < n_out; j++)
+	{
+	  ColumnVector x_next = integrate (tout.elem (j));
+	  for (i = 0; i < n; i++)
+	    {
+	      retval.elem (j, i) = x_next.elem (i);
+	      xdot_out.elem (j, i) = xdot.elem (i);
+	    }
+	}
+    }
+
+  return retval;
+}
+
+Matrix
+DAE::integrate (const Vector& tout, Matrix& xdot_out, const Vector& tcrit)
+{
+  Matrix retval;
+  int n_out = tout.capacity ();
+
+  if (n_out > 0 && n > 0)
+    {
+      retval.resize (n_out, n);
+      xdot_out.resize (n_out, n);
+
+      for (int i = 0; i < n; i++)
+	{
+	  retval.elem (0, i) = x.elem (i);
+	  xdot_out.elem (0, i) = xdot.elem (i);
+	}
+
+      int n_crit = tcrit.capacity ();
+
+      if (n_crit > 0)
+	{
+	  int i_crit = 0;
+	  int i_out = 1;
+	  double next_crit = tcrit.elem (0);
+	  double next_out;
+	  while (i_out < n_out)
+	    {
+	      int do_restart = 0;
+
+	      next_out = tout.elem (i_out);
+	      if (i_crit < n_crit)
+		next_crit = tcrit.elem (i_crit);
+
+	      int save_output;
+	      double t_out;
+
+	      if (next_crit == next_out)
+		{
+		  set_stop_time (next_crit);
+		  t_out = next_out;
+		  save_output = 1;
+		  i_out++;
+		  i_crit++;
+		  do_restart = 1;
+		}
+	      else if (next_crit < next_out)
+		{
+		  if (i_crit < n_crit)
+		    {
+		      set_stop_time (next_crit);
+		      t_out = next_crit;
+		      save_output = 0;
+		      i_crit++;
+		      do_restart = 1;
+		    }
+		  else
+		    {
+		      clear_stop_time ();
+		      t_out = next_out;
+		      save_output = 1;
+		      i_out++;
+		    }
+		}
+	      else
+		{
+		  set_stop_time (next_crit);
+		  t_out = next_out;
+		  save_output = 1;
+		  i_out++;
+		}
+
+	      ColumnVector x_next = integrate (t_out);
+
+	      if (save_output)
+		{
+		  for (i = 0; i < n; i++)
+		    {
+		      retval.elem (i_out-1, i) = x_next.elem (i);
+		      xdot_out.elem (i_out-1, i) = xdot.elem (i);
+		    }
+		}
+
+	      if (do_restart)
+		force_restart ();
+	    }
+	}
+      else
+	retval = integrate (tout);
+    }
+
+  return retval;
+}