--- /dev/null
+## Copyright (C) 2006,2007,2008,2011 Carlo de Falco
+##
+## This file is part of:
+## OCS - A Circuit Simulator for Octave
+##
+## OCS 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.
+##
+## This program 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 this program (see the file LICENSE); if not,
+## see <http://www.gnu.org/licenses/>.
+##
+## author: Carlo de Falco <cdf _AT_ users.sourceforge.net>
+
+## -*- texinfo -*-
+##
+## @deftypefn{Function File} {[@var{out},@var{niter}] =} @
+## tst_backward_euler(@var{cirstruct},@var{x},@var{t},@var{tol},@
+## @var{maxit},@var{pltvars},@var{verbosity},@var{dae_fun})
+##
+## Perform a transient simulation of the system described by
+## @var{cirstruct} over the time interval @var{t} using the backward
+## Euler algorithm.
+##
+## The initial value for the state vector is computed by solving a
+## steady state problem at @var{t}(1), with starting guess @var{x}.
+##
+## @var{tol} and @var{maxit} are parameters passed to
+## @code{nls_newton_raphson}.
+##
+## The output @var{out} will contain the value of the state vector at
+## each point of @var{t}.
+##
+## The optional parameter @var{verbosity} controls the amount of
+## output produced:
+##
+## @itemize @minus
+## @item if verbosity(1) != 0, information on the progress
+## of the algorithm are output at runtime
+## @item if verbosity(2) != 0, the plot of the variables whose names
+## are listed in @var{pltvars} is
+## produced after the computation
+## @end itemize
+##
+## For special purposes one may need to pass modified jacobian and
+## residual functions. This can be done via the cell array of function
+## handles @var{dae_fun}.
+##
+## Such functions should have the same input and output
+## parameter list as the default sub-functions
+## TSTBWEFUNJAC0,TSTBWEFUNRES0, TSTBWEFUNJAC,TSTBWEFUNRES.
+##
+## The optional output @var{niter} returns the number of Newton iterations
+## needed to reach convergence.
+##
+## @seealso{tst_daspk,tst_theta_method,tst_odepkg,nls_newton_raphson}
+##
+## @end deftypefn
+
+function [out, varargout] = tst_backward_euler (outstruct, x, t, tol, maxit, pltvars, verbosity, dae_fun)
+
+ ## Check input
+ ## FIXME: add input check!
+ if ((nargin < 6) || (nargin > 8))
+ error ("tst_backward_euler: wrong number of input parameters.");
+ endif
+
+ if ~exist ("verbosity")
+ verbosity = [0,0];
+ elseif (length (verbosity) < 2)
+ verbosity(2) = 0;
+ endif
+
+ out = zeros (rows (x), columns (t));
+ out(:,1) = x;
+
+ if nargout > 1
+ niter = zeros (length(t),1);
+ endif
+
+ if (verbosity(1))
+ fprintf (1, "Initial value.\n");
+ endif
+
+
+ [A0, B, C] = asm_initialize_system (outstruct, x);
+
+ if (nargin > 8)
+ JAC = @(x) dae_fun{1} (outstruct,x,t(1),B);
+ RES = @(x) dae_fun{2} (outstruct,x,t(1),B,C);
+ [out(:,1), ii, resnrm] = nls_newton_raphson (x, RES, JAC, tol, maxit, verbosity(1));
+ else
+ [out(:,1),ii] = nls_stationary (outstruct, x, tol, maxit);
+ endif
+
+ if (nargout > 1)
+ niter(1) = ii;
+ endif
+
+ for it = 2:length (t)
+
+ if (verbosity(1))
+ fprintf (1,"Timestep #%d.\n",it);
+ endif
+
+ if nargin > 8
+ JAC = @(x) dae_fun{3} (outstruct, x, t(it-1), t(it), A0, B);
+ RES = @(x) dae_fun{4} (outstruct, x, out(:,it-1), t(it-1), t(it), A0, B, C);
+ else
+ JAC = @(x,A1,Jac,res) TSTBWEFUNJAC1(outstruct, x, t(it-1),
+ t(it), A0, B, A1, Jac, res);
+ RES = @(x,A1,Jac,res) TSTBWEFUNRES1(outstruct, x, out(:,it-1),
+ t(it-1), t(it), A0, B, C,
+ A1, Jac, res);
+ UPDT = @(x) TSTBWEFUNUP1 (outstruct, x, t(it));
+ endif
+
+ [out(:,it),ii,resnrm] = nls_newton_raphson (out(:,it-1), RES, JAC, tol, maxit, verbosity(1), UPDT);
+
+ if nargout > 1
+ niter(it) = ii;
+ endif
+
+ if (verbosity(2))
+ utl_plot_by_name (t(1:it), out(:,1:it), outstruct, pltvars);
+ drawnow ();
+ endif
+
+ ## Stop at runtime
+ ## FIXME: maintain this part?
+ if exist("~/.stop_ocs","file")
+ printf("stopping at timestep %d\n",it);
+ unix("rm ~/.stop_ocs");
+ break
+ end
+
+ endfor
+
+ if nargout > 1
+ varargout{1} = niter;
+ endif
+
+endfunction
+
+## Jacobian for transient problem
+function lhs = TSTBWEFUNJAC1 (outstruct, x, t0, t1, A0, B, A1, Jac, res)
+
+ DT = t1-t0;
+ if (nargin < 9)
+ [A1, Jac, res] = asm_build_system (outstruct, x, t1);
+ endif
+ lhs = ((A0+A1)/DT + B + Jac);
+
+endfunction
+
+## Residual for transient problem
+function rhs = TSTBWEFUNRES1 (outstruct, x, xold, t0, t1, A0, B, C, A1, Jac, res)
+
+ DT = t1-t0;
+ if ( nargin < 11 )
+ [A1, Jac, res] = asm_build_system (outstruct, x, t1);
+ endif
+ rhs = (res + C + B*x + (A0+A1)*(x-xold)/DT);
+
+endfunction
+
+## Update for transient problem
+function update = TSTBWEFUNUP1 (outstruct, x, t1)
+
+ [A1, Jac, res] = asm_build_system (outstruct, x, t1);
+ update = {A1, Jac, res};
+
+endfunction
\ No newline at end of file
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