--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/corefcn/dassl.cc	Fri Jul 27 15:35:00 2012 -0700
@@ -0,0 +1,565 @@
+/*
+
+Copyright (C) 1996-2012 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 3 of the License, 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, see
+<http://www.gnu.org/licenses/>.
+
+*/
+
+#ifdef HAVE_CONFIG_H
+#include <config.h>
+#endif
+
+#include <string>
+
+#include <iomanip>
+#include <iostream>
+
+#include "DASSL.h"
+
+#include "defun.h"
+#include "error.h"
+#include "gripes.h"
+#include "oct-obj.h"
+#include "ov-fcn.h"
+#include "ov-cell.h"
+#include "pager.h"
+#include "unwind-prot.h"
+#include "utils.h"
+#include "variables.h"
+
+#include "DASSL-opts.cc"
+
+// Global pointer for user defined function required by dassl.
+static octave_function *dassl_fcn;
+
+// Global pointer for optional user defined jacobian function.
+static octave_function *dassl_jac;
+
+// Have we warned about imaginary values returned from user function?
+static bool warned_fcn_imaginary = false;
+static bool warned_jac_imaginary = false;
+
+// Is this a recursive call?
+static int call_depth = 0;
+
+ColumnVector
+dassl_user_function (const ColumnVector& x, const ColumnVector& xdot,
+                     double t, octave_idx_type& ires)
+{
+  ColumnVector retval;
+
+  assert (x.capacity () == xdot.capacity ());
+
+  octave_value_list args;
+
+  args(2) = t;
+  args(1) = xdot;
+  args(0) = x;
+
+  if (dassl_fcn)
+    {
+      octave_value_list tmp = dassl_fcn->do_multi_index_op (1, args);
+
+      if (error_state)
+        {
+          gripe_user_supplied_eval ("dassl");
+          return retval;
+        }
+
+      int tlen = tmp.length ();
+      if (tlen > 0 && tmp(0).is_defined ())
+        {
+          if (! warned_fcn_imaginary && tmp(0).is_complex_type ())
+            {
+              warning ("dassl: ignoring imaginary part returned from user-supplied function");
+              warned_fcn_imaginary = true;
+            }
+
+          retval = ColumnVector (tmp(0).vector_value ());
+
+          if (tlen > 1)
+            ires = tmp(1).int_value ();
+
+          if (error_state || retval.length () == 0)
+            gripe_user_supplied_eval ("dassl");
+        }
+      else
+        gripe_user_supplied_eval ("dassl");
+    }
+
+  return retval;
+}
+
+Matrix
+dassl_user_jacobian (const ColumnVector& x, const ColumnVector& xdot,
+                     double t, double cj)
+{
+  Matrix retval;
+
+  assert (x.capacity () == xdot.capacity ());
+
+  octave_value_list args;
+
+  args(3) = cj;
+  args(2) = t;
+  args(1) = xdot;
+  args(0) = x;
+
+  if (dassl_jac)
+    {
+      octave_value_list tmp = dassl_jac->do_multi_index_op (1, args);
+
+      if (error_state)
+        {
+          gripe_user_supplied_eval ("dassl");
+          return retval;
+        }
+
+      int tlen = tmp.length ();
+      if (tlen > 0 && tmp(0).is_defined ())
+        {
+          if (! warned_jac_imaginary && tmp(0).is_complex_type ())
+            {
+              warning ("dassl: ignoring imaginary part returned from user-supplied jacobian function");
+              warned_jac_imaginary = true;
+            }
+
+          retval = tmp(0).matrix_value ();
+
+          if (error_state || retval.length () == 0)
+            gripe_user_supplied_eval ("dassl");
+        }
+      else
+        gripe_user_supplied_eval ("dassl");
+    }
+
+  return retval;
+}
+
+#define DASSL_ABORT() \
+  return retval
+
+#define DASSL_ABORT1(msg) \
+  do \
+    { \
+      ::error ("dassl: " msg); \
+      DASSL_ABORT (); \
+    } \
+  while (0)
+
+#define DASSL_ABORT2(fmt, arg) \
+  do \
+    { \
+      ::error ("dassl: " fmt, arg); \
+      DASSL_ABORT (); \
+    } \
+  while (0)
+
+DEFUN (dassl, args, nargout,
+  "-*- texinfo -*-\n\
+@deftypefn {Built-in Function} {[@var{x}, @var{xdot}, @var{istate}, @var{msg}] =} dassl (@var{fcn}, @var{x_0}, @var{xdot_0}, @var{t}, @var{t_crit})\n\
+Solve the set of differential-algebraic equations\n\
+@tex\n\
+$$ 0 = f (x, \\dot{x}, t) $$\n\
+with\n\
+$$ x(t_0) = x_0, \\dot{x}(t_0) = \\dot{x}_0 $$\n\
+@end tex\n\
+@ifnottex\n\
+\n\
+@example\n\
+0 = f (x, xdot, t)\n\
+@end example\n\
+\n\
+@noindent\n\
+with\n\
+\n\
+@example\n\
+x(t_0) = x_0, xdot(t_0) = xdot_0\n\
+@end example\n\
+\n\
+@end ifnottex\n\
+The solution is returned in the matrices @var{x} and @var{xdot},\n\
+with each row in the result matrices corresponding to one of the\n\
+elements in the vector @var{t}.  The first element of @var{t}\n\
+should be @math{t_0} and correspond to the initial state of the\n\
+system @var{x_0} and its derivative @var{xdot_0}, so that the first\n\
+row of the output @var{x} is @var{x_0} and the first row\n\
+of the output @var{xdot} is @var{xdot_0}.\n\
+\n\
+The first argument, @var{fcn}, is a string, inline, or function handle\n\
+that names the function @math{f} to call to compute the vector of\n\
+residuals for the set of equations.  It must have the form\n\
+\n\
+@example\n\
+@var{res} = f (@var{x}, @var{xdot}, @var{t})\n\
+@end example\n\
+\n\
+@noindent\n\
+in which @var{x}, @var{xdot}, and @var{res} are vectors, and @var{t} is a\n\
+scalar.\n\
+\n\
+If @var{fcn} is a two-element string array or a two-element cell array\n\
+of strings, inline functions, or function handles, the first element names\n\
+the function @math{f} described above, and the second element names a\n\
+function to compute the modified Jacobian\n\
+\n\
+@tex\n\
+$$\n\
+J = {\\partial f \\over \\partial x}\n\
+  + c {\\partial f \\over \\partial \\dot{x}}\n\
+$$\n\
+@end tex\n\
+@ifnottex\n\
+\n\
+@example\n\
+@group\n\
+      df       df\n\
+jac = -- + c ------\n\
+      dx     d xdot\n\
+@end group\n\
+@end example\n\
+\n\
+@end ifnottex\n\
+\n\
+The modified Jacobian function must have the form\n\
+\n\
+@example\n\
+@group\n\
+\n\
+@var{jac} = j (@var{x}, @var{xdot}, @var{t}, @var{c})\n\
+\n\
+@end group\n\
+@end example\n\
+\n\
+The second and third arguments to @code{dassl} specify the initial\n\
+condition of the states and their derivatives, and the fourth argument\n\
+specifies a vector of output times at which the solution is desired,\n\
+including the time corresponding to the initial condition.\n\
+\n\
+The set of initial states and derivatives are not strictly required to\n\
+be consistent.  In practice, however, @sc{dassl} is not very good at\n\
+determining a consistent set for you, so it is best if you ensure that\n\
+the initial values result in the function evaluating to zero.\n\
+\n\
+The fifth argument is optional, and may be used to specify a set of\n\
+times that the DAE solver should not integrate past.  It is useful for\n\
+avoiding difficulties with singularities and points where there is a\n\
+discontinuity in the derivative.\n\
+\n\
+After a successful computation, the value of @var{istate} will be\n\
+greater than zero (consistent with the Fortran version of @sc{dassl}).\n\
+\n\
+If the computation is not successful, the value of @var{istate} will be\n\
+less than zero and @var{msg} will contain additional information.\n\
+\n\
+You can use the function @code{dassl_options} to set optional\n\
+parameters for @code{dassl}.\n\
+@seealso{daspk, dasrt, lsode}\n\
+@end deftypefn")
+{
+  octave_value_list retval;
+
+  warned_fcn_imaginary = false;
+  warned_jac_imaginary = false;
+
+  unwind_protect frame;
+
+  frame.protect_var (call_depth);
+  call_depth++;
+
+  if (call_depth > 1)
+    DASSL_ABORT1 ("invalid recursive call");
+
+  int nargin = args.length ();
+
+  if (nargin > 3 && nargin < 6 && nargout < 5)
+    {
+      std::string fcn_name, fname, jac_name, jname;
+      dassl_fcn = 0;
+      dassl_jac = 0;
+
+      octave_value f_arg = args(0);
+
+      if (f_arg.is_cell ())
+        {
+          Cell c = f_arg.cell_value ();
+          if (c.length () == 1)
+            f_arg = c(0);
+          else if (c.length () == 2)
+            {
+              if (c(0).is_function_handle () || c(0).is_inline_function ())
+                dassl_fcn = c(0).function_value ();
+              else
+                {
+                  fcn_name = unique_symbol_name ("__dassl_fcn__");
+                  fname = "function y = ";
+                  fname.append (fcn_name);
+                  fname.append (" (x, xdot, t) y = ");
+                  dassl_fcn = extract_function
+                    (c(0), "dassl", fcn_name, fname, "; endfunction");
+                }
+
+              if (dassl_fcn)
+                {
+                  if (c(1).is_function_handle () || c(1).is_inline_function ())
+                    dassl_jac = c(1).function_value ();
+                  else
+                    {
+                        jac_name = unique_symbol_name ("__dassl_jac__");
+                        jname = "function jac = ";
+                        jname.append (jac_name);
+                        jname.append (" (x, xdot, t, cj) jac = ");
+                        dassl_jac = extract_function
+                          (c(1), "dassl", jac_name, jname, "; endfunction");
+
+                        if (!dassl_jac)
+                          {
+                            if (fcn_name.length ())
+                              clear_function (fcn_name);
+                            dassl_fcn = 0;
+                          }
+                    }
+                }
+            }
+          else
+            DASSL_ABORT1 ("incorrect number of elements in cell array");
+        }
+
+      if (!dassl_fcn && ! f_arg.is_cell ())
+        {
+          if (f_arg.is_function_handle () || f_arg.is_inline_function ())
+            dassl_fcn = f_arg.function_value ();
+          else
+            {
+              switch (f_arg.rows ())
+                {
+                case 1:
+                  do
+                    {
+                      fcn_name = unique_symbol_name ("__dassl_fcn__");
+                      fname = "function y = ";
+                      fname.append (fcn_name);
+                      fname.append (" (x, xdot, t) y = ");
+                      dassl_fcn = extract_function
+                        (f_arg, "dassl", fcn_name, fname, "; endfunction");
+                    }
+                  while (0);
+                  break;
+
+                case 2:
+                  {
+                    string_vector tmp = f_arg.all_strings ();
+
+                    if (! error_state)
+                      {
+                        fcn_name = unique_symbol_name ("__dassl_fcn__");
+                        fname = "function y = ";
+                        fname.append (fcn_name);
+                        fname.append (" (x, xdot, t) y = ");
+                        dassl_fcn = extract_function
+                          (tmp(0), "dassl", fcn_name, fname, "; endfunction");
+
+                        if (dassl_fcn)
+                          {
+                            jac_name = unique_symbol_name ("__dassl_jac__");
+                            jname = "function jac = ";
+                            jname.append (jac_name);
+                            jname.append (" (x, xdot, t, cj) jac = ");
+                            dassl_jac = extract_function
+                              (tmp(1), "dassl", jac_name, jname,
+                               "; endfunction");
+
+                            if (!dassl_jac)
+                              {
+                                if (fcn_name.length ())
+                                  clear_function (fcn_name);
+                                dassl_fcn = 0;
+                              }
+                          }
+                      }
+                  }
+                }
+            }
+        }
+
+      if (error_state || ! dassl_fcn)
+        DASSL_ABORT ();
+
+      ColumnVector state = ColumnVector (args(1).vector_value ());
+
+      if (error_state)
+        DASSL_ABORT1 ("expecting state vector as second argument");
+
+      ColumnVector deriv (args(2).vector_value ());
+
+      if (error_state)
+        DASSL_ABORT1 ("expecting derivative vector as third argument");
+
+      ColumnVector out_times (args(3).vector_value ());
+
+      if (error_state)
+        DASSL_ABORT1 ("expecting output time vector as fourth argument");
+
+      ColumnVector crit_times;
+      int crit_times_set = 0;
+      if (nargin > 4)
+        {
+          crit_times = ColumnVector (args(4).vector_value ());
+
+          if (error_state)
+            DASSL_ABORT1 ("expecting critical time vector as fifth argument");
+
+          crit_times_set = 1;
+        }
+
+      if (state.capacity () != deriv.capacity ())
+        DASSL_ABORT1 ("x and xdot must have the same size");
+
+      double tzero = out_times (0);
+
+      DAEFunc func (dassl_user_function);
+      if (dassl_jac)
+        func.set_jacobian_function (dassl_user_jacobian);
+
+      DASSL dae (state, deriv, tzero, func);
+
+      dae.set_options (dassl_opts);
+
+      Matrix output;
+      Matrix deriv_output;
+
+      if (crit_times_set)
+        output = dae.integrate (out_times, deriv_output, crit_times);
+      else
+        output = dae.integrate (out_times, deriv_output);
+
+      if (fcn_name.length ())
+        clear_function (fcn_name);
+      if (jac_name.length ())
+        clear_function (jac_name);
+
+      if (! error_state)
+        {
+          std::string msg = dae.error_message ();
+
+          retval(3) = msg;
+          retval(2) = static_cast<double> (dae.integration_state ());
+
+          if (dae.integration_ok ())
+            {
+              retval(1) = deriv_output;
+              retval(0) = output;
+            }
+          else
+            {
+              retval(1) = Matrix ();
+              retval(0) = Matrix ();
+
+              if (nargout < 3)
+                error ("dassl: %s", msg.c_str ());
+            }
+        }
+    }
+  else
+    print_usage ();
+
+  return retval;
+}
+
+/*
+## dassl-1.m
+##
+## Test dassl() function
+##
+## Author: David Billinghurst (David.Billinghurst@riotinto.com.au)
+##         Comalco Research and Technology
+##         20 May 1998
+##
+## Problem
+##
+##    y1' = -y2,   y1(0) = 1
+##    y2' =  y1,   y2(0) = 0
+##
+## Solution
+##
+##    y1(t) = cos(t)
+##    y2(t) = sin(t)
+##
+%!function res = __f (x, xdot, t)
+%!  res = [xdot(1)+x(2); xdot(2)-x(1)];
+%!endfunction
+
+%!test
+%!
+%! x0 = [1; 0];
+%! xdot0 = [0; 1];
+%! t = (0:1:10)';
+%!
+%! tol = 100 * dassl_options ("relative tolerance");
+%!
+%! [x, xdot] = dassl ("__f", x0, xdot0, t);
+%!
+%! y = [cos(t), sin(t)];
+%!
+%! assert (x, y, tol);
+
+## dassl-2.m
+##
+## Test dassl() function
+##
+## Author: David Billinghurst (David.Billinghurst@riotinto.com.au)
+##         Comalco Research and Technology
+##         20 May 1998
+##
+## Based on SLATEC quick check for DASSL by Linda Petzold
+##
+## Problem
+##
+##   x1' + 10*x1 = 0,   x1(0) = 1
+##   x1  + x2    = 1,   x2(0) = 0
+##
+##
+## Solution
+##
+##  x1(t) = exp(-10*t)
+##  x2(t) = 1 - x(1)
+##
+%!function res = __f (x, xdot, t)
+%!  res = [xdot(1)+10*x(1); x(1)+x(2)-1];
+%!endfunction
+
+%!test
+%!
+%! x0 = [1; 0];
+%! xdot0 = [-10; 10];
+%! t = (0:0.2:1)';
+%!
+%! tol = 500 * dassl_options ("relative tolerance");
+%!
+%! [x, xdot] = dassl ("__f", x0, xdot0, t);
+%!
+%! y = [exp(-10*t), 1-exp(-10*t)];
+%!
+%! assert (x, y, tol);
+
+%!test
+%! dassl_options ("absolute tolerance", eps);
+%! assert (dassl_options ("absolute tolerance") == eps);
+
+%!error dassl_options ("foo", 1, 2)
+*/